Effect of three dimensional forcing on the wake of a circular cylinder
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
Samik Bhattacharya
Certificate of Approval:
Roy Hartfield
Professor
Aerospace Engineering
Anwar Ahmed, Chair
Associate Professor
Aerospace Engineering
J Khodadadi
Professor
Mechanical Engineering
George Flowers
Dean
Graduate School
Effect of three dimensional forcing on the wake of a circular cylinder
Samik Bhattacharya
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
August 10,2009
Effect of three dimensional forcing on the wake of a circular cylinder
Samik Bhattacharya
Permission is granted to Auburn University to make copies of this thesis at its
discretion, upon the request of individuals or institutions and at
their expense. The author reserves all publication rights.
Signature of Author
Date of Graduation
iii
Vita
Samik Bhattacharya, son of Mr.Jayanta Bhattacharya and Mrs.Sila Bhattacharya, was
born on 3rd November,1983 in Kolkata, India. He recieved his bachelor?s degree in Me-
chanical Engineering in 2005 from National Institute of Technology,Warangal,India. After
his undergraduate degree, he worked as a junior scientist in DRDL,India. In 2007 he joined
the Aerospace Engineering Department of Auburn University,USA. The research work pre-
sented here is the thesis done for the requirement of master?s degree.
iv
Thesis Abstract
Effect of three dimensional forcing on the wake of a circular cylinder
Samik Bhattacharya
Master of Science, August 10,2009
(B.Tech., National Institute of Technology,Warangal,India,2005)
75 Typed Pages
Directed by Anwar Ahmed
The periodic wake of a circular cylinder was investigated with a three dimensional
disturbances,introduced in the flow field through two sinusoidal slits located on two dia-
metrically opposite direction on the cylinder surface. Two speakers were used for periodic
forcing. Experiments were conducted at Reynolds number of 24,000 and 45,000. It was
found that an excitation frequency which was twice the shedding frequency was able to
eliminate the shedding peak. At lower Reynolds number the drag measurement showed
that maximum drag reduction was achieved when the excitation frequency was almost four
times the natural shedding frequency. The basic mechanism of cancellation of shedding
peak was found to be linked to the introduction of three dimensional disturbance which
disrupted the formation of Karmann vortex street. This resulted in a distribution of energy
from the shedding peak to smaller scales. The introduction of three dimensional disturbance
accelerated the separating shear layers which narrowed the wake and made it uniform in
terms of mean velocity.
v
Acknowledgments
I would like to thank the Department of Aerospace Engineering of Auburn University
for giving me an excellent opportunity to complete my master?s degree and to utilise the
experimental facilities. I am grateful to Mr.Andrew Weldon for his help with the fabrication
of experimental set-up. I would also like to thank Dr.Roy Hartfield and Dr.J.Khodadadi
for kindly consenting to be in my thesis committee. Mere acknowledgment or saying thank
you to my advisor, Dr. Anwar Ahmed will not ever be sufficient to describe my gratitude
for all that he has done for me, so I restrain from doing that mistake.
vi
Style manual or journal used Journal of Approximation Theory (together with the style
known as ?aums?). Bibliograpy follows van Leunen?s A Handbook for Scholars.
Computer software used The document preparation package TEX (specifically LATEX)
together with the departmental style-file aums.sty.
vii
Table of Contents
List of Figures x
1 Introduction 1
1.1 Bluff body flow: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Need for control: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Classification of control methods: . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Passive control: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4.1 Modification of body geometry: . . . . . . . . . . . . . . . . . . . . . 4
1.4.2 Surface modification: . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Active flow control: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Effect of sound on the flow over a circular cylinder: . . . . . . . . . . . . . . 8
1.7 Present research: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Experimental setup 12
2.1 The wind tunnel: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Cylinder models: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Instrumentation: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Data acquisition system: . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Pressure measurements: . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Hot wires: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.4 Probe traversing system: . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.5 Speakers: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Results and discussion 18
3.1 Effect of excitation on the vortex shedding: . . . . . . . . . . . . . . . . . . 18
3.2 Effect of excitation on mean velocity distribution: . . . . . . . . . . . . . . . 21
3.3 Effect of excitation on fluctuating quantities: . . . . . . . . . . . . . . . . . 23
3.4 Characteristics of the flow field: . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Kinetic energy in the wake: . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Wake preservation: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7 Wake formation length: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Conclusion 52
Bibliography 53
Appendices 56
viii
A Calibration 57
A.1 Pressure transducer calibration: . . . . . . . . . . . . . . . . . . . . . . . . . 57
A.2 Calibration of the hot wire: . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
A.2.1 Determination of two component of velocity from X-wire: . . . . . . 59
B Uncertainty analysis 63
B.1 Velocity sample uncertainty: . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
B.2 Sample calculation of pressure tranducer calibration uncertainty: . . . . . . 64
ix
List of Figures
2.1 Schematic of experimental setup in the wind tunnel . . . . . . . . . . . . . 17
2.2 Location of the sinusoidal slits on the cylinder surface . . . . . . . . . . . . 17
3.1 Energy spectra for different forcing frequencies . . . . . . . . . . . . . . . . 22
3.2 Cross sectional distribution of mean velocity,Re=24,000 . . . . . . . . . . . 24
3.3 Cross sectional distribution of mean velocity,Re=45,000 . . . . . . . . . . . 25
3.4 Half wake width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 Variation of half wake width . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Cross sectional distribution of velocity fluctuation vprime,Re=24,000 . . . . . . . 28
3.7 Cross sectional distribution of velocity fluctuation vprime,Re=45,000 . . . . . . . 29
3.8 Cross sectional distribution of velocity fluctuation uprime,Re=24,000 . . . . . . . 30
3.9 Cross sectional distribution of velocity fluctuation uprime,Re=45,000 . . . . . . . 31
3.10 Contour plot of the magnitude of the shedding peak,Re=24,000 . . . . . . . 34
3.11 Contour plot of the magnitude of the shedding peak,Re=45,000 . . . . . . . 35
3.12 Cross sectional distribution of turbulent kinetic energy,Re=24,000 . . . . . 36
3.13 Cross sectional distribution of turbulent kinetic energy,Re=45,000 . . . . . 37
3.14 Similarity parameter in wake,Re=24,000 . . . . . . . . . . . . . . . . . . . . 39
3.15 Similarity parameter in wake,Re=24,000 . . . . . . . . . . . . . . . . . . . . 40
3.16 Similarity parameter in wake,Re=24,000 . . . . . . . . . . . . . . . . . . . . 41
3.17 Similarity parameter in wake,Re=45,000 . . . . . . . . . . . . . . . . . . . . 42
3.18 Similarity parameter in wake,Re=45,000 . . . . . . . . . . . . . . . . . . . . 43
x
3.19 Similarity parameter in wake,Re=45,000 . . . . . . . . . . . . . . . . . . . . 44
3.20 Wake formation length,Re=24,000 . . . . . . . . . . . . . . . . . . . . . . . 46
3.21 Wake formation length,Re=24,000 . . . . . . . . . . . . . . . . . . . . . . . 47
3.22 Wake formation length,Re=24,000 . . . . . . . . . . . . . . . . . . . . . . . 48
3.23 Wake formation length,Re=45,000 . . . . . . . . . . . . . . . . . . . . . . . 49
3.24 Wake formation length,Re=45,000 . . . . . . . . . . . . . . . . . . . . . . . 50
3.25 Wake formation length,Re=45,000 . . . . . . . . . . . . . . . . . . . . . . . 51
A.1 Calibration curve for pressure transducer . . . . . . . . . . . . . . . . . . . 58
A.2 Calibration curve for single wire . . . . . . . . . . . . . . . . . . . . . . . . 60
A.3 Calibration curve for x wire . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
xi
Chapter 1
Introduction
1.1 Bluff body flow:
The flow over a bluff body has been the topic of extensive investigation over the years
both due to its practical application and also because of the interesting fluid dynamic charac-
teristics. Detailed review of this subject has been done by Berger and Wille [1],Bearman[2],
Oertel[3] and Williamson [4]. Various features of this flow have been explored by investi-
gating the flow over a circular cylinder which is regarded as a canonical bluff body flow.
Inspite of a simple geometry, the flow over a cylinder contains a rich diversity in behaviour
as interaction of different shear layers, existence of certain instabilities (of which the most
predominant is Von Karmann shedding), periodicity in flow etc. Apart from these the
Reynolds number dependence,response of the flow to perturbation,the resultant drag and
lift force acting on the body,have been the topic of extensive research. The flow over a
circular cylinder is also a benchmark case of wake turbulence. The distribution of different
turbulent quantities in the wake,the existence of turbulence structures of different length
scales and their mutual interaction in terms of energy distribution have been investigated by
several researchers [5],[6],[7]. Lately the introduction of concepts of non linear systems have
enabled the researchers to interpret the different aspects of transition, turbulence and the
flow structures in the light of non linear instability, bifurcation etc. However among the vast
pool of research activities so far, the most prominent candidate which has caught attention
of many researchers is Karmann shedding which is periodic shedding of vortex street from
both sides of the cylinder. This is unique feature of bluff body flow which starts off after a
certain Reynolds number is reached and has a definite frequency which is expressed in non
1
dimensional form as Strouhal number. Vortex shedding has been identified as a primary
instability of the flow which is considered to be an inviscid phenomenon.
During shedding the flow behaves as a non linear oscillator where the controlling param-
eter is the Reynolds number. As the Reynolds number is increased the flow over a cylinder
starts to bifurcate to higher periodicity and gradually it attains the turbulent stage. The
frequency of shedding is very important from practical point of view since once it coin-
cides with the natural frequency of the bluff body, gives rise to large fluctuating forces due
to resonance causing structural vibration which eventually leads to catastrophic structural
failure of the body. This phenomenon is famously known as vortex induced vibration. ([8]
,[9] ,[10],[11],[12],[13], [14]).
Another critical aspect of bluff body flow is flow separation. The boundary layer
formed on the surface of the cylinder can not overcome the adverse pressure gradient and
separates from the surface forming a free shear layer. This separated shear layer, at a
certain Reynolds number becomes unstable via Kelvin Helmholtz instability. The shear
layers roll up and form Helmholtz votices which ride on the Karmann vortex street. After
a certain Reynolds number the Karmann vortex street itself becomes wavy along the span
and thus forms streamwise vortices. The root of the streamwise vortex can be observed as a
pair of mushroom shaped region[15]. The shear layers from both sides of the cylinder cross
the center of the wake at a distance from the center of the cylinder which is known as the
formation length. The formation length is also defined as the region where the outside fluid
crosses the center for the first time due to entrainment. All of these factors contribute to
the formation of low pressure region behind the cylinder which in turn gives rise to drag
acting on the cylinder, and to the three dimensionality which causes turbulence at higher
Reynolds number.
2
1.2 Need for control:
Flow control aims at controlling the different parameters of the flow over a bluff body to
achieve desired flow characteristics. The primary goals of most of the flow control techniques
can be classified as follows,
1. To suppress vortex shedding :
Control of vortex shedding is necessary to prevent vortex induced vibration.For off-
shore structures, oil rigs, bridges, it is very much important from the view point of
structural integrity and safety.
2. To influence three dimensionality in the flow:
Increased three dimensionality in the wake of a body moving through a fluid, help to
reduce drag. It is desired to have increased mixing in case of an application where
transport of some scalar properties are involved ( heat transfer application). In a gas
turbine engine the fuel needs to be properly mixed by atomisation with the working
fluid.
3. To suppress flow induced noise:
The source of noise in a high speed flow is the turbulent boundary layer. Flow induced
noise is a major factor for hypersonic flights.
Controling the location of boundary layer separation point is an important criteria in
engineering applications. On an aircraft wing it is desired to delay the flow separation
on the airfoil at a high angle of attack to prevent stall. In case of a pipe flow boundary
layer separation accounts for the losses in total pressure. In a gas turbine engine, the
efficiency of expansion in a nozzle suffers due to separation inside the nozzle. Transition
Reynolds number signifies the limit of the flow speed after which the boundary layer becomes
turbulent. Depending on the application it may be required to delay or advance transition.
Turbulent boundary layer contains high momentum thus it is more effective in overcoming
the adverse pressure gradient, thus separation gets delayed.
3
A review of flow control research has been done by Choi et al[16].
1.3 Classification of control methods:
Flow control methods can be classified into two groups.
? Passive control
? Active control.
1.4 Passive control:
In this control method passive devices are used to alter the flow features. Following
are the examples of pasive control
1.4.1 Modification of body geometry:
By using a wavy cylinder Ahmed et al [17] found that behind the nodal points of
attachment, a locally narrower wake developed and more rapid wake velocity recovery was
observed compared to the saddle points of attachment. Tanner [18] investigated the effect
of various forms of segmented trailing edge wings and measured drag reduction upto 64%.
Bearman and Owen [19] achieved 30% drag reduction and suppression of vortex shedding
at Reynolds number of 40,000 by using plates whose front face had spanwise sinosoidal
variation. Rodriguez [20] used a three dimensional trailing edge consisting of alternate
segments of blunt base and spanwise cavity as a drag reduction device. He found that an
optimized shape of the configuration led to 40% drag reduction.Tombazis and Bearman[21]
studied the effect of three dimensional geometric disturbance on the wake by using a blunt
based body with a wavy trailing edge. They found that drag reduced due to increased base
pressure,which in turn was a result of dislocation of karman vortex street. Park et al [22]
used a bluff body with a blunt trailing edge and with small tab attached on the upper and
lower trailing edges of the bluff body. The experiment was conducted at Re of 20,000,40,000
4
and 80,000. They found that for an optimum tab configuration the base pressure increased
by 30%. The Karman shedding was also completely eliminated behind the bluff body.
All the above methods essentially introduced some kind of spanwise variation of the
bluff body.Consequently spanwise phase mismatch occurred in the Karmann vortex street
and the two dimensional nature of the vortex street was lost. The resulting three dimen-
sionality disrupted the formation of Karmann vortex street in the near wake of the cylinder.
Due to the increased three dimensionality, the base pressure increased resulting in less drag
on the body.
1.4.2 Surface modification:
Lee and Kim [23] used cylinders with wires wrapped on them helically. As a result of
this modified surface,the vortex formation region was elongated and the vortex shedding
frequency decreased. The wake width narrowed due to disruption of large scale vortices.
Flow around circular cylinder with U and V shaped grooved surfaces was investigated by
Lee and Lim [24]. They found that U type grooves reduced the drag by 18.6% compared
to the smooth cylinder whereas the drag reduction was only 2.5% for V type grooves. Lee
et al [25] used a V grooved micro-riblet with a peak to peak spacing of 300 micrometers.
At a cylinder Reynolds number of 3600 they achieved a maximum drag reduction of 7.6%.
However they noted an increase in drag with increasing Reynolds number. Zhdanov and
Papenfuss [26] investigated the effect of thin plates and dimples on the boundary layer
to achieve base pressure variations and drag. The prototype bluff body was a bus- coach
model. The use of plates and dimples decreased the reynolds stress,mean velocity defect
and the wake width was narrowed down.This was attributed to the formation of weaker and
smaller vortices behind the model.
The above methods of flow control do not interfere with the wake directly. Most of
them affect the boundary layer transition or separation point. On the other hand control
can be made effective by directly modifying the wake. One such method is using splitter
plates in the wake. Roshko[27] used a circular cylinder with a solid splitter plate (about
5
five cylinder diameters) attached to it. Due to the interference of the splitter plate the
base pressure was substantially increased and the vortex formation was inhibited. Use of a
smaller length splitter plate (1.1d) showed that when the leading edge of the splitter plate
was located at downstream positions within about 2.5d, the base pressure and the shedding
frequency was affected. But further downstream movement of the splitter plate was not
effective to alter the base pressure and shedding frequency.
1.5 Active flow control:
Active flow control employs various forcing mechanisms to effect the flow over a bluff
body. Fujisawa et al [28] studied the flow field of a rotationally oscillating cylinder. The
strouhal number based on forcing frequency was 1. Their measurement showed substantial
reduction in the fluctuating velocity at the optimum phase control. Due to the oscillation
the large scale structure of vortex shedding was almost removed in the cylinder wake. Effect
of stream wise oscillation of a circular cylinder on the wake was investigated by Cetiner and
Rockwell [29]. Their result showed that for fef0( where fe=frequency of oscillation of the
cylinder, f0=vortex shedding frequency) =1,0.44,0.74,0.88, they could achieve lock on stage
which was evident in the spectra of transverse force coefficient. They also found that during
one cycle of cylinder oscillation the vortex formation patterns were comprised of a Karmann
like shedding and a nearly frozen array of shed vortices.
Tokamaru and Dimotakis [30] carried out experiments to study the effect of sinosoidal
rotation of cylinder on the wake. The cylinder was rotated sinusoidally in time at a frequency
f and a normalised peak rotation rate ?1. The normalised peak rotation rate was chosen
such that peak peripheral velocity was comparable to the velocity just outside the boundary
layer. The strouhal number based on the forcing frequency was varied between 0.17 and
3.3. The plot of drag coefficient vs forcing strouhal number for a normalised peak rotation
rate of 2 ,showed that the estimated Cd for the unforced case is a factor of six greater than
the forced case.Also for certain forcing frequency the wake structure was synchronised with
6
the forcing frequency. They concluded that the dynamics of the wake was controlled by the
ejection of circulation into the flow rather than the behaviour of the unforced flow.
Inthe studydone byKieftetal[31]acircularcylinderwasheatedandthe corresponding
effect on the vortex formation was found. The Reynolds number for the experiment was
75. Another important non dimensional number for this case is Richardson number which
is defined as the ratio of buoyancy force and inertial force. The Richardson number was
varied between 0 and 1. They found that the induced heat caused a downward motion
for the shed vortex structure. This behaviour was attributed to the difference in strength
between two vortex rows.
Another important method of active flow control is the use of synthetic jet. Glezer and
Amitay [32] used a control device which was used to inject linear momentum to the flow.
The synthetic jet is formed by alternating momentary injection and suction of fluids across
an orifice. But since the working fluid is the ambient fluid the net mass flux is zero where
there is a non zero momentum injection into the flow.They found that the high frequency
synthetic jet over a circular cylinder caused a significant drag reduction. The accelerated
cross flow around the jet orifice caused the stream wise pressure gradient to change such
that the boundary layer downstream becomes thinner allowing the flow to overcome adverse
pressure gradient and thus delaying flow separation.
A relatively new flow control method which has gained prominence in recent times is the
use of plasma actuators. This term refers to a broad class of device based on atmospheric
pressure electrical dischages and include corona discharges, di electric barrier discharges
(DBDs), glow discharges and arc discharges.In DBD plasma actuators two electrodes are
separated by a dielectric material, one of them is left open to atmosphere whereas the other
is embedded into the surface of the body. A DBD plasma is created when a high voltage
is applied to the electrodes. The residual fluid is driven in the form of a horizontal jet
by the induced velocity. This induced velocity is higher in the case of the application of
glow discharge plasma where it has been shown that the higher induced velocity actually
7
caused addition of near wall flow momentum and as a result boundary layer separation was
delayed[ Roth et al [33]].
Prandtl first demonstrated the effect of boundary layer suction on the flow around
a circular cylinder. When the slow flow in the boundary layer is removed by suction,the
boundary layer gets energized by the rotational effect created by it.The same effect can be
achieved by blowing [34]. The main advantage of boundary layer control is attached flow
due to modified pressure gradient and delay of separation of the boundary layer.
Another active control method which directly interfere with the wake is base bleeding.
Bearman[35] successfully used base bleeding to suppress vortex shedding and to reduce
base drag. Like splitter plate the effect of base bleeding was to delay the interaction of the
two separated shear layers and thus to increase the formation length. The base pressure
increased due to an increase in vortex formation length.
1.6 Effect of sound on the flow over a circular cylinder:
In addition to the active techniques mentioned earlier some investigators have used
acoustic disturbances to affect the bluff body wake. Blevins [36] investigated the influence
of sound waves on the vortex shedding from a circular cylinder. The Reynolds number
range for the experiment was 20,000-40,000. His results showed that application of sound
correlated with the span wise vortex shedding. This was confirmed by the signals obtained
from four flush film sensors placed on different span wise locations on the cylinder. In
the absence of excitation the signals were incoherent and irregular. When 143.5 dB sound
at the shedding frequency was introduced the four signals were nearly in phase with less
irregularity which showed that application of acoustic excitation synchronized the shedding
frequency and was able to increase the strength of vortex shedding. Another important
finding from this experiment was that the sound applied near vortex shedding frequency
shifted vortex shedding to the forcing frequency.
Detemple- Laake and Eckelmann [37] carried out detailed experiments to understand
the coupling mechanism between vortex formation and shedding with sound waves. The
8
Reynolds numbers for the experiments were selected between 53 and 250. The ratio of
frequency of the sound wave to the natural vortex shedding frequency of the cylinder (in
the unforced case) was varied between 0.5 and 4. Depending on the sound frequency and the
sound amplitude, twelve different wake structures were found.They were broadly classified
as
? structures independent of the ratio of sound frequency to vortex shedding frequency.
? synchronised structure which was shedding frequency equal to half the sound fre-
quency
? synchronised structures where the shedding frequency was same as the sound fre-
quency.
Hsiao and Shyu [38] introduced acoustic waves in the cylinder wake through a thin slit on
the cylinder surface. The results showed that the separated shear layers were sensitive to
the excitation. When the frequency of the internal acoustic excitation was around the shear
layer instability frequency the drag reduction was maximum and a marked reduction in the
amplitude of the shedding frequency was observed. The flow visualization also showed that
the Karman vortex street was perturbed to form smaller vortices that significantly increased
the three dimensionality of the wake.
Huang [39], performed an experiment with circular cylinder in the Reynolds number
range from 4,000-8,000 by introducing pure tone sound at the natural vortex shedding
frequency into the flow through a thin slit on the cylinder surface. He found that vortex
shedding was suppressed by the excitation but there was an optimum sound level for the
maximum suppression. For a Reynolds number of 5,550, natural shedding frequency of 82
Hz and with a sound level of 70 db at the slit, the natural peaks were almost eliminated
at xd > 7. His results also showed that there was a very narrow excitation range which was
able to suppress the shedding to the maximum. Out of these ranges the excitation had no
effect on shedding.
9
Fujisawa et al.,[40] performed similar experiment with acoustic excitation. The cylinder
diameter was 50 mm with an aspect ratio of 8. The flow velocity was 2 m/s resulting in
a Reynolds number of 9,000. The drag coefficient calculated from the surface pressure
distribution showed that it had a minimum for a slit angle of 90o, and when the excitation
frequency was 4 times the natural shedding frequency i.e. around the unstable frequency
of the shear layer.
In a similar study, Fujisawa et al.,[41]; investigated the effect of internal acoustic ex-
citation with the help of phase averaged Particle Image Velocimetry(PIV). The Reynolds
number of the experiment was 9,000. The phase averaged results showed the formation of
discrete vortices along the shear layer of the cylinder wake when the excitation frequency
was four times the vortex shedding frequency. Due to the interaction of the vortices with
the wake the velocity fluctuation in the flow field was weakened.
1.7 Present research:
It may be noted that these studies with internal acoustic excitation have concentrated
in the low Reynolds number range. The effect of internal acoustic excitation on cylinder
wake at higher Reynolds number is still lacking in the literature. The flow over a cylinder at
higher Reynolds number contains multiple global modes. Also at higher Reynolds number
the amplidue of the global mode increases. Whether or not the internal acoustic excitation
is successful in suppressing the shedding component which is the first global mode to become
unstable and how exactly it influences the turbulent wake needs to be further investigated.
Also all the research done so far, have used a straight slit which essentially introduce a two
dimensional disturbance. By introducing a three dimensional disturbance through a wavy
slit, is likely to be more effective. This is the motivation of the work presented in this thesis.
The objective of this research was to investigate the influence of three dimensional
disturbance created by internal acoustic excitation of different frequencies on the turbulent
wake of a circular cylinder. It is to be noted that the excitation introduced in the flow in the
aforesaid manner works like a synthetic jet. Since the working fluid source for the excitation
10
is the surrounding fluid(in this case, air inside the cylinder),no extra mass flow was added
to the system, though momentum was added thorugh the sinusoidal slits to the flow due to
vibration of the speaker diaphragm. The modification of the flow over the cylinder occurred
owing to the action of the jet on the cross flow over the cylinder.
11
Chapter 2
Experimental setup
Sinusoidal slits were made on the cylinder surface on diametrically opposite locations.
Two loud speakers were used to generate sound at desired frequencies and amplitudes. Thus
the wake was subjected to three dimensional forcing. All the investigations were carried
out at two Reynolds numbers, 24,000 and 45,000. Hot wire anemometers were used for
measuring the turbulent quantities of the wake and pitot tube was used for total pressure
survey. The data collected from the experiments were analysed to understand in detail the
exact mechanism by which this three dimensional disturbance affect the wake. The drag on
the cylinder was calculated from the total pressure data. One of the aim of this research
was to find whether a disturbance with a frequency higher than the shedding frequency is
able to cancel the Karmann shedding. This was investigated with the help of a single wire
placed in the shear layer of the cylinder.
2.1 The wind tunnel:
All experiments were performed in the Auburn University 3x4 ,close circuit,low tur-
bulence subsonic wind tunnel. The tunnel has a contraction ratio of 5,test section with
1.5 meters long and cross section of 1mx1.1m. The floor is made of steel section to which
the experimental setup was attached. The side walls and the roof of the test section is
made up of plexi glass. The speed of the tunnel is controlled from a control pannel and
the corresponding readings were noted from a pitot tube attached to a port in the test
section.The non uniformity in the flow was found to be 1% and a free stream turbulence
level of 0.5%. The cylinder model was placed at a height of 470 mm from the wind tunnel
12
floor to minimize the effect of boundary layer developed on the ceiling and the floor of the
wind tunnel. The test section blockage ratio was 0.045.
To mount the cylinder model in the center of the tunnel,a steel frame was used (see
Figure 2.1). Two elliptic side plate were attached to both end of the cylinder to ensure
two dimensional flow.Separate fixtures were fabricated from plywood plates for holding the
speakers.
2.2 Cylinder models:
Cylinders were made of copper tubings of 41.3 mm outer diameter and thickness 1
mm. The length of the cylinders were 203 mm. So the aspect ratio of the cylinder was
4.9. Sinosoidal slits were made on two diametrically opposite location of the cylinder by
laser cutting operation[see Figure 2.2]. The width of the sinosoidal slit was 0.5 mm and the
length of the slit was 60mm.
2.3 Instrumentation:
2.3.1 Data acquisition system:
All data from the hot wires and pressure sensors used in this study were recorded using a
data acquisition board (National Instrument NI PCI 6035E DAQ board).The A/D converter
has 16 bit resolution over an bipolar input range of ?10 volts. The maximum sampling
rate of the A/D board is 200 kHz and it can handle 16 single-ended or eight differential
analog inputs. All the data acquisition was done by using LabVIEW 8.2 software.Separate
LabVIEW codes were written for data acuisition, signal generation and probe calibration.
All the connections were made in a patch board outside, which was connected to the A/D
board in the CPU of the computer. Proper care was taken to insulate the connection from
outside interference which introduce noise.
13
2.3.2 Pressure measurements:
Total pressure in the wake was measured by using pitot tube. The probe was mounted
in the traverse system placed on the top plexglass roof of the wind tunnel,and was intro-
duced in the test section through the slot.Care was taken to maintain the probe alignment
perpendicular to the flow. The pitot probe was connected to a differential type pressure
transducer (Validyne,model DP 45-14). It is a variable reluctance type transducer which
gives the difference of the pressure from its two input connection. The other input tube
was left open to the atmosphere.Breather between the test section and the diffuser in the
return leg ensures the static pressure to be atmospheric. A carrier demodulator(Validyne,
model CD 12) was used to provide transducer excitation and to amplify and demodulate
the output signal of variable reluctance transducer.The input sensitivity of the carrier de-
modulator is 0.9-75 m V/V for 10 v dc full scale output. The output signal from the signal
conditioner was sampled using the DAQ board.
2.3.3 Hot wires:
The turbulent quantities in the wake were measured with the help of hot wires. Hot
wire measurements were performed using single wires ( DANTEC P15) and x-wires ( DAN-
TEC 55P61). A constant temperature anemometer system (DANTEC MiniCTA) was used
for this purpose.The overheat ratio of the hot wires was adjusted according to the manu-
facturer?s prescribed maximum wire temperature. The total resistance was calculated by
adding
1. the resistance of the cable and the probe holder together (while the probe holder was
shorted using a shorting probe).
2. the resistance of the hot wire probe.
Resistance measurement was done with a voltmeter. The overheat ratio was calculated
thereafter and the dip-switches were adjusted according to the calculation. The frequency
14
response of the hot wire circuitry and the gain settings were maintained at the manufac-
turer?s specifications. The wire of the single sensor probe was made of platinum plated
tungsten with a diameter of 5 micrometer and length 1.25 mm. According to manufac-
turer?s specification the maximum sensor temparature permitted is 300oC. But during the
experiments a wire temperature of 150oC was selected to assure safe operation and longiv-
ity of the wire . The x wires had the same wire diameter and length as the single wire.It
was too made of platinum plated tungsten. The angle between the two wires was 90oC.
The x wire was mounted with the probe axis parallel to the flow direction. So the angle
between the mean flow direction and the wire was 45o. The signal from the anemometer
was constantly monitored in a HITACHI oscilloscope.Like pressure measurements, the hot
wire signal were sampled in the same manner using the DAQ board. The probe holder
was fixed to a steel bar and mounted on the traverse.The anemometer was connected to
the patch board in a differential mode since the MiniCTA anemometer did not have any in
built ground reference ( floating signal source).
2.3.4 Probe traversing system:
Probe access to the tunnel ineterior was provided by slots cut through the plexiglass
plate at the top of the wind tunnel test section. The probe movement was controlled by a two
axis traverse controller (VelMax). The traverse controller was connected to the personal
computer through serial ports. Desired movement of the traverse were programmed by
using the serial port commands, as mentioned in the manufacturer?s manual, in LabVIEW
software. The mounting rod end which housed the hot wire probe was made streamlined
shape.The mounting rod was wrapped with duct tape to ensure smooth movement during
the experiment. The vibration of the probe support was not significant as was checked from
the various power spectrums.
15
2.3.5 Speakers:
Excitation to the flow was provided by two sub woofers. Two set of sub woofers
were used for this purpose (PYRAMID-WX-65X). The spearkers were operated by means
of sinosoidal signals of desired frequencies, generated by LabVIEW and amplified by an
external power amplifier for driving the speakers. It was found that an optimum voltage of
5-7 volt was sufficient for driving the speakers. Higher voltage was found to be harmfull for
the speakers in the high frequency range.
16
Figure 2.1: Schematic of experimental setup in the wind tunnel
Figure 2.2: Location of the sinusoidal slits on the cylinder surface
17
Chapter 3
Results and discussion
The experiments were done at two different Reynolds numbers, 24,000 and 45,000,
which correspond to 9 m/sec and 17 m/sec of free stream velocity in the wind tunnel. The
cylinder was placed in between the end plates in such a way so that the mean axis of the
sinusoidal slit on the top surface was at 90 degree from the attachment line. The blowing
coefficient C? for each case was calculated as C? = vsU?, where vs is the velocity of excitation
from the slot. This was measured by placing the single wire very close to the slot. The wake
measurements without acoustic excitation were accomplished with a solid cylinder model.
Table 3.1 shows the various blowing coefficient values.
3.1 Effect of excitation on the vortex shedding:
A single wire was placed in the upper shear layer zone, yd = 0.5 and xd = 1, to measure
the vortex shedding frequency fs0. It was found to be 50 Hz for Re of 24,000. For Re of
45,000, this was found to be around 78 Hz. The speaker was operated with a number of
different frequencies for the two Reynolds number case; the maximum being 180 Hz. It was
not feasible to operate the speaker at higher frequencies since at higher ranges the amplitude
Re = 24000 Re = 45000
Excitation Frequency (Hz) C? Excitation Frequency (Hz) C?
25 0.2263 38 0.1284
45 0.2213 76 0.1266
50 0.2183 85 0.1237
60 0.2202 100 0.1217
100 0.2086 156 0.1252
180 0.2256 180 0.1278
Table 3.1: Blowing coefficients for different forcing frequencies
18
of the forcing goes down drastically making the forcing ineffective. For this reason in the
higher Reynolds number case the frequency of 310 Hz ( 4fs0) was not selected as it was
found that at this frequency the blowing coefficient is not sufficient for the experiment.
Figure 3.1 shows the power spectrum plotted for different forcing frequencies. It is
evident that for Re of 24,000 case when the frequency of the acoustic excitation was almost
same as the natural shedding frequency the peak of the shedding component in the spectrum
plot shifted towards the forcing frequency side with a nominal decrease in the magnitude
of the component as seen from figure 3.1. This trend of nominal shift in frequency and
reduction in magnitude continued for forcing frequency of 45 Hz. However there was a
remarkable decrease in the peak when the forcing frequency was 60 Hz. The shedding peak
was almost eliminated at this forcing frequency. This trend remained same for a forcing
frequency of 100 Hz and 180 Hz. Lastly in the event of excitation with a sub harmonic
frequency of 25 Hz (around fs02 ) the only difference in the power spectra is the appearance
of a distinct peak in the sub harmonic range of the spectrum with slight increase in the
shedding component.
For Re of 45,000 case, the power spectrum shows that in the event of excitation with
a frequency almost equal to the shedding frequency the shedding peak was considerably
strengthened. When the forcing frequency was 85 Hz a distinct peak appeared around
176 Hz. In case of excitation with 100 Hz the peak shifted to 100 Hz and the shedding
peak disappeared. The shedding peak was completely eliminated when higher excitation
frequency of 156 Hz and 180 Hz was applied.
From the spectrum plots discussed so far it is clear that when the forcing frequency is
twice the shedding frequency the acoustic excitation successfully eliminated the shedding
peak completely. Except Huangs work (Huang X.Y, 1995) where he reported to have
eliminated the shedding peak with a acoustic excitation of same frequency at a downstream
distance greater than xd = 7, all the other research done with internal acoustic excitation
have shown that in the low Reynolds number range, a forcing frequency which is around four
times the shedding frequency was necessary to neutralize the vortex shedding completely.
19
Hsiao et al (1991) did their experiment with a 6cm outer diameter cylinder and their result
at Re of 24,000 (fig. 10 in the paper) showed that only when the forcing frequency was
at least of the order one than vortex shedding frequency which was 18 Hz, excitation was
able to eliminate the shedding . But in the present work, the shedding frequency was 50
Hz for Re of 24,000 case due to the use of a different diameter cylinder. Also the three
dimensionality was introduced through a sinusoidal slit which invariably helps to increase
the perturbation in the flow. So it is concluded that the main factor for cancellation of
shedding is the degree of three dimensionality introduced which in turn depend on the
slit geometry, blowing coefficient and the frequency of excitation. It is possible to achieve
cancellation of shedding peak even with an excitation of frequency less than the shear layer
instability frequency provided the blowing coefficient or in other words the amplitude of
excitation is high and the resultant three dimensionality introduced is effective in disrupting
the shedding pattern . This argument supports the flow visualization study done by Hsiao
et al (1991) where it was shown that the basic mechanism for cancellation of shedding was
the destruction of Karman vortices into smaller eddies near the cylinder.
The flow in the wake of a circular cylinder is a highly nonlinear phenomenon. It
contains multiple modes of disturbances where the Karman vortex shedding is considered
as the primary mode. When an external disturbance having almost the same frequency of
the primary mode is introduced in the system which is in the form of an acoustic excitation
in the present experiment, it can couple with the primary mode. The effect of coupling may
either be to attenuate or amplify it depending on the phase difference of the two modes.
The present work, as discussed in the previous paragraphs, showed weakening of shedding
peak at Re of 24,000 and strengthening at Re of 45,000. This behavior of the spectral plot
can be attributed to the inherent non linearity of the turbulent wake.
Regarding the use of the parameter which aptly describes the effectiveness of forcing,
it is suggested that blowing coefficient is a better term to use than sound pressure level as
used by previous researchers. The excitation created by the speaker diaphragm forces a jet
out of the slit, into the flow. It is not the acoustics rather the amplitude and frequency
20
Re = 24,000 Re = 45,000
Excitation Frequency (Hz) Cd Excitation Frequency (Hz) Cd
No forcing 1.13 No forcing 1.20
50 1.08 76 1.02
180 0.56 180 0.84
Table 3.2: Drag coefficients for different forcing frequencies
of the jet which is important for effective shedding control. Furthermore acoustics depend
not only on the signal input but also on the material used in model construction, internal
cavity resonance due to standing waves etc.
3.2 Effect of excitation on mean velocity distribution:
Mean velocity profiles were measured by traversing an x wire sensor (DANTEC 55P15)
in the wake starting from 1 diameter to 10 diameters downstream of the cylinder. The
frequency for the acoustic excitation was maintained at fs0 and 180 Hz. Figure 3.2 and
figure 3.3 illustrate the effect of forcing with 180 Hz excitation on the mean velocity profiles
in the two Reynolds number cases. Due to the forcing the upper and lower shear layers
got accelerated. This acceleration of shear layers is evident in the presence of a large
velocity gradient around the region yd = ?1. This increase in velocity of the free shear
layers effectively narrows down the wake thus making the region more uniform in terms of
flow velocity. Apart from the clear indication of a narrowing wake, figure 3.2 and 3.3 also
shows that up to about xd = 5, the velocity of flow in the centerline of the wake has in fact
came down in the case of forcing with 180 Hz excitation. This trend was not visible after
wards. From xd = 6 to 10 the velocity profiles for the forcing case maintains the accelerating
character of the shear layers and more uniform velocity profiles, thus indicating lower value
of momentum loss from the no forcing case, which ultimately contribute to lower drag. The
table 3.2 shows the Cd values computed from the velocity profiles.
It is interesting to note that at Re of 24,000, the drag reduction was almost 50%
compared to 30% in case of Re of 45,000. To determine the effect of forcing on the evolution
of the wake the half wake width was determined from the mean velocity profiles. The half
21
Figu
re
3.1:
Energy
sp
ect
ra
for
diff
eren
tfor
cin
gf
requencies
22
wake width ? is defined as the distance of the location from the center of the wake where
the velocity defect is half the maximum velocity defect( see figure 3.4). From figure 3.5 it
is evident that forcing caused the wake to narrow down in both the cases.
3.3 Effect of excitation on fluctuating quantities:
The cross sectional distribution of velocity fluctuation in the wake of the circular cylin-
der is shown in figure 3.6 to 3.9, where the results under acoustic forcing at 180 Hz have
been compared with that of no forcing case. The normal and stream wise velocity fluc-
tuations are mostly reduced by the application of forcing in lower Reynolds number case.
This is attributed to the appearance of a more uniform wake in the case of forcing. In
figure 3.6 and 3.7, around yd = 0.5,?0.5 the v fluctuation increased primarily due to the
three dimensionality introduced by the forcing which injects momentum into the flow. At
all stream wise position the suppression of fluctuation is evident in case of 180 Hz forcing.
However this suppression is not strong in the higher Reynolds number case as seen from
the figure 3.7 and 3.9. Due to the high flow velocity in this case the magnitude of the
forcing disturbance is not that effective in suppressing the velocity fluctuation compared to
the low Reynolds number case. The suppression of the fluctuation can be related to the
presence of stream wise vortices in the cylinder wake. Bays-Muchmore and Ahmed (1993)
have shown that the creation of stream wise vortices depend on the dominant foci structure
present along the secondary separation line. The peak values of turbulent shear stress and
kinetic energy production occur where these stream wise vortices merge with the braids.
So it may be assumed that forcing strongly affects the location of secondary separation line
and consequently the production of the stream wise vortices which in turn results in less
fluctuation.The assymetry in the distribution of the fluctuating quantities can be attributed
to the high degree of disturbance in the very near wake of the cylinder.
23
Figu
re
3.2:
Cr
oss
section
al
distri
but
ion
of
me
an
velo
cit
y,Re
=24,
000
24
Figu
re
3.3:
Cr
oss
section
al
distri
but
ion
of
me
an
velo
cit
y,Re
=45,
000
25
Figure 3.4: Half wake width
26
(a) Re=24,000
(b) Re=45,000
Figure 3.5: Variation of half wake width27
Figu
re
3.6:
Cr
oss
section
al
distri
but
ion
of
velo
cit
yfluctu
ation
vprime ,Re=24,000
28
Figu
re
3.7:
Cr
oss
section
al
distri
but
ion
of
velo
cit
yfluctu
ation
vprime ,Re=45,000
29
Figu
re
3.8:
Cr
oss
section
al
distri
but
ion
of
velo
cit
yfluctu
ation
uprime ,Re=24,000
30
Figu
re
3.9:
Cr
oss
section
al
distri
but
ion
of
velo
cit
yfluctu
ation
uprime ,Re=45,000
31
3.4 Characteristics of the flow field:
In order to understand the overall effect of the forcing on the wake of the circular
cylinder the magnitude of the shedding peak was determined from the spectrum plot at
each data points (33 x 10), taken by traversing the x wire in the whole wake. The data was
used to plot the contours as shown in figure 3.10.The contour plot signifies the distribution of
energyinthesheddingcomponentintheentirewakeupto xd = 10. Thisdistributionisuseful
in determining how the vortical structures develop in the near wake of a circular cylinder
under forcing compared to that of no forcing case. In the no forcing case, the maximum of
the energy was contained in the two shear layers emanating from the top and bottom side of
the cylinder. This was around yd = ?0.5 and ranged up to xd = 2 approximately. This was
the region where spectrum of the hot wire signal registered strongest peaks of the vortex
shedding frequency. In the center of the wake as two vortices from the top and bottom side
of the cylinder met each other, the peak in the spectrum plot shifted to 2fs0, wherefs0 is
the vortex shedding frequency. Gradually these structures convected downstream and the
energy content in the main shedding component reduced which signifies distribution of the
energy to smaller scales. On the other hand, the introduction of the forcing with 180 Hz
excitation, through the top and bottom slit of the circular cylinder had some remarkable
effect on the wake. From figure 3.10 it is evident the energy of the main shedding component
was not localized around the separating shear layer any more in case of 180 Hz forcing, rather
it was distributed in the wake in a uniform manner. Also the wake had got narrower as
indicated by the vertical width of the contour plot. This is attributed to the disturbance
introduced in the flow through the sinusoidal slits which have broken down the regular
development of the vortices from the two sides. Consequently the shear layer now consists
of smaller diameter vortices instead of the large vortical structures. The velocity in the
shear layer also increased as it consisted of smaller diameter eddies which had greater flow
velocity.Figure 3.11 shows the energy distribution in the shedding peak for different cases in
32
the higher Reynolds number case.The corresponding contour levels can be estimated from
the colorbar in the figure.
3.5 Kinetic energy in the wake:
The smaller eddies carried less energy downstream than the bigger eddies. Along with
this as the uniformity in the flow velocity increased, the wake narrowed down downstream.
These two factors contributed towards the suppression of the normal and stream wise ve-
locity fluctuations, which also implies that the available turbulent kinetic energy decreased
downstream due to the forcing. This suppression due to forcing was more pronounced in the
lower Reynolds number case as evident from the figure 3.12 which shows the distribution
of turbulent kinetic energy in the wake (TKE = 12 uprime2+vprime2U2
?
). In case of Re of 45,000, the
kinetic energy of turbulence came down due to forcing with 180 Hz disturbance at xd = 6to8.
But no marked difference was observed thereafter (figure 3.13). For this calculation, the
contribution of in the wake is only retained though Harsha and Lee [45] have suggested
using vprime2 = wprime2 for turbulent kinetic energy computation.
3.6 Wake preservation:
The wake behind a bluff body can be broadly categorised in two regions
1. Near wake region
2. Far wake region
Extensive studies have been carried out to characterise the far wake([44],[43]). The wake
can be said to have reached an asymptotic state when all flow properties reach an universal
distribution which is independent of the initial condition.The mean flow development in
the far wake which is generally at a large downstream distance from the bluff body, is
characterised by the drag of the body. On the other hand the near wake ( just behind the
bluff body) is strongly influenced by the characteristics of the body as well as the upstream
flow condition.A change in turbulence structure of the flow takes place in the near wake.
33
(a) No forcing
(b) 180 Hz
Figure 3.10: Contour plot of the magnitude of the shedding peak,Re=24,000
34
(a) No forcing
(b) 180 Hz
Figure 3.11: Contour plot of the magnitude of the shedding peak,Re=45,000
35
Figu
re
3.12:
Cr
oss
section
al
distri
but
ion
of
tu
rbu
len
tkinetic
en
ergy
,Re=24,000
36
Figu
re
3.13:
Cr
oss
section
al
distri
but
ion
of
tu
rbu
len
tkinetic
en
ergy
,Re=45,000
37
The wall of the bluff body generates vorticity and that gets advected with the mean flow.
In the near wake a free turbulence condition exists. The near wake is also signified by the
adjustments of pressure fields and by viscid inviscid interaction.The wake is supposed to
have reached a self preserving state when these following asymptotic trends are reached.
W0 ? X?12
b ? X 12
W0 is the maximum velocity defect and b is the half wake width. Also a self preserving
wake is characterised by the parameter (W0U )
radicalBig
X
? . Far away from the wake this equilibrium
parameter attains an universal value of 1.63. The term ? is called the wake momentum
thickness which is defined as ? = integraltext??? UU?(1? UU?)dy. Thus the behavior of the measured
values of the similarity parameters indicate the manner the wake is reaching the asymptotic
state.The distribution of this parameter in the stream wise direction for different forcing
conditions are shown in figure 3.14 to 3.19.
For Reynolds number of 24,000 case, the distribution of the values of (W0U )
radicalBig
X
? in the
noforcing case indicates, in the near wake, upto xd = 11 the asymptotic value has not been
reached.But the trend of the values towards the asymptotic limit is evident.When the three
dimensional disturbance of 180 Hz was forced, this trend was hampered. The local maxima
of the similarity parameter around xd = 5 can be attributed to the increase in velocity
defect(w) for the forcing case. As was pointed out in section 3.2 the centerline velocity was
found to decrease in case of forcing with 180 Hz disturbance. The same explanation can be
applied to the higher Reynolds number also ( Figure 3.17 and 3.19).
3.7 Wake formation length:
The wake formation length indicates the point in the wake where the velocity fluctua-
tion reaches a maximum value. It can also be defined as the point of maximum fluctuation
of the second harmonic component. It can be noted that in the centerline of the wake, the
second harmonic component of the shedding has the maximum energy but with a frequency
double the shedding frequency. It is because in the centerline of the wake vortices from
38
(a) Noforcing
(b) 25 Hz
Figure 3.14: Similarity parameter in wake,Re=24,000
39
(a) 45 Hz
(b) 50 Hz
Figure 3.15: Similarity parameter in wake,Re=24,000
40
(a) 60Hz
(b) 180 Hz
Figure 3.16: Similarity parameter in wake,Re=24,000
41
(a) Noforcing
(b) 38 Hz
Figure 3.17: Similarity parameter in wake,Re=45,000
42
(a) 76 Hz
(b) 156 Hz
Figure 3.18: Similarity parameter in wake,Re=45,000
43
(a) 180Hz
Figure 3.19: Similarity parameter in wake,Re=45,000
44
both side interact with each other. Another definition of wake formation length says it is
the point where the outside fluid crosses the wake centerline for the first time. Here the
streamwise velocity fluctuation in the centerline of the wake has been considered for finding
the wake formation length.
Figure 3.20 to 3.25 shows the wake formation lengths for different cases of forcing.
For the noforcing case(Figure 3.20) in Reynolds number 24,000 case, the wake formation
length was found to be around 2d.As the forcing frequency increased the wake formation
length was found to increase gradually.But the corresponding maximum fluctuation level
came down.This is in accordance with section 3.3 where it was shown that the application
of forcing reduces the fluctuation level of velcocity components in the wake. Figure 3.22
shows that when 180 Hz forcing was applied the peak in the fluctuation of streamwise
velocity attained its minimum value and the corresponding point of maximum fluctuation
in the centerline of the wake shifted to around 4d. This increase in wake formation length
is attributed to the local disturbance created by the forcing which disrupts the formation of
a regular vortex street. As the development of large scale karman vortices was disturbed,
the character of the regular wake was changed. This is evident in the change in the wake
formation length. The same reason holds true for the higher Reynolds number case also.
In this case the wake formation length was shifted to around 3d for forcing with 180 Hz
(Figure 3.25)
45
(a) No forcing
(b) 25 Hz
Figure 3.20: Wake formation length,Re=24,000
46
(a) 50 Hz
(b) 60 Hz
Figure 3.21: Wake formation length,Re=24,000
47
(a) 180 Hz
Figure 3.22: Wake formation length,Re=24,000
48
(a) No forcing
(b) 38 Hz
Figure 3.23: Wake formation length,Re=45,000
49
(a) 76 Hz
(b) 156 Hz
Figure 3.24: Wake formation length,Re=45,000
50
(a) 180 Hz
Figure 3.25: Wake formation length,Re=45,000
51
Chapter 4
Conclusion
The wake of a circular cylinder was investigated with a three dimensional disturbance,
caused by forcing from two loud speakers, which was introduced in the flow field through
two sinusoidal slits located on two diametrically opposite direction on the cylinder surface.
Experiment was done at two different Reynolds numbers. For Reynolds number 24,000
(shedding frequency about 50 Hz) it was observed that a forcing frequency of 60 Hz was
able to eliminate the shedding peak completely. For Reynolds number 45,000 (shedding
frequency about 78 Hz) the shedding component was eliminated by 100 Hz forcing. But in
this case a forcing with 76 Hz excitation resulted in strengthening of the peak. The mean
velocity plot showed that the wake width gets considerably narrowed in case of a forcing
with 180 Hz excitation which also reduced the drag for the low Reynolds number case.
Previous research, which introduced two dimensional disturbances through a straight slit,
have shown that in lower Reynolds numbers ( typically 9,000) a forcing frequency which
is almost four times the shedding frequency has to be selected for complete elimination
of the von Karmann shedding component. Results obtained from this experiment lead
to the conclusion that even a forcing frequency less than four times shedding frequency
can eliminate the shedding peak in a turbulent wake of a circular cylinder. Provided the
blowing coefficient is sufficient to create three dimensional disturbance which in effect breaks
the vortex street into smaller eddies. Due to this, the energy in the wake was uniformly
distributed in the smaller structures from the main shedding component. The acceleration
of the two separating shear layers due to the forcing narrowed the wake thus registering the
uniformity in velocity.
52
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55
Appendices
56
Appendix A
Calibration
This appendix describes the calibration procedure for the pressure transducer and the
hot wires.The calibration for both of them were carried out before each experiment.
A.1 Pressure transducer calibration:
The pressure transducer was calibrated against a known pressure from a micro manome-
ter. The fluid used in the manometer was water. A piston arrangement was used for apply-
ing known amount of pressure.The working principle of the micrometer is same as normal
manometer but the indication system is based on micrometer and conduction. When the
micrometer plunger barely touches the water column,the indicator needle deflects due to
conduction of current. So during pressure measurement,subsequent increase in pressure can
be determined by first raising the micrometer plunger to required height and then increasing
the pressure till the water column touches the micrometer plunger,again indicated by the
deflection in the needle.The follwing steps were follwed for pressure transducer calibration.
1. The carrier demodulator ( always connected to the pressure transducer) was switched
on.
2. The port ( marked with a + sign) of the pressure transducer was connected to one of
the outlet of a ?T? pipe joint
3. The other two ports were connected to the manometer and the piston respectively(
piston rod at extreme end position). The water in both the arms of the manometer
should be at the same level.
4. The micrometer plunger was first touched the water column then lifted up by 0.1 inch
.
5. The piston was operated slowly such that the water column touched the plunger and
the needle deflected to indicate there was an increment of 0.2 inch pressure in the
manometer.
6. The reading in the digital display of the carrier demodulator was noted down along
with the water column pressure in the manometer.
7. Step 4 was repeted upto 2 inch of water column pressure.
8. A straight line was fitted to the data. The equation of the straight line was used to
compute an unknown pressure corresponding to a known voltage.
Table A.1 shows the values obtained during a typical calibration.
57
Voltage ( V ) Pressure ( inches of water )
0.78 0.2
1.54 0.4
2.23 0.6
2.94 0.8
3.71 1.0
4.46 1.2
5.22 1.4
5.95 1.6
6.71 1.8
7.36 2.0
Table A.1: Calibration chart for pressure transducer
Figure A.1: Calibration curve for pressure transducer
58
Voltage ( V ) Velocity ( ft / sec )
1.79417 21.09011
1.859322 27.963432
1.913088 34.690122
1.951538 40.159858
1.993016 46.806027
2.024436 52.274944
2.050236 57.328674
2.07492 62.262415
2.091009 65.743002
2.106076 69.222534
Table A.2: Calibration chart for single wire
A.2 Calibration of the hot wire:
The hot wires were calibrated insitu in the wind tunnel. The insitu calibration was
preferred to a dedicated calibrator, since the former takes care of the disturbance caused
by the probe holder, the effect of geometry of the tunnel etc. The reference velocity for
the calibration was found from a pitot tube placed at almost same height of the hot wire.
But care was taken such that the wake of the pitot tube did not interfere with the hot
wire probe.The pitot tube was connected to the Validyne pressure transducer. The tunnel
velocity was increased in step from the begining value, from the control pannel. The corre-
sponding pressure reading was found from the display of carrier demodulator and using the
pressure calibration curve it was converted to pressure in inch of H2O. The output signal
of the constant temperature anemometer was sampled at a rate of 4k Hz and a total of 12k
samples were sampled. Following this procedure 12-14 data points were acquired.All these
steps were implemented by a LabVIEW code. After the calibration, a transfer function
which was a 4th degree polynomial, was fitted to the data. The curve fitting was carried
out in MATLAB software. Table A.2 shows a typical calibration chart for a single wire.
For the calibration of the x-wire, the cross wire was kept at an angle of 45o with the mean
flow vector. The calibration was done in the same way as the single wire. The signal from
the two wires were sampled simultaneously.Table A.3 shows a typical calibration chart for
a x wire.
A.2.1 Determination of two component of velocity from X-wire:
X wires or cross wires are used to determine two velocity components of a flow field.
Generelly the wires are kept inclined to each other at an angle ( Most of the cases it is 90o).
And one of the wire faces the flow at 45o. If the plane of the two probes coincides with
the x-y plane, the u and v component can be obtained from the cross wire data. The hot
wire works on the principle of heat convection by the fluid flowing over the wires. The heat
transfer is maximum mainly due to the velicty perpendicular to the wire (vN). Although
the velocity tangential to the wire (vT) also contribute to the heat transfer. So the effective
59
Voltagewire1 (V) Voltagewire2 (V) Velocity ( ft / sec )
1.939586 1.687787 12.24
2.010026 1.751915 20.39
2.081031 1.8147 29.58
2.142906 1.867818 38.93
2.190952 1.909919 47.33
2.228734 1.943295 54.79
2.268396 1.978856 63.57
2.296547 2.004542 70.25
2.317002 2.022515 75.40
2.336462 2.040051 80.59
2.360009 2.062149 87.15
2.370573 2.071888 90.48
Table A.3: Calibration chart for x wire
Figure A.2: Calibration curve for single wire
60
Figure A.3: Calibration curve for x wire
61
cooling velocity can be written as
veff =
radicalBig
v2N +k2Tv2T +k2Nv2BN; (A.1)
where vBN is the velocity perpendicular to both the wire and the prongs. kT and kN are
empirically determined constants. If the angle between the wires is 90o and one of the wire
makes an angle of ?o with the mean flow vector ( u,say along x direction ), then from [A.1]
we get
v2A,eff = (ucos??vsin?)2 +k2T(usin? +vcos?)2 +k2Nw2 (A.2)
v2B,eff = (usin? +vcos?)2 +k2T(ucos??vsin?)2 +k2Nw2 (A.3)
where vN = ucos? ? vsin? and vT = usin? + vcos? and w = vBN. If the sensors are
sufficiently long kT ? 0and kN ? 1.If the third velocity w component is small it can be
neglected. Further if ? = 45o
v2A,eff = (ucos??vsin?)2 (A.4)
v2B,eff = (usin? +vcos?)2 (A.5)
so we get
u = 2?12(vA,eff +vB,eff) (A.6)
v = 2?12(vA,eff ?vB,eff) (A.7)
62
Appendix B
Uncertainty analysis
In order to quantify the experimental uncertainties involved with a hot wire measure-
ment,the following uncertainty calculation was carried out in accordance with the method
prescribed in [42].The reference case selected for the uncertainty evaluation was that of
Reynolds number of 24,000 which corresponds to 9 m/sec.The uncertainties involved in the
calculation of mean velocity profiles are addressed here.For calculation of uncertainty the
following sources of error were considered (uncertainty due to temperature and pressure
variation is ignored).
1. Pressure transducer error
From the data sheetprovidedbythe manufacturer, the accuracy ofpressure transducer
was found to be 0.5% of full scale output.
2. Pressure transducer calibration error
The source of this uncertainty is related to curve fitting errors. A straight line was
fitted to the data given in Table A.1.The residual at each data point was found out by
using curve fitting toolbox in MATLAB.The residuals denote the error at each data
point.The standard deviation of the errors( in % form) were calculated. The relative
standard uncertainty was calculated using the formula
relativestandarduncertainty = 2? 1100 standarddeviation(errors,%) (B.1)
3. Hot wire calibration error
As discussed earlier,a fourth order polynomial was fitted to the data presented in
Table A.2.The residuals and the corresponding relative standard uncertainty were
calculated in the same way as pressure transducer calibration.
4. A/D board resolution error
The A/D board resolution error was calculated using the formula
relativestandarduncertainty = 1?3 1U EAD2n ?U?E (B.2)
where EAD is the A/D board input range,n is its resolution in bits,U the velocuty
and ?U?E is the slope ( sensitivity factor ) of the inverse calibration curve (single wire
calibration) For the A/D board used in this experiments (NI-PCI 6035E),EAD = 20v,
?U
?E = 125.71 at 30ft/sec,and n = 16.
63
Errorsource Value Coveragefactor(k) Relativestandarduncertainty
Calibrator 0.02 2 0.01
Pressure transducer calibration 0.02 2 0.01
Hot wire calibration 0.0014 2 0.0007
A/D board resolution 0.0013 ?3 0.0002
Table B.1: Uncertainties for a single velocity sample acquired with a single wire for mean
velocity profile calculation
Voltage ( V ) Pressure ( inches of water ) residues
0.78 0.2 -0.00188
1.54 0.4 -0.0081
2.23 0.6 0.0047
2.94 0.8 0.012
3.71 1.0 0.0031
4.46 1.2 -0.00039
5.22 1.4 -0.0066
5.95 1.6 -0.004679
6.71 1.8 -0.01089
7.36 2.0 0.01274
Table B.2: Calibration chart for pressure transducer with residues
B.1 Velocity sample uncertainty:
The relative uncertainties are presented in Table B.1.
So the total uncertainties involved is 2?0.012 +0.012 +0.00072 +0.00022 = 0.0283 =
2.83%
B.2 Sample calculation of pressure tranducer calibration uncertainty:
In this section a sample calculation of the uncertainties is presented whose source is the
curve fitting errors. TableA.1 is again presented here as B.2 with an extra column which
contains the residues (errors due to the fitting of a straight line to the data).
As mentioned earlier MATLAB?s cfit toolbox was utilised for this computation.It stored
the residues in a structure output1.residue and the pressure values were stored in a variable
y. The following MATLAB code was executed to get the relative standard uncertainty (rsu)
due to pressure transducer calibration. rsu = 2?std(100?output1.residue./y)/100 which
gives 0.02 as result.
64