investigation of unsteady pressure over the surface of a circular cylinder in a turbulent flow
DESCRIPTION
University of AdelaideFinal Project Report‘INVESTIGATION OF UNSTEADY PRESSURE OVER THE SURFACE OF A CIRCULAR CYLINDER IN A TURBULENT FLOW’FINAL PROJECT REPORTMasters Project The University of Adelaide Department of Mechanical EngineeringUnder the guidance of Dr Con Doolan Student Name : Student ID Santosh Ballal Amarnath: 1187621University of AdelaideFinal Project ReportExecutive Summary:Bluff bodies when kept in a fluid stream produces unwanted noise, known as an Aeolian tonTRANSCRIPT
University of Adelaide Final Project Report
‘INVESTIGATION OF UNSTEADY PRESSURE
OVER THE SURFACE OF A CIRCULAR
CYLINDER IN A TURBULENT FLOW’
FINAL PROJECT REPORT
Masters Project
The University of Adelaide
Department of Mechanical Engineering
Under the guidance of Dr Con Doolan
Student Name : Santosh Ballal Amarnath
Student ID : 1187621
University of Adelaide Final Project Report
Executive Summary:
Bluff bodies when kept in a fluid stream produces unwanted noise, known as an
Aeolian tone. It occurs in many engineering situations, for example, flow across a
landing gear of an aircraft, flow across an antenna of an airplane/submarine/car, heat
exchangers etc. Flow over a circular cylinder can be considered as a common
representation of flow across a bluff body. The purpose of this project is to examine the
unsteady pressure over the surface of a circular cylinder in a turbulent flow, which
supports the dipole sources of unwanted sound. This will enable us to better understand
the noise generation process and thus assist us in the design of quite bluff bodies.
A Literature review is presented and it shows that while Direct Numerical
Simulation (DNS) and Large Eddy Simulation (LES) are reasonably accurate methods
to calculate the aerodynamic noise produced by the bluff bodies, they are very
computationally expensive. A much improved hybrid method that uses Unsteady
Reynolds Averaged Navier Stokes (URANS) solutions with a statistical model is
discussed. It was found out that the turbulent flow effects that are produced by the
unwanted dipole noises are controlled by a single time scale parameter τc. The
experimental value of this time scale parameter is not available in literature and
therefore has to be estimated or determined experimentally. Therefore, finding the
experimental value of the time scale parameter was one of the primary objectives of this
project.
In order to measure the unsteady transient pressure on the surface of a circular
cylinder in a cross flow, an experimental setup was designed. The experimental rig
consisted of a long cylinder with a microphone setup inside the cylinder to record the
surface pressure. The experiment was conducted by placing the whole rig in the wind
tunnel and the bluff body unsteady surface pressure was recorded.
The Reynolds number (Re) of the flow was roughly 18,500, the shedding
frequency fs was approximately 28 Hz. The recorded transient pressure data was found
to be a stationary ergodic random data. The meaning and physical significance of this
random data is discussed and presented in detail. The main descriptive properties such
as the mean square values of the time series, probability density functions (PDF),
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autocorrelation functions, power spectral density (PSD) and spectrograms of the data
are presented and discussed.
Using the temporal statistical model of Doolan (2010) and the experimental
results, the value of time scale parameter τc is estimated. It was found that the value of
τc depends on the form of the coefficient used in the exponential model. The project
management description presented shows the tasks and schedule of the project. The
summary and scope for the future project work are presented. Finally conclusions were
made based on the analysis performed.
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Acknowledgments:
I would like to acknowledge and extend my gratitude to the following persons
who have made the completion of this project work possible. First and foremost, I
would like to thank Dr Con Doolan, my supervisor who has extended his support all
through the project and his guidance and time to time feedback on my work. Dr Antoni
Blazewicz, my project moderator for his insightful feedback on the project work. Dr
Michael Riese, Manger of engineering services, for his help in design and
manufacturing of the experimental rig and suggestions on engineering drawings. Mr
Silvio De Ieso, for his help in integration of the microphone with the experimental rig.
Ms Dorothy Missingham, for her inputs on report writing and structure of the report.
Assoc.Prof. Eric Hu, coursework coordinator for his guidelines on project work and
execution.
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Table of Contents
Chapter 1 - Introduction: ...............................................................................................2
Chapter 2 - Literature Review and Background Study: ..................................................5
2.1 Introduction: ........................................................................................................5
2.2 Background Information on Bluff body flows & Review: ....................................7
2.2.1. Bluff body flows: .........................................................................................7
2.2.2. Flow over circular cylinder: .........................................................................8
2.2.3. Vortex shedding Regimes: ............................................................................9
2.2.4. Fluctuating side force and spanwise correlation scales on a cylinder: ......... 14
2.3. Circumstances leading to the project & Research Gap: ..................................... 16
2.3.1 Bluff Body Noise Prediction – Aeolian Tones: ............................................ 16
2.3.2. Temporal Statistical Model (Doolan, 2010) - (Theory): .............................. 17
2.3.3. Review of Pressure Measurement Methods: ............................................... 20
2.4 Summary: .......................................................................................................... 22
Chapter 3 – Project Objectives and Tasks in the project: .............................................. 23
3.1 Project Objectives: ............................................................................................. 23
3.2 Project Tasks:..................................................................................................... 23
Chapter 4 – Design of the Experimental Setup: ............................................................ 25
4.1 Design of the experimental rig: .......................................................................... 25
4.1.1. Concept Generation – Placing the microphone inside the cylinder: ............. 26
4.1.2. Concept Generation – Assembly of the rig: ................................................ 29
4.2 Experimental Design - Integration: .................................................................... 32
Chapter 5 – Post Processing Methods and Techniques: ................................................ 34
5.1 Readings before the experiment: ........................................................................ 34
5.1.2 Reynolds Number and Dynamic Pressure Calculations: .............................. 36
5.2 Readings during the experiment: ........................................................................ 37
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5.2.1 Strouhal Number, Shedding period, Shedding Frequency Calculation: ........ 37
5.2.2 Pressure Calculations: ................................................................................. 37
5.3 Post Processing of the Results: ........................................................................... 39
5.3.1 Representation of the surface pressure data (Results): ................................. 39
5.3.2 Curve fitting technique to find the value of τc (Analysis): ............................ 40
Chapter 6 – Results and Analysis: ................................................................................ 43
6.1 Project Results: .................................................................................................. 43
6.1.1 Results - Readings before the experiment: ................................................... 43
6.1.2 Results - Readings during the experiment:................................................... 46
6.1.3 Results – Representation of surface pressure data: ....................................... 48
6.2 Curve fitting technique to find the value of τc (Analysis): .................................. 70
6.2.1. Curve Fitting Technique using Model 1: ..................................................... 71
6.2.2. Curve Fitting Technique using Model 2: ..................................................... 73
Chapter 7 – Project Management Description: ............................................................. 77
7.1 Project Resource Listing: ................................................................................... 77
7.2 Project Timeline: ............................................................................................... 78
7.3 Risk Analysis: .................................................................................................... 81
7.4 Project Outcomes and Deliverables: ................................................................... 83
Chapter 8 – Project Summary, Conclusion and Future work: ....................................... 84
8.1 Project Summary: .............................................................................................. 84
8.2 Conclusion of the Project: .................................................................................. 86
8.3 Future work of the Project: ................................................................................ 88
References:.....................................................................................................................
Appendix A: Gantt Chart ................................................................................................
Appendix B: Matlab Code ..............................................................................................
Appendix C: Manufacturing Drawings ...........................................................................
Appendix D: Project Snapshots ......................................................................................
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Chapter 1 - Introduction:
Bluff body flows are present in many engineering situations, e.g. flow over
antennae of aircraft, protrusions from a submarine, aircraft landing gear, long chimneys,
towers etc... When, a bluff body is placed in a fluid stream it may produce an unwanted
noise. Additionally, the flow will create unsteady loading on the bluff body (Norberg,
2003). As there are several such engineering situations present, it is important to
understand the nature of the flow and its implications. General representations of bluff
body flow are shown in figure 1.1.
Source: Doolan, Advance Topics in Aerospace Engineering - Lecture notes
In general, flow over a circular cylinder can be considered as a flow around a
bluff body (Doolan, 2010). Figure 1.2 shows us the flow around a circular cylinder at
different Reynolds number. The flow patterns changes with change in Reynolds number.
In the case of an unsteady cross flow over the surface of a cylinder, a boundary layer is
formed all along on surface of the cylinder. This boundary layer separates and forms
free shear layers at the top and the bottom surfaces of the cylinder due to the adverse
pressure gradients. A von Karman vortex street is created as the free shear layers grow
behind the cylinder and become unstable. This phenomenon is known as vortex
shedding, which results in large fluctuating pressure forces. The von Karman vortex
street is shown in figure 1.3. Interestingly these pressure fluctuations have a special
significance in engineering applications due to the fluctuating side force it creates and
the correlation it has with the shedding frequency (Norberg, 2003). The transient
pressure on the cylinder’s surface supports noise with a dipole character (Doolan, 2010).
Figure 1.1: General representation of bluff body flows
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Source: Munson, Young & Okiishi (2005)
Source: NASA, Goddard Earth Science
Figure 1.3: Shear layers growing behind the cylinder and forming into a von Karman vortex street
Figure 1.2: Flow patterns for flow over a cylinder at different Reynolds number
(A) Re = 0.2 (B) Re =12 (C)Re = 120 (D)Re = 30,000 (E)Re = 500,000
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Many attempts have been made to measure the surface pressure data in the past
and also in recent years and there have been many new understandings on the features
of the wake over cross cylindrical flow. However, very little attention has been given to
measurement and statistical analysis of the unsteady pressure on the surface of a circular
cylinder in a cross flow. A detailed study of the turbulent wall pressure fluctuations is
needed to better understand the peculiar flow physics present in the wake of the bluff
bodies and to help develop new computational methods that efficiently calculate bluff
body noise (e.g. Doolan 2010). This forms the research gap for the project and the
research gap is presented in detail in the literature review.
The objectives of the project are:
To design an experimental set up to measure the unsteady pressure on the
surface of a circular cylinder.
Perform wind tunnel tests to record the transient pressure data.
Perform a statistical analysis and determine the properties of the data in the time
and frequency domains.
Using a curve fitting technique, determine the experimental value of the time
scale parameter τc. and to understand and draw conclusions concerning any
patterns within the data.
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Chapter 2 - Literature Review and Background Study:
The literature review of the project includes critical review of key published
works and contents of bluff body flows – specifically, flow over circular cylinder and
surface pressure measurements and the need for research to address the gaps in the
literature. The review will demonstrate the relationship between the preceding research
work and the current objectives of the project. The literature review will also cover the
background information, why the project is important and the circumstances leading to
the current project and work already carried out in the same field. The literature review
is presented below.
2.1 Introduction:
Bluff bodies produce unwanted noise when placed in a fluid stream. This
situation is very common in many engineering situations. Hence it is necessary to
understand the basic mechanism of this noise generation process and its characteristics.
Understanding them will help us in reduction of this unwanted noise. The wake has
three dimensional flow features within (see figure 2.1), the wake retains the vortex
shedding form as a von Karman Street but superimposed with three dimensional
velocity fluctuations of different wavelength and phase (Doolan, 2010). Hence, the
noise generated from a bluff body in a turbulent flow has a unique acoustic signature
that takes the form of spectral broadening.
Source: Boston University
Figure 2.1: Turbulent wake in a cross flow over a cylinder
Separation Turbulent Wake
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In order to calculate this noise there is a need to estimate the effects of flow
turbulence. In theory, DNS (Direct Numerical Simulation) of the Navier Stokes
equations may be used to calculate all the turbulence and acoustic information (Inoue &
Hatakeyama, 2002). This method is only feasible for low Reynolds number. For high
Reynolds number flows and noise simulations LES (Large Eddy Simulation) may be
used (Seo & Moon, 2007). However, LES is computationally very expensive and is not
yet suitable for everyday design work. Two dimensional -Unsteady Reynolds Averaged
Navier Stokes is the only viable alternative but doesn’t completely account for turbulent
flow effects. Doolan (2010) proposed a hybrid model of using 2D – URANS (Unsteady
Reynolds Averaged Navier Stokes) coupled with statistical methods to account for the
turbulent flow effects.
The spectral broadening of the noise is due to a temporal beating effect and the
noise radiation at different phases along the span of the bluff body (Doolan, 2010). The
temporal beating is statistically equivalent to narrow band random noise introduced into
a sinusoidal function (Bendat, 2000). The narrow band random noise contains the
turbulent flow effects and this can be represented statistically. This narrow band random
noise has been shown to be effectively modelled using a single time scale parameter τc
(Doolan, 2010). This time scale parameter needs to be estimated to account for the
turbulent flow effects but there is no experimental or numerical data present in literature
to assist in determining a value for this parameter τc. Doolan (2010) estimated this time
scale parameter as a function of vortex shedding period (T) at a particular Reynolds
number that is available in the literature for the statistical model. Thus there is a need to
conduct research at different Re in this area. Thus one of the primary objectives of this
project is to perform an experiment and calculate the value of this parameter τc. The
estimation of this time scale parameter by Doolan (2010) was introduced into the
statistical model to account for turbulent flow effects and calculating far field noise
using an acoustically compact case where the wavelength of the noise generated was
greater than the dimensions of the source producing it.
However, before an attempt to comprehend the noise generation process and
measure it to account for flow turbulence effects, there is a need to review the basic
concepts of flow over bluff bodies, particularly flow over circular cylinders and also to
understand clearly the regimes of vortex shedding. This project reviews the concepts of
flow over a circular cylinder and also reviews pressure measurement methods around
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the surface of a circular cylinder in a cross flow. Using the data from pressure
measurements one can estimate the effect of flow turbulence in a turbulent flow.
Additionally, the data can be used to perform spectral analysis and understand the
unique attributes of the acoustic source. Understanding these attributes has a practical
significance (e.g. reduction of noise from landing gear). Although there have been
various attempts to measure surface pressure over cylinder in cross flow, there has been
less investigation of its transient characteristics in turbulent shedding regime. Thus
further research on these gaps and performing some statistical analysis will help our
understanding of bluff body flows.
2.2 Background Information on Bluff body flows & Review:
The general aspects of bluff body flow are reviewed, flow over a circular
cylinder is considered as flow over bluff body and hence it is studied. The vortex
shedding regimes are studied along with the fluctuating side force & spanwise
correlation scales on a circular cylinder.
2.2.1. Bluff body flows:
In case of a streamlined body flow the flow attaches to the body contours and
this can be considered as an inviscid flow (no viscous effects). In case of a bluff body
flow the flow separates from the body and vortices are formed by the rolling up of shear
layers. The flow around a bluff body can be inviscid, but not the case in majority of
practical situations. Streamline body flow and bluff body flow is shown in figure 2.2
(A) and (B) respectively.
In general flow over circular cylinder can be considered as a flow over a bluff
body (Doolan, 2010), as the flow separates in case of a turbulent flow (see figure 2.1 &
2.2 (B)). There are various forms of instabilities associated in a flow past a circular
cylinder. These instabilities involve the wake and shear layer and boundary layer (Singh
& Mittal, 2004). Knowledge about unsteady loading on bluff bodies (circular cylinder)
due to the turbulent flow is necessary for aerodynamic design and control (Norberg,
2003). Hence, before understanding the features of instabilities, general understanding
of flow over cylinders is important.
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Source: John, Wind Engineering & Doolan, Advance Topics in Aerospace Engineering -
Lecture notes
2.2.2. Flow over circular cylinder:
In fluid dynamics, a wake is created downstream a solid body (for example a
circular cylinder) moving through a fluid, caused by the flow of the fluid around the
body. Vortices are created that detach periodically from either side of the body. This
phenomenon is called vortex shedding (a von Karman vortex street). These vortices
create fluctuating pressure forces around the cylinder which might create structural
vibrations, acoustic noise or resonance (Williamson, 1996). The frequency of the
shedding of vortices is known as shedding frequency and denoted as fs. The non-
dimensional shedding frequency was given by Strouhal (1878) and it is known as
Strouhal number St. (St = (fs*d) / U, where d is the diameter of the cylinder and U is the
free stream velocity) and the fundamental Strouhal number, St0 ~ 0.2 (Strouhal, 1878).
Interestingly these pressure fluctuations have a special significance in engineering
applications due to the fluctuating side force it creates and the correlation it has with the
shedding frequency. Particularly, its relation with Reynolds number is studied in various
papers to understand the behavior of flow in different shedding regimes ie., laminar,
transition and turbulent. In recent years there has been an advancement understanding of
the features of the wake. Figure 2.3 shows the general aspects of the flow over circular
cylinder. The following section presents the findings of different shedding regimes and
also understanding of the 3 instabilities are presented.
Figure 2.2: Streamlined & bluff body flow
Streamlined Body Flow without Separation
(A)
Bluff Body Flow with Separation and Wake
(B)
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Source: John, Wind Engineering, Flow around bluff bodies – Lecture Notes
2.2.3. Vortex shedding Regimes:
The vortex shedding can be categorized as laminar shedding, transitional and
finally turbulent shedding. The shedding is laminar initially when the Reynolds number
is low. As the Reynolds number increases the laminar shedding moves to a transitional
phase and finally becomes turbulent when the Reynolds number becomes high. Roshko
(1954) investigated the development of wakes from vortex streets and his findings show
that the vortex street is developed only after Re > 40, and it is stable and regular for Re
< 150, with velocity fluctuation in this range around Re ~ 80. Roshko (1954) presented
from his experiments, that for Re < 40 a pair of standing vortices is present behind the
cylinder and the flow around the cylinder has a symmetric, viscous configuration and at
Re = 40 it loses the symmetric configuration and forms a stable street with alternate
breaking away from the surface. Norberg’s (1994) experiments show the onset of
vortex shedding begins at Reynolds number (Re) ~ 47 and the flow is very steady with
symmetric vortices along the span of the cylinder. This onset is a manifestation of a
Hopf bifurcation (Provansal et al. 1987). For Re > 47, although the shedding remains
laminar, the flow becomes unsteady and asymmetric. The shedding is laminar and 2D
till Re ~ 190.
Figure 2.3: Flow over a circular cylinder
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Roshko (1954) showed that 150 ≤ Re ≤ 300 is the transition range. The
transition from laminar to turbulent is believed to occur always in the free vortex layer,
and hence the circulating fluid becomes turbulent before it breaks away. Thus each
vortex passing downstream is composed of turbulent fluid. This is shown in figure 2.4.
For Re > 190, a series of complex 3D instabilities appear in the wake. These
instabilities can be in the form of vortex loops, deformation of primary vortices, and
formation of streamwise and spanwise vortices. This is the beginning of the transition
regime. Norberg (2000) presents this transition as 2D to A* and from A* to B. Where,
A* mode is highly disturbed flow state which has characteristics of both mode A
(declining phase which stabilization in near-wake vortex shedding) and large scale
dislocations (Williamson, 1992). During this transition phase the spanwise correlation
of velocity fluctuation decreases dramatically along with decrease in shedding
frequency and associated spectral quality (Williamson, 1996).
Source: Roshko(1954)
Mode A* exists between Re ~190 to 230 (Norberg, 2000). Mode B instability
starts at Re~230. Mode B instabilities involves the formation of vortices that have a rib-
like streamwise flow. This mode is dominated with 3D wake features and spanwise
correlation is expected to increase with increase in Reynolds number and side force
coefficient also continues to increase (Zhang et al, 1995). The simulation by Zhang et al
showed that the local maximum side force, expressed in terms of lift coefficient, CL
occurs at Re~260. This correlates to the point where there is peak in base suction as
shown in figure 2.5 (see also figure 2.8). The graph of base suction pressure and
Reynolds number shows this peak at Re~260 and has been presented by Willamson &
Roshko (1990), Norberg (1987), Bearman (1969), Flaschbart (1932), Shih et al (1992)
& Henderson (1995) in literature. This point also coincides with the point of re-
introduction of high spectral quality of the shedding frequency at Re ~ 260.
Figure 2.4: Transition from laminar to turbulent
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Source: Williamson (1996)
For Re > 260, the transition to turbulent shedding starts and the transition
happens within the range of Re ~260 to 300 (Norberg, 2000).Williamsons’s (1996) and
Morkovin’s (1964) experiments presented that at such small Reynolds number the wake
transition appear to be linked to multiple and strongly interacting wake instabilities. As
Reynolds number increases the transition appears to be quicker and more distinctive
(Norberg, 2000). As the Reynolds number increases further the shear layer separation
from upper and lower surface of the cylinder starts becoming unstable via the Kelvin-
Helmholtz mode of instability, point where any separated layer becomes unstable. The
boundary layer becomes turbulent and causes substantial reduction in drag forces
experienced by the cylinder. This is shown in figure 2.6.
Figure 2.5: Plot of base suction coefficients (-Cpb) over a large range of Reynolds numbers
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There is an interaction between shear layer vortices and boundary layer vortices.
Furthermore, when Re > 2 x 105, the boundary layer on the surface of the cylinder
undergoes transition from laminar to turbulent. After this point the flow remains
turbulent. Roshko (1954) calls 300 ≤ Re ≤ 10,000+ as the irregular range, and in this
region the downstream flow which consists of turbulent fluid, the vortices diffuses
rapidly as they move forward and soon get annihilated, and hence no evidence of
shedding frequency remains. Figure 2.7 shows visualization of laminar and turbulent
vortex streets at different Reynolds number. The following section presents the
characteristics of side force and spanwise coefficients with Reynolds number which
provides us with further understanding of mode transition to turbulent flow.
Source: Singh & Mittal (2004)
Figure 2.6: Plot of drag coefficients (-Cd) over a large range of Reynolds numbers
Drag Crisis
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Source: Williamson (1996)
Figure 2.7: Visualization of laminar and turbulent vortex streets. These
photographs show the development of Karman vortex streets over a wide range of
Re
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2.2.4. Fluctuating side force and spanwise correlation scales on a cylinder:
The pressure fluctuations around the surface of the cylinder creates a fluctuating
side force and Norberg (2003) conducted experiments to measure pressure around the
circumference of cylinder and estimated sectional r.m.s side force coefficients at
different Reynolds number using a technique based on the integration of pressure
around the circumference of the cylinder. The range of Re was from 0.7 x 103 to 2.1 x
105. The experiments showed that there was a 10-fold increase in sectional r.m.s
coefficient (from CL = 0.045 to 0.47) in the range of Re ~ 1.6 x 103 to 20 x 10
3. Also the
maximum sectional r.m.s side force coefficient (CL = 0.52) occurred at the upper end of
the tested Reynolds number range. Along with the side force coefficients a spanwise
correlation coefficients were also measured, based on near-cylinder velocity fluctuations
just outside the separated shear layers within the range of Re ~ 75 x 103 to 0.23 x 10
5. It
was found out that at the onset of mode B instability (Re ~ 230) the spanwise
correlation length is about the twice the wavelength of most unstable mode A instability
ie., Ʌ/d ~ 7. The spanwise correlation increases dramatically with maximum peak value
being Ʌ/d ~ 30 and keeps increasing up to Re ~ 300. Then there is a gradual decrease in
spanwise correlation length with increase in Reynolds number, apart from a local
maximum of Ʌ/d ~ 15 at Re ~ 5.1 x 103. Figures 2.8 and 2.9 shows the graph of side
force and spanwise correlation coefficient with Reynolds number respectively. The
experiment conducted by Norberg (2003) provided further evidence for a fundamental
change in shedding mode from high quality to low quality mode of turbulent shedding
ie,. Re ~ 5 x 103 and 8 x 10
3 respectively.
Recent studies have uncovered 3D vortex dynamics phenomena in low Reynolds
number flows. However, how these features are carried forward when there is increase
in Reynolds number is yet to be precisely understood. The effects of these 3D features
on steady and unsteady fluid forces on a cylinder are not very clear. The precise origins
of mode A and B instabilities are unknown also under what particular conditions they
are formed are yet to be answered.
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Source: Norberg (2003)
Figure 2.8: Plot of side force coefficients (-CL) over a large range of Reynolds numbers
Figure 2.9: Plot of Normalized spanwise correlation length over a range of Reynolds
numbers
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2.3. Circumstances leading to the project & Research Gap:
This section presents the circumstances that are leading to the existence of this
project and it covers the bluff body noise prediction process and review of pressure
measurement process.
2.3.1 Bluff Body Noise Prediction – Aeolian Tones:
Aeolian tones are common in bluff body flows. These are created by the fluctuating
surface pressure caused by the von Karman vortex street. Doolan (2010) has presented a
new method for calculating the aerodynamic noise generated by bluff bodies. The
method presented uses 2D - Unsteady Reynolds Averaged Navier Stokes (URANS)
turbulent flow simulations to calculate the acoustic source terms. The method presented
uses statistical method to account for turbulent flow effects that are not accounted in
flow simulations. This statistical approach was used to introduce narrow band random
noise and Carle’s compact acoustic analogy was used to calculate far field noise.
Doolan (2010) presented URANS as a hybrid model to measure acoustic terms which
was more efficient and effective than Large Eddy Simulation (LES) and Direct
Numerical Simulation (DNS).
The superimposed 3D fluctuations are present in a turbulent flow stream forms
an acoustic signature as a spectral broadening of the Aeolian tone and its harmonics
(Doolan, 2010). This spectral broadening is mainly due to two effects – Temporal
beating and spanwise de-correlation of surface pressure (Norberg, 2003). The effect of
temporal beating is studied using the temporal statistical model which contains the
equivalent information of narrow band random noise signal. The temporal statistical
model uses the URANS force signal as an input. This model has a time scale parameter
τc that describes the random noise in the fluctuating force signal. The analytical
properties of this time scale parameter are the same as the properties of the narrow band
noise function which is actually an exponential decaying sinusoid (Bendat, 2000). The
autocorrelation function found for this model is also a decaying sinusoid (Doolan,
2010). This time scale associated with this decay needs to be estimated in order to
account for turbulence effects. Appropriate experimental or numerical data that can be
used to estimate the decay rate are not present in the literature. However, this parameter
has been estimated as a function of vortex shedding period (T) at a particular Reynolds
number (Doolan, 2010). This estimation is limited to a single set of data available in the
literature (Norberg, 2003). The final results presented by Doolan (2010) showed that a
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statistical method was able to introduce the narrow band random noise effects and the
technique could be used to calculate far-field aerodynamic noise. However, in order to
calculate noise using a non-compact acoustic analogy a statistical correction to
individual surface pressure signals is necessary. The temporal statistical model, by
Doolan (2010), used for the statistical correction is presented in section 2.3.2 below.
2.3.2. Temporal Statistical Model (Doolan, 2010) - (Theory):
The temporal statistical model is used to create a transient force record for a
compact cylinder in a turbulent flow that is similar to an experimental signal in
statistical terms. Hence the aim is to model a signal which will have the same statistical
properties when compared with the true experimental signal. As mentioned earlier, the
temporal statistical model uses the URANS force signal as an input. Now taking
average of N tonal URANS records, each with a random phase shift, we get
(1)
Where,
FT is the ‘‘true” signal that contains the correct statistical properties
FU is the simulated URANS signal
ɸi is the random phase shift of the ith record of which there are N in total
B is a parameter that ensures that the energy (or rms) of each signal is identical
The tonal URANS signal is given by,
(2)
By substituting (2) in (1) and simplifying, we get
(3)
Where, C = AB. Taking the limit N infinity, Eq. 3 becomes
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(4)
Where, Ɛ[x] is the mean or expected value of x.
Now taking the real component, we get,
(5)
Assuming the phase has Gaussian statistics, its probability density function P(ɸ) is
given as,
(6)
Where, σ(t) is the standard deviation. Hence, using the standard statistical theory,
(7)
By substituting the (7) in (5), we get
(8)
The true signal is a product of the cosine function, which represents the pure tone and
the exponentially decaying function represents the random noise signal due to
turbulence. This decaying function is dependent on a distribution of variance σ(t)2 with
time. The true signal de-correlates with time. The true signal depends on the variance,
which can be modelled based on analysis of literature. The variance can be modelled in
two ways.
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Model 1:
(9)
(10)
Model 2:
(11)
(12)
It can be shown that the true signal has the same statistical properties as a narrow
band random noise by computing the autocorrelation function of the true signal. It has
been found out that the autocorrelation function of the true signal is actually an
exponentially decaying function (Doolan, 2010), which is the correct form for narrow
band random noise (Bendat, 2000). Thus we can conclude that equation (10) & (12)
introduces narrow band random noise into the signal and is evident that it’s controlled
by a single time scale parameter τc. The FFT of autocorrelation function gives us the
spectral density. Now by multiplying a tonal signal by a decaying exponential with the
correct decay rate will produce a power spectrum identical to an experimental record
that contains narrow band random noise. This can be used for further analysis. The
following section will review the pressure measurement methods which will be used in our
project.
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2.3.3. Review of Pressure Measurement Methods:
Several pressure measurement techniques are presented in the literature. Norberg (2003) has
presented several pressure measurement techniques (ring of pressure taps, segmented pneumatic
averages, cross correlation method & distribution of r.m.s pressures with one transducer and
two transducers) to measure the pressure and in-turn calculate the side force coefficient. Ring of
pressure taps method is based on measurement of wall pressures at multiple positions around a
single cross section (circumference) of the cylinder. Other methods are related to the surface
pressure measurements at different points along the length of the cylinder and then averaged to
get the final pressure. The aim of the project is to measure the pressure at the centre of the
cylinder, measuring away from the cylinder brings in end wall effects. Hence other methods are
not helpful in our case. Ring of pressure taps best suits our requirement, thus other methods will
not be reviewed further. The ring of pressure taps method was first adapted by Drescher (1956)
with a set of 12 taps on the circumference of the cylinder. Later on Mohr (1981), Tunstall
(1970), Van Nunen et al (1972), West and Apelt (1997), Norberg (2003) & Ackerman et al
(2009) used the ring of pressure method but the number of pressure taps around the
circumference of the cylinder varied.
Unfortunately, the design of the experimental set up to measure pressure was not presented
in the literature by Drescher (1956), Mohr (1981), Tunstall (1970) & Van Nunen et al (1972).
On the other hand, West and Apelt (1997) used miniature transducers mounted below the
surface of the cylinder. The transducers had a tapping size of 0.6mm diameter and 1.5mm
length. Ackerman et al (2009) used a single 0.062 inches diameter kulite 25D ultra-miniature
pressure transducers with the B screen (pressure sensing surface) was flush with the cylinder
surface at the midspan. Ackerman et al (2009) performed second set of experiments with same
category of transducers but with a different diameter (0.093 inches) and 4 sets of transducers.
All the pressure measurement experiments presented in the literature were used to calculate lift
coefficients. However, in this project the objective is different. Norberg (2003) presented the
pressure measurement results in the form of graph of pressure vs time, shown in figure 2.10
below. Goldstein (1996) has presented several methods of fluid mechanics measurement, of
which, a measurement technique of cavity mounted transducer, with a pin hole leading from the
surface to the cavity is best suited for our application. Using the available literature as a basis
for our design and coupling it with the Goldstein’s fluid mechanics measurement, there is a
need to design experimental setup for the project application which forms another objective of
the project. Figure 2.11 shows the cavity mounted technique with the pin hole leading from the
surface to the cavity. The design of the experimental setup using this technique is presented in
detail in chapter 4 of this report.
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Source: Norberg (2003)
Source: Goldstein (1996)
Figure 2.10: Plot of pressure vs frequency. Data plotted using ring of pressure taps
method numbers
Figure 2.11: Cavity mounted technique with the pin hole leading from the surface to the cavity
Cavity
Pin Hole
Uc - is the flow velocity
λ – is the wavelength
d1 – is the characteristic
dimension
d – is the transducer
dimension
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2.4 Summary:
In summary, the bluff bodies produce unwanted noise when placed in a fluid
stream, and considering their presence in many engineering situations there is a need to
understand their behaviour when the flow is turbulent. Furthermore, there is a need to
estimate the effect of flow turbulence to calculate the noise generated. The bluff body
flows were discussed and a circular cylinder was considered as a representation of a
bluff body in general. The study of flow over circular cylinder showed that, in a cross
flow there is a vortex shedding process and this process creates a fluctuating pressure
forces around the cylinder. The non dimensional shedding frequency is given by
Strouhal number and the fundamental Strouhal number Sto ~ 0.2.
The shedding frequency and the pressure forces are related and its relation with
the Reynolds number is studied to comprehend the flow in different laminar, transition
and turbulent shedding regimes. The study of flow over the cylinder in different vortex
shedding regimes showed that on set of vortex shedding happens between Re ~ 40 to 47
and stays laminar in the range of Re ~ 150 to 190. The transition from laminar to
turbulent happens in the range of Re~ 190 to Re ~ 300. Transition occurs from 2D to
mode A* (having large scale dislocations) and then to mode B (formation of vortices
with rib like structures). The transition from laminar to turbulent is believed to occur
always in the free vortex layer, and hence the circulating fluid becomes turbulent before
it breaks away. Finally the turbulent regime starts in the range of Re ~ 260 to 300. The
vortices diffuse rapidly as they move downstream and soon get obliterated. The precise
origins of these modes are yet to be uncovered.
The study of bluff body noise prediction showed that Direct Numerical
Simulation (DNS) of the Navier Strokes Equation may be used to calculate the
turbulence and acoustic information, but is limited for low Reynolds number flows.
Large Eddy Simulations is used for turbulent flows, however they are computationally
expensive. Doolan’s (2010) hybrid model uses 2D-URANS model to calculate the far
field noise and to account for turbulent flow effects, a temporal statistical model is used.
However, the time scale parameter τc , which introduces the turbulent effects in the
narrow band random noise is unknown and has to be estimated. There is very little
experimental or numerical data available on this parameter. The research gaps from the
literature review are transformed into objectives of the project which is presented in
detail in chapter 3.
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Chapter 3 – Project Objectives and Tasks in the project:
This chapter lists the objectives of the project and the individual tasks that link
to the project objectives.
3.1 Project Objectives: The objectives of the project are summarized below from the literature review:
1. Design of a experimental set up to perform a wind tunnel test that will
measure the unsteady transient pressure on the surface of a circular cylinder
in cross flow.
2. Conduct the experiment to record the transient pressure data in a turbulent
flow over the surface of the circular cylinder.
3. Perform a statistical analysis on the data from the experiment to
experimentally determine the value of the time scale parameter τc. as defined
in the model of Doolan (2010).
4. Investigate the wall pressure data to attempt to shed new insights into the
turbulent flow behavior.
The design of the experimental setup is presented in chapter 4 of this report. The
methods and techniques used in the statistical analysis are presented in the chapter 5 of
this report.
3.2 Project Tasks:
The table 3.1 below shows the individual tasks that links to the project objectives.
The schedule for the tasks is presented in chapter 7 of this report.
Table 3.1
Projective objective Project Tasks
1. Design of the
experimental set up
1. Review of the requirements
2. Generate design concepts as per requirements
3. List out all pros and cons of the concepts
4. Draw conclusion and freeze on a particular design
5. Create 3D model as per the design
6. Generate 2D manufacturing drawings
7. Review of the drawings with supervisor and workshop
8. Submission of drawings for manufacturing
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2. Conducting the
Experiment to obtain
the transient pressure
data
1. Inspection of the manufactured experimental rig
2. Calibration of the microphone and obtain its sensitivity
3. Integration of the experimental rig with the wind tunnel,
power source, DAQ and computer
4. Testing the experimental set up
5. Recording the temperature, velocity and pressure of the
fluid flow
6. Work out the density of the air
7. Conducting the experiment and recording the transient
pressure data
8. Repeat the experiment with microphone at several
location along the circumference of the cylinder
9. Tabulate the results
3.Analysis of the results
1. Review of the data – check if data is a random data of
voltage of time
2. Covert the voltage to sound pressure level using the
sensitivity
3. Find out the probability density function and analyze the
data in the amplitude domain
4. Find out the autocorrelation function and analyze the
data in the time domain
5. Create the auto-spectrum of the data, which gives you
the frequencies over the entire time domain
6. Find out the spectrogram of the data
7. Plot the power spectral density for the experimental data
8. Use the transient force signal presented in the temporal
statistical model and simulate the power spectral density
with different values of time scale parameter τc, and see
which value of τc fits the curve with the experimental
data, and there by finding out the experimental value of
τc .
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Chapter 4 – Design of the Experimental Setup:
This chapter outlines the design process used to create the experimental setup.
The design process has been categorized into two parts. The first part will explain the
design methodology. The second part will explain the design of the overall experiment
which integrates the rig, wind tunnel and the computing system.
4.1 Design of the experimental rig:
The experimental rig is designed to measure the transient pressure on the surface of
the circular cylinder.
From the wind tunnel specifications and experimental requirements the following
design inputs are obtained:
1. Diameter of the cylinder, D = 40mm.
2. Length of the cylinder, Lcyl = 450mm.
3. Wind Speed, U ~ 6 m/s (approximately)
From the literature review and project objectives the following design inputs are
obtained:
1. Cavity mounted technique will be used with one tap at the center of the cylinder
and below its surface to measure the noise generated when placed in a wind
tunnel.
2. The non-dimensional shedding frequency, the fundamental Strouhal number is,
St ~ 0.2
3. Tap dimensions are taken from West and Apelt (1997), with hole diameter of
0.6mm and depth of 1.5mm. These values are acceptable for this application, as
the resonance frequency with these dimensions is much greater than the
shedding frequency. The calculation is shown below. Figure 4.1 shows us the
tapping.
Resonance frequency, 𝑓𝑜 = 𝐶/𝜆𝑜,
Where, C is speed of sound = 343 m/s
𝜆𝑜 is fundamental wavelength
Length of the tap column, L = 𝜆𝑜/4 = 1.5mm
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Diameter of the tap, D = 𝜆𝑜/2 = 0.6mm
Therefore,
𝑓𝑜 = 343/4 ∗ 0.0015 = 5716.66 Hz (considering L as characteristic length)
𝑓𝑜 = 343/4 ∗ 0.0006 = 142916.66 Hz (considering D as characteristic length)
Shedding frequency,
𝑓𝑠 = 𝑆𝑡 ∗ 𝑈/𝐷 = 0.2 ∗ 6/0.04 = 30 Hz
Therefore,
𝑓𝑜 = 190.55 𝑓𝑠 (considering L as characteristic length)
𝑓𝑜 = 4763.88 𝑓𝑠 (considering D as characteristic length)
In both the cases the resonance frequency is more than 10 times the shedding frequency
which is acceptable.
4.1.1. Concept Generation – Placing the microphone inside the cylinder:
The design inputs were used to generate three concepts. The cylinder is divided
into three segments as shown in figure 4.2, in the isometric view. The centre segment is
called an insert and it holds the microphone. The other two segments are symmetrical
pieces of the cylinder. The three concepts are discussed in detail below.
Concept 1: The tapping is made right below the surface of the cylinder and the
microphone is fitted into it with a tight fit. The sensitive surface of the microphone is
flush with the bottom surface of 0.6mm diameter tapping. This concept can be seen in
figure 4.2. The advantages and disadvantages of this concept are listed below.
Figure 4.1: Tapping with the microphone, cavity and pin hole
Microphone Cavity
Pin Hole Cylinder
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Advantages:
The concept is very simple and easy in terms of design
Disadvantages:
Mounting and dismounting the microphone in the hole is difficult
Manufacturing the insert is complicated, because of the internal drilling
operation
Concept 2: The tapping is made right on the surface of the cylinder at its centre. The
microphone is mounted onto an insert piece which is manufactured separately, with a
hole to mount the microphone and a pin hole for the tapping. Initially the microphone is
mounted on to the insert piece and then the wire is taken out from a hole that is made in
the insert as shown in the cut section of figure 4.3. Now the insert piece looks like a
small cylinder, which goes into the insert hole that was initially made right on the
surface of the cylinder. The microphone’s base surface rests on the base of the insert
hole. The insert and insert piece have a tight fit. This concept is shown in figure 4.3.
The advantages and disadvantages of this concept are listed below.
Advantages:
The concept is very simple and easy in terms of design
Mounting and dismounting the microphone in the hole is easy
Disadvantages:
Manufacturing the insert piece is difficult. The reason being the top surface of
the insert piece should accurately follow the curvature of the cylinder.
Removing the insert piece from the insert hole is difficult.
Insert
Cylinder
Microphone
Figure 4.2: Isometric view and cut section along the axis of the cylinder with the microphone
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Concept 3: This is very similar to the concept 2 except for the design of the insert
piece. The insert piece is a small section of the cylinder and along the circumference of
the cylinder’s cross section. This is shown in figure 4.4, section along the circumference
of the cylinder at the centre. The insert piece is mounted onto the insert using the
locater pins (silver steel pins), thus holding the insert and insert piece in place without
the necessity of interference fit. This will facilitate easy mounting and dismounting of
insert piece and microphone. The microphone is held in position with the help of grub
screws. This concept is shown in figure 4.4(A) & (B). The advantages and
disadvantages of this concept are listed below.
Advantages:
Manufacturing the insert piece is relatively easy.
Mounting and dismounting the insert piece and microphone is easy.
Disadvantages:
Number of components have increased because of the addition of grub screws
and silver steel pins
Insert
Insert Piece
Figure 4.3: Isometric view and cut section along the axis of the cylinder with the insert piece & microphone
Figure 4.4(A): Isometric view
(A)
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Concept 3 is used in this project, because it has evolved from concepts 1 and 2 and is
better in terms of achieving the objective of mounting and dismounting of the
microphone from the cylinder.
4.1.2. Concept Generation – Assembly of the rig:
This section presents the ways in which each individual components of the rig
are assembled and their material specifications. The individual components include the
cylinder, insert, insert piece, end caps, end plates and the microphone. The design of the
interface between the components is presented below.
Cylinder and Insert:
The assembly of the cylinder and the insert can be done in several ways. Both
cylinder and insert is made out of aluminium. The following options were considered.
Gluing, interference fit and threaded join. Gluing was the simplest option, however
gluing will make the assembly a permanent fix which was not desired and hence ruled
out. Interference fit was a feasible option, but had few disadvantages, frequent
dismantling was difficult and butting at the ends was not very accurate. Finally the
threaded join option was considered as the most feasible option to assemble the insert
with the cylinder because the process of assembly and dismantling is very easy.
Furthermore, butting was accurate and the manufacturing standards were readily
available. The assembly is shown for all cases in figure 4.5. Two pieces of a standard
40mmX3mm aluminium tube were used as raw material and the insert was machined
from a 40mm diameter aluminium bar.
Silver Steel Pin
Insert
Insert Piece
Grub Screw
Insert Piece
Figure 4.4(B): Isometric view and cut section along the circumference & axis of the cylinder at the center
with the insert piece, grub screws, silver steel pins & microphone
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Insert , Insert piece & Microphone:
The assembly concept of insert, insert piece and microphone is taken from
concept3 of section 4.1.1 (Also refer figure 4.4). The insert piece is made out of PMMA
material and microphone is a standard 1208 measurement type microphone. Figure 4.6
shows the assembly of insert, insert piece and microphone. Silver steel pins are fixed
permanently in the insert by strong interference fit. The pins are reamed at the top so
that they could be a good fit between the pins and the hole in insert piece, and later on
could be removed with some force. The microphone is held exactly in the center of the
hole with the help of 2 grub screws as shown in the figure 4.6.
Assembly using glue Assembly using interference fit
Assembly using thread run out
Insert
Thread run out
Cylinder
Figure 4.5: Cut section along the axis of the cylinder showing assembly of cylinder and insert
Figure 4.6: Cut section along the circumference of the cylinder showing assembly of
insert, insert piece and microphone
Insert Piece
Microphone
Grub Screw Silver Steel Pin
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Cylinder, End caps & End Plates:
The assembly between cylinder and the end cap is done with the help of simple
grub screw. The end cap is made out of 40mm standard aluminium bar. The end cap and
cylinder has a through hole for the grub screw. The assembly is shown in figure 4.7.
The assembly of end cap and end plate is done using a simple nut and bolt mechanism.
The end plate is an integral part of wind tunnel fixture which is made up of PMMA. The
bolt has a hole which is a provision for microphone wire to come out of the assembly.
The end cap has a clearance hole for the bolt. The assembly is shown in the figure 4.7.
All the concepts generated during the design phase are shown above. The design
dimensions are adapted to best fit the application and also dependent on the interfacing
component. The complete set of mechanical part drawings, assembly drawings and
manufacturing drawings is shown in the appendix c at the end of this report.
End Cap
Cylinder
Grub Screw
End Plate Bolt with a hole
End Cap
Figure 4.7: Cut section along the axis of the cylinder showing assembly of cylinder, end
cap and end plate
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4.2 Experimental Design - Integration:
This section will detail out the design of the whole set up which integrates the
rig and the wind tunnel. Furthermore, this section will explain the experimental
methodology.
The cylinder assembly with the microphone is mounted in the wind tunnel such
that the cross flow over the cylinder surface is achieved. The microphone is connected
to a power source, which in turn is connected to a single channel data acquisition
system. Computer is used to record the data and compute the results. The experimental
set up is shown in figure 4.8. The experiment methodology is explained below.
A pitot tube is placed within the wind tunnel to measure the velocity of the flow.
A thermometer is used to record the temperature of the air. Using the ambient air
pressure and temperature, the density of the air can be readily calculated. Now the
cylinder assembly is rotated such that the microphone is in line with the flow. When the
wind starts flowing in a cross flow over the surface of the cylinder it generates wall
pressure fluctuations. The microphone is designed to give an output of voltage with
time when connected with the power source. Before placing this microphone in the
assembly it is calibrated to obtain its sensitivity so as to provide the readings in Pascal
which is the measure of pressure that is required. The experiment is repeated with
placing the microphone at different angles along the circumference of the cylinder and
the flow is kept constant. All the data is recorded and tabulated. Figure 4.9 shows the
locations of the microphone along the circumference of the cylinder. The parameter θ
can be used to define the location of the tap, with θ = 00 being flow parallel to the tap.
Then θ increases in steps of 30 degrees clockwise. The post processing of the data is
presented in detail in chapter 5 of this report.
Note: θ = 00, positions the microphone at the approximate stagnation point on the
cylinder.
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Figure 4.8: Experimental Set up showing the cylinder assembly in a cross flow in a wind tunnel
Figure 4.9: Experimental cases showing the position of the tap in a cross flow of a wind tunnel
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Chapter 5 – Post Processing Methods and Techniques:
This chapter will brief the methods that are used to perform analysis of the
results. This includes the readings that are taken before the experiment, during the
experiment and post processing of the results to achieve the set objectives. Furthermore,
it sets out the tabular format used for the data recorded as well as various methods and
techniques used for the post processing.
5.1 Readings before the experiment:
The control dial of the wind tunnel is set to the required RPM such that a
required velocity is achieved. However, the actual velocity has to be measure from the
flow using a pitot tube. Using the Pitot tube the pressure reading is taken and using the
thermometer temperature reading is taken. The diameter and the length of the cylinder
are known. The microphone will be calibrated to give output in volts which will be a
measure of pressure in Pascal and sensitivity will be recorded. The readings are
tabulated as shown in table 5.1 below.
Table 5.1
Serial Number Parameter Recorded Values
1 Sensitivity from calibration
of the microphone
2 Pressure reading from pitot
tube
3 Temperature reading from
the thermometer
4 Diameter of Cylinder D = 40 mm
5 Length of the cylinder Lcyl = 450 mm
6 Aspect Ratio =
Using the values recorded the following calculations can be made and presented below.
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5.1.1 Flow Velocity Calculations:
The following steps are used to calculate the flow velocity.
Step1: Calculation of air density
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝒂𝒊𝒓 𝒂𝒕 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 𝑻, 𝜌 =𝑚 𝑃
𝑛 𝑅 𝑇 𝐾𝑔/𝑚3
𝑤𝑒𝑟𝑒,
𝑚 𝑖𝑠 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 = 28.97 𝑘𝑔 𝑎𝑡 1000 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑑𝑟𝑦 𝑎𝑖𝑟
𝑛 𝑖𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠
𝑅 𝑖𝑠 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑎𝑙 𝑔𝑎𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 8.3145 𝐽/𝑘.𝑚𝑜𝑙
𝑇𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝜌 =28.97 ∗ 𝑃
1000 ∗ 8.3145 ∗ 𝑇 𝐾𝑔/𝑚3
𝑇𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝜌 = 0.0034848 ∗ 𝑃
𝑇 𝐾𝑔/𝑚3
Using the recorded results from table 5.1, the density of air can be calculated.
Step 2: Calculation of velocity
We have,
𝑻𝒉𝒆 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒕𝒊𝒂𝒍 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 𝒊𝒏 𝒑𝒊𝒕𝒐𝒕 𝒕𝒖𝒃𝒆,
Therefore,
𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚, m/s
The Pitot tube gives us ΔP, hence
m/s
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5.1.2 Reynolds Number and Dynamic Pressure Calculations:
𝑹𝒆𝒚𝒏𝒐𝒍𝒅𝒔 𝑵𝒖𝒎𝒃𝒆𝒓,
Where,
𝜇 𝑖𝑠 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑜𝑓 𝑎𝑖𝑟 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇
𝐷 𝑖𝑠 𝑡𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑒 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟
𝑫𝒚𝒏𝒂𝒎𝒊𝒄 𝑷𝒓𝒆𝒔𝒔𝒖𝒓𝒆, 𝑄 =1
2 𝜌 𝑉2 𝑃𝑎
The readings are tabulated as shown below in table 5.2.
Table 5.2
Serial Number Parameter Calculated Values
1 Density of the air 𝜌 = 𝐾𝑔/𝑚3
2 Velocity of the flow V = m/s
3 Reynolds Number Re =
4 Dynamic Pressure PDyn =
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5.2 Readings during the experiment:
The experiment is conducted as per the procedure described in section 4.2 of this
report. The transient pressure data is recorded for a period of two minutes at a sampling
rate of 2048 Hz at all angle of θ (see figure 4.9 for details). The output will be a graph
of voltage vs time. The X (time in seconds) and Y (pressure in Pascals) coordinates are
exported and tabulated in an excel sheet. The tabular column used in the experiment is
shown in table 5.3. The voltage can be converted to Pascal, which is the measure of
sound. Also, this can be converted to dB. The following calculations are made.
5.2.1 Strouhal Number, Shedding period, Shedding Frequency Calculation:
𝑺𝒉𝒆𝒅𝒅𝒊𝒏𝒈 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 , fs is an output from the experiment
The extraction of the parameter fs in explained in detail in section 5.3 of this report
𝑽𝒐𝒓𝒕𝒆𝒙 𝑺𝒉𝒆𝒅𝒅𝒊𝒏𝒈 𝑷𝒆𝒓𝒊𝒐𝒅 , Seconds
𝑺𝒕𝒓𝒐𝒖𝒉𝒂𝒍 𝑵𝒖𝒎𝒃𝒆𝒓,
Where,
D and V are cylinder diameter and flow velocity respectively
5.2.2 Pressure Calculations:
𝑷𝒓𝒆𝒔𝒔𝒖𝒓𝒆 𝒊𝒏 𝑺𝑷𝑳 , P = V * S
Where,
V is flow velocity in m/s and S is the sensitivity of the microphone
𝑷𝒓𝒆𝒔𝒔𝒖𝒓𝒆 𝒊𝒏 𝒅𝑩 , dB = 20 Log10(Prms/Pref)
Where,
Pref = 2*10-5
Pa
The experiment data and the calculated results are tabulated as shown below in table 5.3
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Table 5.3
Time (seconds) Voltage (volts) Sound Pressure Level (Pa) Sound in dB
0
to
120
Serial Number Parameter Calculated Values
1
Shedding
Frequency fs = Hz
2
Vortex Shedding
Period T = Seconds
3 Strouhal Number St =
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5.3 Post Processing of the Results:
This section details out the methodology used to represent data. This section focuses
mainly on methodology of two components – Results and Analysis.
5.3.1 Representation of the surface pressure data (Results):
The output data obtained is expected to be stationary and ergodic random process
of surface pressure as a function of time. In addition the experimental conditions are
kept very steady (constant temperature, pressure, velocity etc…) to ensure that the data
is stationary random data. The analysis of the stationary and ergodic random data can be
done by using the following statistical methods, each of these methods are described in
detail below.
1. Mean Square Values
2. Probability Density Functions
3. Autocorrelation Functions
4. Power Spectral Density
5. Spectrograms
Matlab is used to find out the mean square values, probability density functions,
autocorrelation functions, power spectral density and finally spectrogram of the data.
There is a need to filter the data, it is expected that the data recorded will contain noise
from the fan and the surroundings. These noises in general will have high frequencies.
The bluff body noise will have very low frequency which can be estimated by finding
the value of shedding frequency. The Matlab code used for analysis and plotting the
graphs for the data is presented in Appendix B of this report. The output graphs and
results can be represented in several ways. Chapter 6 details out the results in depth and
discussion of results are also presented there. Using the filtered data, the following
methodologies are used to interpret the results:
Time series is plotted and in depth analysis is made to see if there are any
patterns with the data and also compared with the literature.
The probability density functions of the data are found out. The Matlab
command ‘xcorr’ is used to do this and then the probability densities can be
worked out from the frequencies. Then the skewness and kurtosis of the density
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functions are determined. This shows the magnitude by which the data deviates
from the Gaussian distribution.
The autocorrelation functions are determined. The Matlab command ‘xcorr’ is
used to do this. This gives the dependency of the values of the data at one time
on the values at another time. In general the expected relation is such that the
pressure data becomes increasingly de-correlated with time.
The power spectral density plots are plotted and the frequency where the peak
occurs represents the shedding frequency fs. The Matlab command ‘pwelch’ is
used to do this. This value is then recorded and used to calculate the vortex
shedding period and Strouhal number as shown in section 5.2.1. This value is
also used to find out the time scale parameter τc.
Spectrograms are plotted to get time and frequency representation and perform
studies on spectral or frequency component occurring at any instant that is of
particular interest. The Matlab command ‘spectrogram’ is used to do this.
The following section presents the methodology used to find out time scale
parameter.
5.3.2 Curve fitting technique to find the value of τc (Analysis):
In order to use the right method to achieve our objective of finding the time scale
parameter τc, we need to study the output signal. Using the experimental results and the
filtered data, we can find out the power spectral density as mentioned in the previous
section, which gives us a plot of dB/Hz vs frequency for the filtered data. An expected
outcome or example of such a signal is shown below which is generated using a pwelch
command in matlab. This is shown in figure 5.1.
From literature study, we know that the 3D wake effect in the cylinder in a cross
flow is present in the surface pressure data that we measured in the form of acoustic
signature. We know that this acoustic signature is present as a spectral broadening of the
sound generated.
From literature we know that, the spectral broadening is made due to:
The first component is the amplitude modulation of the cylinder pressure surface
which occurs due to the vortex dislocation. Which we know is statistically
equivalent to a narrow band noise plus introduced into a sinusoidal function.
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Using Doolans (2010) temporal statistical model presented in section 2.3.2 of this
report, the true force signal shows both the tonal effect and the turbulent effects. The
effect due to turbulence is equivalent to a narrow band random noise signal. From
equation (10) and (12) of section 2.3.2, we have,
Model 1
Model 2
Figure 5.1: A sample plot of power spectral density for an experimental data
Statistical Correction
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The power spectral density function of the true signal for both the models is
simulated or generated for various values of τc to see which value best fits the spectral
density from the experimental results that is shown in figure 5.1. Thus, obtaining the
experimental value of the time scale parameter τc which was the desired objective of the
project. We then determine which model best fits our requirement. A sample figure of a
curve fitting technique is shown in figure 5.2 below.
Experimental Signal
Statistically Simulated
Figure 5.2: A sample plot of power spectral densities of an experimental and
statistically simulated signal using curve fitting technique
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Chapter 6 – Results and Analysis:
This chapter details out the results from the experiment and analysis of the
results to find out the experimental value of time scale parameter. The experiment is
conduced as per the procedure explained in section 4.2.
The transient pressure data is recorded for all tap angles (θ) (see figure 4.9 for
details). However, the data, results and analysis discussed in this chapter correspond to
and are limited to 4 angles (θ = 00, 90
0, 180
0, 270
0) of tap. For rest of the angles, the
data and results are available in the DVD that is attached to the end of the report.
Section 6.1 details out the results and calculation of the project and it exercises the
procedure detailed out in the sections 5.1, 5.2 and 5.3.1. Section 6.2 details out the
curve fitting technique and it exercises the procedure detailed out in section 5.3.2.
Furthermore the data is interpreted in a physical sense and the results are
compared with the available literature. The data obtained has both high and low
frequency noises in it. Using the ‘butterworth’ filter in Matlab the high frequency data
representing the noise from the motor and the surrounding environment are filtered out
and the noise (in the frequency range of 0 Hz to 100 Hz) from bluff body is allowed to
pass through the filter. This filtered data is used for all future purposes. The Matlab
code is presented in appendix B.
6.1 Project Results:
This section follows the procedure as presented in chapter 5. The results for the
readings before the experiment, during the experiment and post processing are
presented in detail and a brief discussion is also presented after each section.
6.1.1 Results - Readings before the experiment:
From section 5.1, the readings before the experiment are recorded and tabulated
below in table 6.1. The calculations of flow velocity and Reynolds number are also
shown below. The calculated results are also tabulated in table 6.2.
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Table 6.1
Serial Number Parameter Recorded Values
1 Sensitivity from calibration
of the microphone
2 Pressure reading from pitot
tube ΔP = 30 Pascals
3 Temperature reading from
the thermometer
4 Diameter of Cylinder D = 40 mm
5 Length of the cylinder Lcyl = 450 mm
6 Aspect Ratio =
The air density,
𝜌 = 0.0034848 ∗ 𝑃
𝑇 𝐾𝑔
𝑚3
𝜌 = 0.0034848 ∗ 101.3 ∗ exp 3
273 + 17.77 𝐾𝑔/𝑚3
𝜌 = 1.2141 𝐾𝑔/𝑚3
The flow velocity,
m/s
The Reynolds number,
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Table 6.2
Serial Number Parameter Calculated Values
1 Density of the air 𝜌 = 1.2141 𝐾𝑔/𝑚3
2 Velocity of the flow V = 7.03 m/s
3 Reynolds Number Re = 18554.6
4 Dynamic Pressure PDyn = 30 Pa
Discussion:
The results can be seen from table 6.1 and 6.2. The aspect ratio of the cylinder
was found out to be 11.25, which falls into a higher range (except for a few values) as
compared to the values of the aspect ratio presented by Norberg(2003) in the table 1 of
fluctuating lift on cylinder. The sensitivity of the microphone was calibrated and found
out to be 0.9164. Ideally the microphone should have sensitivity of 1 Pa/Volts. In
practical cases, there will be some losses in the transmission wire and also with the
microphone’s sensitive surface. To account for this, the recorded transient pressure data
was multiplied with the sensitivity of the microphone.
The control dial of the wind tunnel was set to a motor RPM such that the free
stream velocity of 6m/s (maximum output from the wind tunnel) could be achieved.
However, when more accurate measurements were made using a pitot tube, the free
stream velocity of the air was found out to be approximately ~ 7 m/s. The Pitot tube
measurement was made at the centre of the tunnel, in the uniform potential flow. The
Reynolds number was calculated and it is approximately ~ 18500. Comparing this value
with the literature review presented in chapter 2, it is clear that the flow falls in the
turbulent wake regime. Hence we have a turbulent flow. Therefore, it is possible to
investigate the surface pressure data over a circular cylinder in a turbulent flow.
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6.1.2 Results - Readings during the experiment:
From section 5.2, the readings and the calculations during the experiment are
recorded. The experimental data of pressure and time for all tap angles are presented in
the DVD that is attached at the end of the report. The calculations presented here are
only for 4 tap angles. The pictorial representation for the tap angles are shown in figure
6.1 below. The shedding frequency, vortex shedding period and Strouhal number
calculations are tabulated below in table 6.3. The shedding frequency is recorded from
the spectral density graph which is presented in section 6.1.3.4 of this report.
Table 6.3
Tap Angle θ
(Degrees)
Shedding
Frequency (Hz)
Vortex Shedding Period
(Seconds)
Strouhal Number
0 27.1250 0.0369 0.1543
90 27.3750 0.0365 0.1558
180 55.0000 0.0182 0.3129
270 27.5625 0.0363 0.1568
Figure 6.1: Experimental cases showing the position of the tap in a cross flow of a wind tunnel
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Discussion:
The results can be seen from table 6.3 above. The shedding frequencies for
different tap angles are shown and the frequencies are almost same for the tap angles 0,
90 and 270 degrees, the variation is less than 0.5%. The same holds good with the
vortex shedding period values and the Strouhal numbers for all 3 cases. The assumed
value of fundamental Strouhal number was 0.2. However, the calculated value is
approximately ~ 0.155, which is still reasonable as it lies in the actual range which is
between 0.1 and 0.2 and also consistent with Norbergs (2003) value of Strouhal
number, which is 0.194 for a Re ~ 20,000 and a 40mm diameter cylinder.
The difference in values of the shedding frequencies between the tap angle 90
and 180 is interesting. It is observed that the shedding frequency of tap angle 180
degree is approximately double the value at tap angle 90 degree, ie., fs180 ~ 2 * fs90. A
similar kind of observation with the shedding period shows that the shedding period of
tap angle 90 degree is approximately double the shedding period of 180 degree, ie., T90
~ 2 * T180 . The physical interpretation of such an observed phenomenon can be
described with the help of a vortex shedding in a cross flow figure (see figure 6.2). The
tap at 180 degrees reads the first shedding period time when the 1st vortex reaches point
A, by this time the second vortex is half its way through and hence by the time it
reaches point B, it records a time which is half the time as recorded by the tap at 90
degrees. The shedding frequencies get compounded as the tap is at 180 degrees along
the line of the flow as shown below.
A B
Flow
Figure 6.2: Cylinder in a Cross Flow showing Vortex Shedding Phenomenon
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6.1.3 Results – Representation of surface pressure data:
This section details out the experimental data and uses the statistical methods
discussed in section 5.3.1 to represent the recorded transient surface pressure data in a
more meaningful manner. This section is divided into 5 components.
1. Time Series (Mean Square Values) – Gives intensity of the data in general sense
2. Probability Density Functions – Gives the properties of the data in amplitude
domain
3. Auto Correlation Functions – Gives the properties of the data in time domain
4. Power Spectral Density – Gives the properties of the data in frequency domain
5. Spectrograms – Gives an understanding of the development of frequency with
time.
Furthermore the results are discussed in detail and compared with any available
literature. Each of the method mentioned above is described below.
6.1.3.1 Time Series:
The time series is the plot of recorded transient pressure vs time. The time series
for 4 different tap angles mentioned above are presented below. The recorded data is
very long (120 seconds) to present it in a single plot. Hence the series is broken down
and only first 30 seconds for each tap angle is presented below. The rest of the data is
available in the DVD attached with the report.
Time series for tap angle 0 degrees:
Figure 6.3: Transient pressure data (pressure vs time) for tap angle 0 degrees
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Time series for tap angle 90 degrees:
Time series for tap angle 180 degrees:
Figure 6.4: Transient pressure data (pressure vs time) for tap angle 90 degrees
Figure 6.5: Transient pressure data (pressure vs time) for tap angle 180 degrees
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Time series for tap angle 270 degrees:
Discussion:
The time series are shown in figure 6.3 through figure 6.6. From all the graphs,
by visual inspection the surface pressure data recorded is clearly stationary ergodic
random data. Additionally, the nature of the experiment doesn’t require the mechanism
of producing the data of interest (surface pressures) to be time dependent, also the
whole experiment was conducted in a steady environment. Hence we can conclude that
the data obtained is stationary and ergodic. Furthermore the intensity of the data reduces
with change in tap angle. It is lowest when the tap angle is 180 degrees, as seen in
figure 6.5.
Furthermore the pressure fluctuations reach a set of peak values and then
reduces in a cyclic pattern. This can be described as the temporal beating effect. It can
be seen that on an average for every one second there are 2 peaks and one off peak or
vice versa. By comparing the discussion from literature presented in section 2.1, we can
conclude that the spectral broadening of the noise is caused by this temporal beating
effect and it is equivalent to a narrow band random noise introduced into a sinusoidal
Figure 6.6: Transient pressure data (pressure vs time) for tap angle 270 degrees
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function. We can compare this theory with the experimental signal. Taking a closer look
at the graphs, it is evident (see figure 6.7) that the recorded random data contains some
sinusoidal behaviour but with some deviation. The deviation is caused due to turbulent
flow effects.
Bendat (2000) describes the parameters that are used to describe the random
data in a more physical sense. In general sense the intensity of a random data is given
by root mean square values. It is often desirable to think of a physical data in terms of
static or time invariant component and a fluctuation or dynamic component. The mean
of the data represents the static component where as the variance describes the dynamic
component. These parameters are calculated and tabulated below in table 6.4. The
Matlab code used to calculate these parameters are presented in appendix B of this
report. As mentioned earlier, the intensity of the data is ~ 85% less when the tap angle is
180 degrees when compared with the intensity of the data at 90 degree tap angle. The
mean or the static component of the data tends to be near zero as expected.
Figure 6.7: A closer look at the pressure data for tap angle 0 degrees
(4 sec-8sec) 25% zoom,(14 sec-16sec) 70% zoom, (24.1 sec-24.4sec) 95% zoom
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Table 6.4
Tap Angle θ
(Degrees)
Room Mean Square
Pressure (Pa)
Mean (μx)
0 0.1081 0.0081 * 10-5
90 0.2086 0.0251* 10-5
180 0.0331 0.0185* 10-5
270 0.1632 0.0115* 10-5
There are few time series data available in literature. The time series plot by
Norberg (2003) has a Reynolds number of 20,000 which is closer to the Reynolds
number used in the project, Re ~ 18,500. The cylinder diameters are the same for both
the cases. The time series plot is shown below in figure 6.8. It can be seen that, the
experimental data and the data as seen from the literature are similar in nature. The data
in the literature looks to be stationary and ergodic as it is the case with our experimental
data. The temporal beating effect is also evident and very similar to that of the
experimental data.
Source: Norberg (2003)
Figure 6.8: Time series plot of pressure vs frequency by Norberg (2003)
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6.1.3.2 Probability Density Functions (PDF):
PDF gives us the properties of the data in the amplitude domain. It is similar to a
histogram except that the frequencies are expressed in probability density terms. The
PDF plots of recorded transient surface pressure are presented below. The PDF for 4
different tap angles mentioned above are presented below. The rest of the results are
available in the DVD attached with the report. The histogram is also represented along
with the PDF plots.
PDF plot for tap angle 0 degrees:
Figure 6.9: PDF and histogram plot for tap angle 0 degrees
Gaussian
Curve
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PDF plot for tap angle 90 degrees:
PDF plot for tap angle 180 degrees:
Figure 6.10: PDF and histogram plot for tap angle 90 degrees
Figure 6.11: PDF and histogram plot for tap angle 180 degrees
Gaussian
Curve
Gaussian
Curve
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PDF plot for tap angle 270 degrees:
Discussion:
The PDF plots are shown in figure 6.9 through 6.12 above. The principle
application for a probability density function measurement of physical data is to
establish a probability description for the instantaneous values of the data. The
experimental PDF obtained are nearly bell shaped. However, they are not pure Gaussian
distribution. They are close to a Gaussian distribution but have some skewness and
kurtosis when compared with a pure Gaussian distribution. The skewness and kurtosis
of the PDF plots are determined and tabulated below in table 6.5.
Figure 6.12: PDF and histogram plot for tap angle 270 degrees
Gaussian
Curve
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From the table, the skewness for all the cases is negative. However, the
magnitude of the skewness is small. A negative skew indicates that the tail on the left
side of the probability density function is longer than the right side and the bulk of the
values (including the median) lie to the right of the mean. It is evident that the skewness
of the PDF with tap angle 180 degree is the highest in magnitude when compared with
other three PDF’s skewness. From the table, it can be seen that kurtosis is highest for
the PDF with the tap angle of 180 degrees. Higher kurtosis means more of
the variance is the result of infrequent extreme deviations, as opposed to frequent
modestly sized deviations. Furthermore, by comparing the experimental PDF’s with
Norberg’s (2003) representation of PDF’s (negatively skewed) from figure 6.8, we can
see that there are similarities in terms of skewness and kurtosis.
Table 6.5
Tap Angle θ
(Degrees)
Skewness
Kurtosis
0 -0.0164* 10-4
2.1973
90 -0.0338* 10-4
2.2723
180 -0.1040* 10-4
4.3285
270 -0.0208* 10-4
2.3498
The PDF obtained from the experiment can be compared with the standard
PDF’s from theory. Thereby we can differentiate and categorise the experimental PDF
to the nearest category of PDF in theory. The figure 6.13 shows us the Standard set of
PDF’s for (a) Sine wave, (b) Sine wave plus random noise, (c) Narrow band random
noise and (d) Wide band random noise from Bendat (2000). Now comparing the
experimental PDF’s with figure 6.13, we can safely categorize that the experimental
PDF obtained has a shape which is somewhere between the case (b) and (c). Hence we
can safely categorize that the obtained experimental PDF’s are a mixture of sine wave
plus random noise and a pure random noise. This is consistent with the discussion
presented in literature review.
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s
Source:\Bendat (2000)
Figure 6.13: PDF (a) Sine wave, (b) Sine wave plus random noise, (c) Narrow band
random noise (d) Wide band random noise degrees
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6.1.3.3 Autocorrelation Functions:
The Autocorrelation function for random data describes the general dependency
of the values of the data at one time on the values of another time. This function is
usually a real valued even function and is always maximum at time lag = 0. The
autocorrelation plots of recorded transient surface pressure are presented below. The
autocorrelation for 4 different tap angles mentioned above are presented below. The rest
of the results are available in the DVD attached with the report. The main application of
this function measurement of physical data is to establish the influence of values at any
time over values at a future time.
Autocorrelation plot for tap angle 0 degrees:
Figure 6.14: Autocorrelation Function for tap angle 0 degrees
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Autocorrelation plot for tap angle 90 degrees:
Autocorrelation plot for tap angle 180 degrees:
Figure 6.15: Autocorrelation Function for tap angle 90 degrees
Figure 6.16: Autocorrelation Function for tap angle 180 degrees
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Autocorrelation plot for tap angle 270 degrees:
Discussion:
The Autocorrelation plots are shown in figure 6.14 through 6.17 above. It is
evident from that graph, that the autocorrelation function is de-correlating with time lag
with the local maximum occurring at the time lag = 0. Both x and y axis are limited
between values -1 and 1. Beyond this point the function de-correlates and reaches to 0
as lag tends towards infinity. However, this de-correlation is not very consistent with
time lag moving towards infinity. The function gets correlated at intermittent points and
then again de-correlates with increase in time. This behaviour is shown in figure 6.18
below. However in general sense the de-correlation is evident as time lag increases.
Another interesting observation from the graph is that there is some anti-correlation (see
figure 6.16) that is occurring when the tap position is at 180 degrees. However, this
anti-correlation exists for a short period of time. Thereafter the function suddenly gets
de-correlated and gradually reaches to zero as time tends to infinity.
Figure 6.17: Autocorrelation Function for tap angle 270 degrees
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Figure 6.18: Autocorrelation Function showing some correlation with time
De-correlation with time
Some Correlation as
time lag increases
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6.1.3.4 Power Spectral Density (PSD):
The PSD for random data describes the general frequency composition of the
data in terms of the spectral density of its mean square values. The PSD plots of
recorded transient surface pressure are presented below. The PSD for 4 different tap
angles mentioned above are presented below. The rest of the results are available in the
DVD attached with the report. The main application of this function measurement of
physical data is to establish the frequency composition of the data, which in turn bears
important relationships to the physical system involved. In this project, using PSD, we
can extract the frequency values where peak occurs. This peak value refers to the
shedding frequency of the system.
PSD plot for tap angle 0 degrees:
Figure 6.19: PSD plot for tap angle 0 degrees
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PSD plot for tap angle 90 degrees:
PSD plot for tap angle 180 degrees:
Figure 6.20: PSD plot for tap angle 90 degrees
Figure 6.21: PSD plot for tap angle 180 degrees
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PSD plot for tap angle 270 degrees:
Discussion:
The PSD plots are shown in figure 6.19 through 6.22 above. The data is filtered
and only low frequencies in the range of 0 to 100 Hz are considered, as they relate to the
bluff body wall pressure fluctuation. The PSD plots shows several peaks occurring at
different frequency values. However, the major peaks are seen in the range of 20 to 30
Hz for tap angles 0, 90 and 270 degrees. In case of PSD plot seen in figure 6.21, for tap
angle of 180 degrees, the peak occurs between 50 to 60 Hz. The exact point of the peaks
is extracted from the Matlab program and tabulated in table 6.6 below. These points
correspond to the shedding frequency of the system. Taking a closer look at the plots,
we can see that the signal is purely harmonic in its nature. There are other peaks visible
in the plots. However, these are not of a greater significance. A detail analysis of the
tabulated results in table 6.6 is already provided in section 6.1.2. The analysis is
summarized below. It is observed that the shedding frequency of tap angle 180 degree is
approximately double the value at tap angle 90 degree, ie., fs180 ~ 2 * fs90.
Figure 6.22: PSD plot for tap angle 180 degrees
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Table 6.6
Tap Angle θ (Degrees) Shedding Frequency (Hz)
0 27.1250
90 27.3750
180 55.0000
270 27.5625
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6.1.3.5 Spectrogram:
A spectrogram is a time-varying spectral representation of the data. It represents
a signal in a joint time-frequency domain. The spectrogram plots of recorded transient
surface pressure are presented below. The spectrograms for 4 different tap angles
mentioned above are presented below. The rest of the results are available in the DVD
attached with the report.
Spectrogram for tap angle 0 degrees:
Figure 6.23: Spectrogram for tap angle 0 degrees
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Spectrogram for tap angle 90 degrees:
Spectrogram for tap angle 180 degrees:
Figure 6.24: Spectrogram for tap angle 90 degrees
Figure 6.25: Spectrogram for tap angle 180 degrees
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Spectrogram for tap angle 270 degrees:
Discussion:
The spectrograms are shown in figure 6.23 through 6.26 above. The
frequency variations along with the time can be seen from these spectrograms. The
spectrogram shown in figure 6.23, 6.24 and 6.26 shows a strong frequency response at
two locations. The signal is harmonic in nature. There are minute differences in
frequency width or broadening. Spectrogram for tap angle 0 degrees (see figure 6.23)
shows a larger broadening and the nature is very strong. The peak in the frequency
occurs between 27 to 29 Hz and the second peak frequency occurs between 58 to 60 Hz.
Furthermore, there is an intermediate peak occurring between 43 to 47 Hz. The signal is
also intermittent, with small periods of time where the intensity of vortex shedding is
greatly reduced or perhaps stops completely.
Figure 6.26: Spectrogram for tap angle 270 degrees
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Spectrogram for tap angle 90 degrees (see figure 6.24) shows a minute shift in
the frequency variation when compared with the spectrogram of tap angle 0 degrees.
Frequency broadening is observed to be from 27 to 29 Hz and the second peak
frequency broadening is from 58 to 60 Hz. However, the intensity has decreased when
compared with the previous case. The intermediate peak that occurred in the previous
case fades away.
Spectrogram for tap angle 180 degrees (see figure 6.25) shows a large difference
when compared with the spectrograms from the previous two cases discussed. The first
peak is very weak and occurs at 28 Hz and has very little broadening. The second peak
is the maximum peak and the broadening effect is evident from the plot and occurs
between 52 to 58 Hz. Spectrogram for tap angle 270 degrees (see figure 6.26) is same as
the spectrogram for tap angle 90 degrees.
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6.2 Curve fitting technique to find the value of τc (Analysis):
This section follows the procedure as presented in chapter 5 section 5.3.2. Using
the PSD plots from section 6.1.3.4 and using the temporal statistical model we find out
the PSD for the true signal. Model 1 and Model 2 presented in 5.3.2 are used. The
Matlab code used for this analysis is presented in detail in Appendix B of the report.
Using the curve fitting technique defined, the PSD plots are plotted and are presented
below. The power spectral density function of the true signal for both the models is
simulated or generated for various values of τc to see which value best fits the spectral
density from the experimental results.
The curve fitting technique is shown for the 4 tap angles described earlier. The
rest of the results are presented in the DVD attached at the end of this report. The two
models used are summarized below. The time scale parameter τc is modelled as multiple
of vortex shedding period T. The section 6.2.1 is presented with analysis of model 1 and
curve fitted graphs are presented along with the recorded values of time scale parameter.
The section 6.2.2 is presented with analysis of model 2 and curve fitted graphs are
presented along with the recorded values of time scale parameter.
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6.2.1. Curve Fitting Technique using Model 1:
Using the model 1 we find out the PSD for the true signal. Using trial and error
method, a best fit value of τc was obtained. The results for trial 1 are tabulated in table
6.7.
Table 6.7
Model 1 :
Trial 1 : Time scale parameter τc = 0.1*T
Tap Angle
θ (Degrees)
Curve fitted PSD Plots
0
90
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180
270
It is evident from the graph that the value of τc = 0.1*T almost matches with the
experimental results. However, there are very minute discrepancies in terms of
broadening in case of tap angle 0 and 90 degrees. In general sense the value of τc =
0.1*T fits well for model 1. Other values of τc were used to see if there were any more
possible matches and was unsuccessful. Finally we can conclude that τc = 0.1*T works
quite well for model 1. The procedure is repeated for model 2 and is presented in the
section below.
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6.2.2. Curve Fitting Technique using Model 2:
Using the model 2 we find out the PSD for the true signal. Using trial and error
method, a best fit value of τc was obtained. The results for trial 1 are tabulated in table
6.8.
Table 6.8
Model 2 :
Trial 1 : Time scale parameter τc = 0.1*T
Tap Angle
θ (Degrees)
Curve fitted PSD Plots
0
90
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180
270
It is evident from the graph that the value of τc = 0.1*T doesn’t match with the
experimental results. The whole procedure was repeated for several trials values of τc .
The following trial values were used. τc = 1*T, τc = 10*T. It was found out from the
PSD plots that τc = 1*T was close to the experimental results and τc = 10*T was too
high. Hence an optimal value, somewhere near to τc = 1*T was chosen and the whole
procedure was repeated. The final obtained optimal value and graphs is shown in table
6.9 below.
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Table 6.9
Model 2 :
Optimal Trial : Time scale parameter τc = 1.25*T
Tap Angle
θ (Degrees)
Curve fitted PSD Plots
0
90
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180
270
It is evident from the graph that the value of τc = 1.25*T matches very well with
the experimental results for model 2. Finally we can conclude that τc = 1.25*T works
perfectly well for model 2. This is in agreement with the initial results of Doolan (2010)
who used a similar value of τc to model the noise generated by cylinders in cross flow
for a wide range of Reynolds number.
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Chapter 7 – Project Management Description:
This section lists the resources for the project, project timeline, analysis and
management of risks and finally project outcomes and deliverables
7.1 Project Resource Listing:
The list of hardware/software tools, laboratory facilities, project fund and library
resources needed to support the project work is specified below in table 7.1.
Table 7.1
Type or
Category of
Resource
Specific Items
Availability
Software
Tools
MS office and Microsoft Project
3D modeling and 2D drawing software
(CATIA)
Analysis software (MATLAB)
PDF readers
Document writing and editing software
Photo editing software
Available – in CATS
Suite
Hardware
Tools,
Machines,
Components
and
Equipments
Computer, Printer and Scanner
Vernier Calipers
Wind Tunnel
Amplifiers
Data Acquisition System
Microphone set up within a circular cylinder
Pressure measurement microphone
Power source
Available – in CATS
Suite, Machine Shop
and Holden
Laboratory
Project
Funds
AUD 1500 is allocated
Books and
journal
articles
Research Papers, e-Journals, Books and
CD’s on Bluff Bodies and Aerodynamics
Available – in Barr
Smith Library and on
My Uni
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7.2 Project Timeline:
The project timeline for individual tasks is shown below in table 7.2. The mile
stone chart shows us the major deliverables of the project. This is shown in table 7.3.
The gantt chart is shown in the appendix A of this report.
Table 7.2
Project Timeline Project Tasks
1. Design of the
experimental set up
Week 1- Week 12
1st March – 4
th June
2010
(Semester1)
All Tasks Completed
Review of the requirements
Generate design concepts as per requirements
List out all pros and cons of the concepts
Draw conclusion and freeze on a particular
design
Create 3D model as per the design
Generate 2D manufacturing drawings
Review of the drawings with supervisor and
workshop
Submission of drawings for manufacturing
2. Conducting the
Experiment to obtain the
transient pressure data
Midyear break
5th
July – 23rd
July
Inspection of the manufactured experimental rig
Calibration of the microphone and obtain its
sensitivity
Integration of the experimental rig with the
wind tunnel, power source, DAQ and computer
Testing the experimental set up
Recording the temperature, velocity and
pressure of the fluid flow
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All Tasks Completed
Work out the density of the air
Conducting the experiment and recording the
transient pressure data
Repeat the experiment with microphone at
several location along the circumference of the
cylinder
Tabulate the results
3.Analysis of the results
Week 1 to Week 9
26th
July – 8th
October
2010
(Semester 2)
All Tasks Completed
Review of the data – check if data is a random
data of voltage of time
Covert the voltage to sound pressure level using
the sensitivity
Find out the probability density function and
analyze the data in the amplitude domain
Find out the autocorrelation function and
analyze the data in the time domain
Create the auto-spectrum of the data, which
gives you the frequencies over the entire time
domain
Find out the spectrogram of the data
Plot the power spectral density for the
experimental data
Use the transient force signal presented in the
temporal statistical model and simulate the
power spectral density with different values of
time scale parameter τc, and see which value of
τc fits the curve with the experimental data, and
there by finding out the experimental value of τc.
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Table 7.3
MILE STONE CHART
Mile Stone
Number
Important Project Milestones Due Date
1 Completion of project proposal 10th Feb 2010
2 Completion of project definition with feasibility
study
12th March 2010
3 Final design of all project drawings, documents
and experimental set up
23rd April 2010
4 Completion of Mid Project Report 4th June 2010
5 Completion of Lab Experiment 26th July 2010
6 Completion of Analysis of Results 8th Oct 2010
7 Completion of Final Project Report 29th Oct 2010
8 Submission of Final Research Article and
Presentation
5th Nov 2010
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7.3 Risk Analysis:
Risk in this project is occurrence of an undesirable event that may affect project
activities directly or indirectly which in turn can affect the main project
goals/objectives. In risk analysis we have indentified possible risks that could occur
during the project, and then presented action plan to mitigate the risks. The risks
involved in the project are directly proportional to the size of the project and the
generation of technology used. Table 7.4 below shows the risk analysis for this project.
Table 7.4
No
Risk items
Effects
Level of
risk
Causes /
Possible
reasons
Preventive Measures
and Risk Execution
Plan
1. Faulty/Am
biguous
requiremen
ts
Ends up
with wrong
requirement
s and wrong
design/draw
ing
Delay
project
activities
Moderat
e Designers
mistakes
Misrepres
entation
Lack of
informati
on
Get every job
reviewed and sign
off
In case of
occurrence, divide
and prioritize the
work and complete
the design
2. Change/Ad
ditional
Requireme
nts
Ends up
with change
in project
scope
Increase
project
costs
Changes in
all
subsequent
project
activities
High Unaccou
ntability
of
external
factors
Misrepres
entation
Lack of
informati
on
Get every job
reviewed and sign
off
Keep additional
buffer resources
In case of
occurrence, suggest
alternative plans,
prepare a new plan
for additional
resources and
execute the plan
accordingly
3. Availabilit
y of project
resources at
the right
May
increase
project cost
High Miscom
municatio
n within
the
Keep track of the
oncoming project
activity and make
sure necessary
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time Delay in
project
activities
project
lack of
lead time
Bad
supply
chain
managem
ent
resources are
available
Buy/order the
materials with good
lead time
In case of
occurrence, divide
the work and run
parallel work with
available resources
4. Equipment
/ Software/
Hardware
Breakdown
(Ex:
Storing lot
of
information
in a single
word file)
May cause
delay in
that
particular
activity
Moderat
e Improper
usage of
the
machine
or
hardware
Faulty
manufact
uring or
improper
maintena
nce
Improper
use of
software
or
hardware
tool
Get necessary
training on how to
operate the
machine.
Alternatively study
the necessary
manuals
Try to allocate a
nominal size and
space for all
software packages
Keep buffer time
for use of machines
and equipments
Keep necessary
back up from time
to time
5. Improper /
delay in
communica
tion
Direct
effect on
particular
activity and
thus cause
delay and
additional
resources
Moderat
e Lack of
coordinat
ion or
lack of
informati
on flow
in the
project
Keep a record of all
the communication
and if required get a
sign off from the
other party as a
means of
acknowledgement
In case of
occurrence, use
corrective actions
and keep a record
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7.4 Project Outcomes and Deliverables:
All the project outcomes and deliverables are listed below in table 7.5
Table 7.5
Outcomes
Deliverables
Understanding the pressure measurement
technique over the surface of a cylinder in
a turbulent flow.
Understanding the nature of the time scale
parameter τc
Understanding how τc accounts to the
Turbulent flow effects
Understanding the acoustic signature of
Noise generated in the cross cylinder flow
Understanding the transient behavior of
Flow in turbulent regime
Project Definition Statement
Literature Review
Project Plan
Project Drawings
Model of the Experimental Rig
Preliminary Report
Results and Analysis of Experimental Data
Final Project Report
Seminar Presentation PPT
Research Paper
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Chapter 8 – Project Summary, Conclusion and Future work:
The project is summarized and from the results the conclusions are drawn. The
future work of the project is also discussed in this section.
8.1 Project Summary:
A brief introduction to bluff body flows was given. It was established that a
circular cylinder can be considered as a bluff body. Different flow patterns in a cross
flow of a circular cylinder at different Reynolds number were discussed and presented.
The background study was done and general understanding of bluff body noise
prediction process were discussed. From a detail literature review it was found out that
the spectral broadening of the unwanted noise is due to temporal beating effect, which is
statistically equivalent to narrow band random noise and contains the turbulent flow
effects, which is controlled by a single time scale parameter τc..
Furthermore, the literature review covered the different flow regimes and
enabled in better understanding of flow over a circular cylinder. The temporal statistical
model used in the statistical correction of the Doolan (2010) model was summarized.
The different pressure measurement methods were reviewed and ring of pressure taps
was selected along with the cavity mounting technique. The major research gaps were
found out from the literature review. The research gaps from the literature review
formed into project objectives. The primary objective being, to find the experimental
value of the time scale parameter τc. The project tasks or individual activities that link to
each of the project objectives was shaped and presented in detail.
The design of the experimental set up was discussed in detail and different
designs options were discussed along with their advantages and disadvantages. An
optimal design was chosen and the design was completed along with the manufacturing
drawings. The experimental rig was manufactured. The experiment was conducted by
placing the rig in a wind tunnel, keeping the steady state conditions the transient
pressure signal was recorded and tabulated. The methods and techniques that are used in
the project were discussed and presented in detail.
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Using the methods and techniques discussed the transient pressure data was
analysed. The meaning and physical significance of this random data was discussed and
presented in detail. The main descriptive properties– mean square values of the time
series, probability density functions (PDF), autocorrelation functions, power spectral
density (PSD) and spectrogram are presented and discussed.
Finally, using the theory of temporal statistical model a curve fitting technique
was described in detail. The method uses a statistical model and simulates a PSD which
is equivalent to the experimental signal. The statistical analysis was presented in detail.
There are two equations/models present and both the models are used to determine the
time scale parameter. The statistical analysis was performed and the experimental value
of the time scale parameter τc was found. Finally the project management description is
presented and it shows the tasks and schedule of the project.
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8.2 Conclusion of the Project:
An effort was made to investigate the unsteady surface pressure over a circular
cylinder in a turbulent flow. A cavity mounted technique with the pin hole leading from
the surface to the cavity was successfully implemented to measure the surface pressure.
The experimental rig was manufactured and placed in a wind tunnel and the Reynolds
number of the flow was approximately Re ~ 18500, Thereby, making the flow turbulent.
In case of a cross flow over a circular cylinder, we can conclude that the
shedding frequency at the tap angle 180 degree is approximately double the value and
vortex shedding period is half the value as compared with the shedding frequency and
vortex shedding period at tap angle 90 degree. Furthermore, we can conclude that the
data obtained from such recordings are usually stationary and ergodic. Also the intensity
of the pressure is very less at the tap angle 180 degrees.
The time series of the transient force signal has a temporal beating effect. We
can conclude that the spectral broadening of the noise is caused by the temporal beating
effect. Furthermore, we can compare this with literature and concluded that temporal
beating effect is equivalent to narrow band random noise introduced into a sinusoid
function.
The probability density function shows that the data is negatively skewed.
Hence we can conclude that the data is not a pure Gaussian distribution. Furthermore,
the autocorrelation function de-correlates with time and reaches to zero as time tends to
infinity and its maximum at time lag equal to zero seconds. Hence at the starting of the
vortex shedding process, the vortices are perfectly correlated and as it moves further
downstream the flow it gets more turbulent and then de correlates.
The transient force signal was perfectly harmonic in our case. The PSD plots
showed the two peaks and they correspond to the spectrogram showing two frequency
lines with some amount of broadening. The major peak in the PSD plot relates to the
vortex shedding in the cylinder cross flow. The true signal can be modelled using two
equations. The equations are summarized below.
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Model 1
Model 2
Using the curve fitting technique, the value of time scale parameter was
estimated. It was determined that the value of the time scale parameter τc = 0.1*T for
model 1 and τc = 1.25 * T for model 2. Hence we can finally conclude that the effect of
turbulence can be found out using either one of these models with their corresponding
values of τc. Using these models, the statistical correction in Doolans (2010) hybrid
model can be made and using it with the two dimensional Unsteady - RANS signal,
bluff body noises can be calculated.
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8.3 Future work of the Project:
The future work of the project involves, conducting similar experiments with
different setup or arrangement of cylinders. For instance, a circular cylinder can be
placed downstream of an elliptical body and then the transient pressure data can be
recorded and the results could be compared with each of the attributes described in this
project, to find out the similarities and the differences in each of the attributes.
Furthermore, tandem cylinders experiment can be conducted by placing two cylinders
next to each other and the transient surface pressure data can be recorded over the
cylinder which is downstream the flow and similar kind of analysis could be performed
to find out the nature of the data and estimate the time scale parameter and see if it
matches with the experimental results obtained from this project. Additionally, multiple
pressure taps could be placed along the circumference of the cylinder and the lift from
the cylinder could be investigated.
University of Adelaide Preliminary Report
References:
Ackerman J. R , J. P. Gostelow, A. Rona, W. E. Carscallen, 2009, Measurements of
Fluctuating Pressures on a Circular Cylinder in Subsonic Cross flow , National
Research Council of Canada, Ottawa K1A 0R6, Canada
Anatol Roshko, 1954, On the development of turbulent wakes from vortex streets,
National Advisory Committee for Aeronautics, California Institute of Technology,
Report 1191.
Bearman PW, 1969 Vortex shedding from a circular cylinder in the critical Reynolds
number regime. Journal of Fluid Mechanics, 37:577
Boston University, < http://www.bu.edu/tech/files/2010/03/q.0205L.jpg>, viewed on 1st
june 2010.
Con J. Doolan,2009, Advance Topics in Aerospace Engineer, Lecture Notes, School of
Mechanical Engineering University of Adelaide, Australia
Con J. Doolan, 2010, Computational Bluff Body Aerodynamic Noise Prediction Using a
Statistical Approach, Applied Acoustics, School of Mechanical Engineering University
of Adelaide, 5005, Australia
C. Norberg, 1987 Effects of Reynolds numbers and a low-intensity freestream
turbulence on the flow around a circular cylinder. Chalmers Univ. Technol. Publ. No.
8712, S-412-96. Goteborg, Sweden.
C. Norberg, 2000 Flow around a circular cylinder: Aspects of fluctuating life,
Journal of Fluids and Structures, Volume 15, Issue 4, Pages 459-469
C. Norberg, 2003 Fluctuating lift on a circular cylinder: review and new measurements,
Journal of Fluids and Structure, 17:57 – 96 ,
Drescher, H., 1956, Messung der auf querangestr.omte Zylinder ausge.ubten zeitlich
ver.anderten Dr.ucke. Zeitschrift f .urFlugwissenschaften und Weltraumforschung 4, 17–
21.
University of Adelaide Preliminary Report
Flaschbart 0,1932,Messungen ebenen und gewalben platten ergenbisse der
aerodynamischen. Vers. Gdttingen IV Leiferung 96:317. See Muttray H. 1932. Handb.
Exp. Phys. 4:323.
Henderson RD, 1995, Details of the drag curve near the onset of vortex shedding.
Physics of Fluids, Submitted.
J. Bendat, A. Piersol, 2000, Random data analysis and measurement procedures,
Measurement Science and Technology 11, 1825-1826.
John Cheung, 2010, Wind Engineering, Lecture Notes, School of Mechanical
Engineering University of Adelaide, Australia
J. Seo, Y. Moon, Aerodynamic noise prediction for long-span bodies, Journal of Sound
and Vibration 306 (2007) 564 – 579.
Mohr, K.-H, 1981, Messungen instation.aren Dr.ucke bei Queranstr.omung von
Kreiszylindern unter Ber. ucksichtigung fluidelastischer Effekte. Ph.D. Thesis, KFA J .
ulich GmbH, Germany. Report Jul-1732
Morkovin M. V, 1964, Flow around circular cylinder a kaleidoscope of challenging fluid
phenomena In Proceedings of the Symposium on Fully Separated Flows, Philadelphia
(ed. A. G. Hansen), pp. 102-118, New York: ASME.
NASA, Goddard Earth Science, < http://en.wikipedia.org/wiki/File:Vortex-street-
animation.gif>, viewed on 1st June 2010.
O. Inoue, N. Hatakeyama, Sound generation by a two-dimensional circular cylinder in a
uniform flow, J. Fluid Mech. 471 (2002) 285-314.
Provansal. M. Mathis, C. & Boyer, L, 1987, Benard-von Karman instability: transient
and forced regimes. Journal of Fluid Mechanics 182, 1-22.
Richard J. Goldstein, 1996, Fluid Mechanics Measurements, ISBN 1-56032-306-X.
Shih WCL, Wang C, Coles D, Roshko A, 1992, Experiments on flow past rough
circularcylinders at large Reynolds numbers. Proc. 2nd Int. Coll. Bluff Body
Aerodynamics. Melbourne, Australia., Dec. 7-10, p. 150.
University of Adelaide Preliminary Report
S. P. Singh, S. Mittal, 2009 Flow past a cylinder: shear layer instability and drag crisis,
department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208
016, India.
Tunstall, M.J, 1970, Fluctuating pressures on circular cylinders in uniform and turbulent
flows. Lab. Note RD/L/N 45/70, Central Electricity Research Laboratories (CERL).
van Nunen, J.W.G., Persoon, A.J., Tijdeman, H, 1972, Analysis of steady and unsteady
pressure and force measurements on a circular cylinder at Reynolds numbers up to 7:7 _
106: NLR TR 69102 U, National Aerospace Laboratory, The Netherlands.
V. Strouhal, Ueber eine besondere Art der Tonerregung, Annalen der 424 Physik und
Chemie 241
West, G.S., Apelt, C.J., 1993. Measurements of fluctuating pressures and forces on a
circular cylinder in the Reynolds number range 104 to 2:5 _ 105: Journal of Fluids and
Structures 7, 227–244
West, G.S., Apelt, C.J., 1997. Fluctuating lift and drag forces on finite lengths of a
circular cylinder in the subcritical Reynolds number range. Journal of Fluids and
Structures 11, 135–158
Williamson CHK, Roshko A, 1990, Measurements of base pressure in the wake of a
cylinder at low Reynolds numbers, 2. Flugwiss. Welfraumforsch. 14:3846
Williamson,C.H.K, 1992 The natural and forced formation of spot-like &vortex
dislocations'' in the transition of a wake. Journal of Fluid Mechanics 243, 393-441
Williamson, C.H.K, 1996, Vortex dynamics in the cylinder wake. Annual Review of
Fluid Mechanics, 28:477- 539.
Zhang, H. Q., Fey, u., Noack, B. R, Kognig, M. & Eckelmann H, 1995, On the
transition of the cylinder wake. Physics of Fluids 7, 779-793.
University of Adelaide Preliminary Report
Appendix A: Gantt Chart
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University of Adelaide Final Project Report
Appendix B: Matlab Code
University of Adelaide Final Project Report
%---------------------------------------------------------------------
---- % Project Title: 'INVESTIGATION OF UNSTEADY PRESSURE % OVER THE SURFACE OF A CYLINDER IN A TURBULENT FLOW’'
% Masters Project % The University of Adelaide % Department of Mechanical Engineering
% Under the guidance of Dr Con Doolan % Student Name : Santosh Ballal Amarnath % Student ID : 1187621
% DAQ Script %---------------------------------------------------------------------
----
clear all close all clc
numbermics = 1; %Number of microphones
gain = 100; %Gain written on amplifier
fs = 2048; %Sampling frequency
f_PSD = fs*16; %Frequency Resolution
time_total = 120; %Time to Record Data in seconds
Pa_curve_coefficient= 0.059126348;
offset = [0];
ratio = [1];
%NI PXI-4496 Data Cards: if(~exist('AI')) AI= analoginput('nidaq','PXI1Slot3'); end
%Add required channel(s) connected to mic(s): addchannel(AI,0,'Mic1');
%Recording Information: set(AI,'Samplerate',fs); samples = time_total*fs; set(AI,'SamplesPerTrigger',samples);
%------------------------------------- %FIRST DAQ: %-------------------------------------
start(AI); [data,time] = getdata(AI); olddata = data;
University of Adelaide Final Project Report
%Calibration, Equalise Signals: for i=1:numbermics data(:,i)=(ratio(i)*data(:,i)); %Multiply by Ratio data(:,i)=data(:,i)+offset(i); %Add Offset end
%Convert to Pascals: data=data/gain; %Remove Gain data=data*1000; %Put into Millivolts data=Pa_curve_coefficient*data; %Convert to Pascals
%Save Data: save angle330
disp('-------------');
University of Adelaide Final Project Report
%---------------------------------------------------------------------
---- % Project Title: 'INVESTIGATION OF UNSTEADY PRESSURE % OVER THE SURFACE OF A CYLINDER IN A TURBULENT FLOW’'
% Masters Project % The University of Adelaide % Department of Mechanical Engineering
% Under the guidance of Dr Con Doolan % Student Name : Santosh Ballal Amarnath % Student ID : 1187621
% Data Analysis Script %---------------------------------------------------------------------
----
clear all close all clc
%---------------------------------------------------------------------
---- %Declaring variables used in the code
numbermics = 1; %Number of microphones
TimeNumber = 12; %Time divided into 10
parts:120(s)/10=12
gain = 100; %Gain written on amplifier
fs = 2048; %Sampling frequency
f_PSD = fs*16; %Frequency Resolution
time_total = 120; %Time to Record Data in seconds
Pa_curve_coefficient = 0.059126348; %Coefficient to Convert to Pascals
pref=20*10^-6; % Reference Pressure
offset = [0]; %Curve Offset
ratio = [0.9164]; %Sensitivity of the microphone
angle = 90; % Angle at which fluid is flowing, with zero refering % to stagnation point
load angle90.mat; % Opening the recorded data
olddata = data; %Storing the old data so that data could be
overwritten %---------------------------------------------------------------------
---- %Calibration, Equalise Signals: for i=1:numbermics data(:,i)=(ratio(i)*data(:,i)); %Multiply by Ratio
University of Adelaide Final Project Report
data(:,i)=data(:,i)+offset(i); %Add Offset end %---------------------------------------------------------------------
---- %Convert to Pascals: data=data/gain; %Remove Gain data=data*1000; %Put into Millivolts data=Pa_curve_coefficient*data; %Convert to Pascals %---------------------------------------------------------------------
---- %Butterworth Filter: fc = 1; % Lower Cut-off frequency (Hz) fc_1 = 100; % Higher Cut-off frequency (Hz) order = 4; % Filter order Wn = [2*fc/fs,2*fc_1/fs]; [B,A] = butter(order,Wn); Filtered_Data = filtfilt(B,A,data); %---------------------------------------------------------------------
---- %PSD & SPL: for i=1:numbermics [PSD(:,i),f]=pwelch(Filtered_Data(:,i),hann(f_PSD),f_PSD/2,f_PSD,fs); %PSD=PSD*2; PSD1(:,i)=10*log10(PSD(:,i)/pref^2); fftvalue(:,i)=sqrt(PSD(:,i)); SPLb(:,i)=20*log10(fftvalue(:,i)/pref); presb(:,i)=trapz(f,PSD(:,i)); OASPL(:,i)=10*log10(presb(:,i)/pref^2); end %---------------------------------------------------------------------
---- %PSD Plot (dB log): figure plot(f,PSD1) title('Power Spectral Density Plot (Log Scale)') xlabel('Frequency (Hz)') ylabel('Spectral Density (dB/Hz)') axis([10^0 10^2 20 80]) saveas(gcf, ['Angle_' num2str(angle) '_PSD(LOG)'], 'fig') %---------------------------------------------------------------------
---- %PSD Plot (Linear): figure plot(f,pref*10.^(PSD1./20)) title('Power Spectral Density Plot (Linear Scale)') xlabel('Frequency (Hz)') ylabel('Pressure (Pa)') axis([20 80 0 0.125]) saveas(gcf, ['Angle_' num2str(angle) '_PSD(LINEAR)'], 'fig') %---------------------------------------------------------------------
---- %PDF Plot: figure N=length(Filtered_Data); [n,xout] = hist(Filtered_Data,200); deltap=xout(100)-xout(99); Px = (n./N)/deltap; subplot(2,1,1), plot(xout,Px) title('Probability Density Function Plot') xlabel('Pressure(Pa)- x ') ylabel('Probability Density Function')
University of Adelaide Final Project Report
subplot(2,1,2), histfit(Filtered_Data) title('Histogram Plot') xlabel('Pressure (Pa): x ') ylabel('Frequency') saveas(gcf, ['Angle_' num2str(angle) '_PDF'], 'fig') %---------------------------------------------------------------------
---- %Decaying Component N=length(Filtered_Data); [Auto,LAGS] = xcorr(Filtered_Data,'coeff'); figure tau=[-N+1:N-1]./fs; plot(tau,Auto'./(cos(2*pi*27.67.*tau))) axis([0 2 -2 5]) title('Decaying Signal (exp(x))') xlabel('Time Delay (Tau)') ylabel('Rx(Tau)') saveas(gcf, ['Angle_' num2str(angle) '_Decaying_Component'], 'fig') %---------------------------------------------------------------------
---- %Auto-correlation figure plot(tau,Auto) axis([-1 1 -1 1]) title('Auto-correlation Plot') xlabel('Time Delay (Tau)') ylabel('Rx(Tau)') saveas(gcf, ['Angle_' num2str(angle) '_Auto-correlation'], 'fig') %---------------------------------------------------------------------
---- %spectrogram figure spectrogram(Filtered_Data,hann(f_PSD/20),0,f_PSD,fs) %SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs) title('Spectrogram Plot') axis([10 80 0 120]) saveas(gcf, ['Angle_' num2str(angle) '_Spectrogram'], 'fig') %---------------------------------------------------------------------
---- %Butterworth Filter: fc_1 = 22; % Lower Cut-off frequency (Hz) fc_11 = 32; % Higher Cut-off frequency (Hz) order_1 = 4; % Filter order Wn_1 = [2*fc_1/fs,2*fc_11/fs]; [B1,A1] = butter(order_1,Wn_1); Filtered_Data_1 = filtfilt(B1,A1,data); % --------------------------------------------------------------------
----- %Curve Fitting finding tauc Index=find(PSD1==max(PSD1)); %Finding the index where max freq occurs f0=f(Index,:)%Finding the fundamental freq T=1/f0 %Finding the shedding frequency time st= f0*0.04/7.03; %Finding the strouhal number
%Simulating the input signal Input_Signal = (cos(2*pi*f0.*time)).*exp(-sqrt(time./(4*0.1*T))); Length_Data=length(Filtered_Data); RMS_Data=norm(Filtered_Data)/sqrt(Length_Data); %RMS of experimental
data RMS_Sim=norm(Input_Signal)/sqrt(Length_Data); %RMS of Simulated signal Scaling_Ratio=10*RMS_Data/RMS_Sim; %Scaling Factor
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plot(time,Input_Signal) %Decaying Cos wave signal
%pwelch of input signal with scaling factor [PSD_New,f_new]=pwelch(Scaling_Ratio^2*Input_Signal,hann(f_PSD),f_PSD/
2,f_PSD,fs); PSD_New=10*log10(PSD_New/pref^2); X1=abs(fft(Input_Signal,fs)); %FFT of autocorrelation function F1 = [0 : fs - 1];%Frequency
figure plot(f_new,PSD_New,'-x',f,PSD1) legend('Statistically Simulated','Experimental'); axis([10^0 10^2 -10 95]) title('Power Spectral Density Plot') xlabel('Frequency (Hz)') ylabel('Spectral Density (dB/Hz)') saveas(gcf, ['Angle_' num2str(angle) '_Curve_Fitting_Tau_c'], 'fig') %---------------------------------------------------------------------
-- % Pressure & Time figure plot(time,Filtered_Data) title('Variation of Pressure with Time') xlabel('Time (s)') ylabel('Pressure (Pa)') axis([0 120 -1.2/2 1.2/2]) saveas(gcf, ['Angle_' num2str(angle) '_Press_Vs_Time'], 'fig') %---------------------------------------------------------------------
---- %Time Plots for small intervals: for i=0:3 for j=1:3 z=9+i; figure(z) subplot(3,1,j), plot(time,Filtered_Data) title('Variation of Pressure with Time') xlabel('Time (s)') ylabel('Pressure (Pa)') axis([(j+(i*3))*10-9 (j+(i*3))*10 -1.2/2 1.2/2]) end saveas(gcf, ['Angle_' num2str(angle) 'Fig' num2str(z)], 'fig') end %---------------------------------------------------------------------
----
save angle90_New % Rename this file everytime you run the matlab file
disp('-------------');
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%---------------------------------------------------------------------
---- % Project Title: 'INVESTIGATION OF UNSTEADY PRESSURE % OVER THE SURFACE OF A CYLINDER IN A TURBULENT FLOW’'
% Masters Project % The University of Adelaide % Department of Mechanical Engineering
% Under the guidance of Dr Con Doolan % Student Name : Santosh Ballal Amarnath % Student ID : 1187621
% Data Representation Script %---------------------------------------------------------------------
----
clear all close all clc
%---------------------------------------------------------------------
---- %Declaring variables used in the code
numbermics = 1; %Number of microphones
TimeNumber = 12; %Time divided into 10
parts:120(s)/10=12
gain = 100; %Gain written on amplifier
fs = 2048; %Sampling frequency
f_PSD = fs*16; %Frequency Resolution
time_total = 120; %Time to Record Data in seconds
Pa_curve_coefficient = 0.059126348; %Coefficient to Convert to Pascals
pref=20*10^-6; % Reference Pressure
offset = [0]; %Curve Offset
ratio = [0.9164]; %Sensitivity of the microphone
%angle = 330; % Angle at which fluid is flowing, with zero refering % stagnation point
load angle0.mat data d1=data; load angle30.mat data d2=data; load angle60.mat data d3=data; load angle90.mat data d4=data;
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load angle120.mat data d5=data; load angle150.mat data d6=data; load angle180.mat data d7=data; load angle210.mat data d8=data; load angle240.mat data d9=data; load angle270.mat data d10=data; load angle300.mat data d11=data; load angle330.mat data d12=data; alldata=[d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12];
pressure=[norm(d1)/sqrt(length(d1)); norm(d2)/sqrt(length(d1)); norm(d3)/sqrt(length(d1)); norm(d4)/sqrt(length(d1)); norm(d5)/sqrt(length(d1)); norm(d6)/sqrt(length(d1)); norm(d7)/sqrt(length(d1)); norm(d8)/sqrt(length(d1)); norm(d9)/sqrt(length(d1)); norm(d10)/sqrt(length(d1)); norm(d11)/sqrt(length(d1)); norm(d12)/sqrt(length(d1))]
for j=1:12 data = alldata(:,j); %---------------------------------------------------------------------
----- %Calibration, Equalise Signals: data=(ratio*data); %Multiply by Ratio data=data+offset; %Add Offset %---------------------------------------------------------------------
----- %Convert to Pascals: data=data/gain; %Remove Gain data=data*1000; %Put into Millivolts data=Pa_curve_coefficient*data; %Convert to Pascals %---------------------------------------------------------------------
----- %Butterworth Filter: fc = 20; % Lower Cut-off frequency (Hz) fc_1 = 30; % Higher Cut-off frequency (Hz) order = 4; % Filter order Wn = [2*fc/fs,2*fc_1/fs]; [B,A] = butter(order,Wn); Filtered_Data = filtfilt(B,A,data); %---------------------------------------------------------------------
---- Length_Data=length(Filtered_Data); RMS_Data(j,:)=norm(Filtered_Data)/sqrt(Length_Data); %RMS of
experimental data Mean_Data(j,:)= mean(Filtered_Data); Var_Data(j,:) = var(Filtered_Data); Std_Data(j,:) = std(Filtered_Data);
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Skewness_Data(j,:) = skewness(Filtered_Data) Kurtosis_Data(j,:)= kurtosis(Filtered_Data) %---------------------------------------------------------------------
----- end Theta=[0:30:330]'; plot(Theta,RMS_Data)
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Appendix C: Manufacturing Drawings
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Appendix D: Project Snapshots
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A Circular Cylinder with a Microphone inside
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The Experimental Rig
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The Experimental Rig placed in a Wind Tunnel
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The Experimental Setup with the Rig, a Single Channel
DAQ, Power Source and a Computer