investigation of unsteady pressure over the surface of a circular cylinder in a turbulent flow

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


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),


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.


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.


21 | P a g e


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


24 | P a g e

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 .


25 | P a g e

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


26 | P a g e

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


27 | P a g e

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


28 | P a g e

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)


29 | P a g e

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


30 | P a g e

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


31 | P a g e

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


32 | P a g e

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.


33 | P a g e

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


34 | P a g e

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.


35 | P a g e

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

𝑤𝑕𝑒𝑟𝑒,

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

𝑇𝑕𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝜌 =28.97 ∗ 𝑃

1000 ∗ 8.3145 ∗ 𝑇 𝐾𝑔/𝑚3

𝑇𝑕𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 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


36 | P a g e

5.1.2 Reynolds Number and Dynamic Pressure Calculations:

𝑹𝒆𝒚𝒏𝒐𝒍𝒅𝒔 𝑵𝒖𝒎𝒃𝒆𝒓,

Where,

𝜇 𝑖𝑠 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑜𝑓 𝑎𝑖𝑟 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇

𝐷 𝑖𝑠 𝑡𝑕𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑕𝑒 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 =


37 | P a g e

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


38 | P a g e

Table 5.3

Time (seconds) Voltage (volts) Sound Pressure Level (Pa) Sound in dB

0

to

120


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


40 | P a g e

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


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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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



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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


52 | P a g e

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.


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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Gaussian

Curve

Gaussian

Curve


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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.


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.

http://en.wikipedia.org/wiki/Variance

http://en.wikipedia.org/wiki/Deviation_(statistics)


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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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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.



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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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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.



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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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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.



69 | P a g e

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)


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)


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


79 | P a g e

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.


80 | P a g e

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


81 | P a g e

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


82 | P a g e

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


83 | P a g e

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


84 | P a g e

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.


85 | P a g e

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.


86 | P a g e

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.


87 | P a g e

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.


88 | P a g e

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.

http://www.bu.edu/tech/files/2010/03/q.0205L.jpg


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.

http://en.wikipedia.org/wiki/File:Vortex-street-animation.gif

http://en.wikipedia.org/wiki/File:Vortex-street-animation.gif


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.


Appendix A: Gantt Chart


Appendix B: Matlab Code


%---------------------------------------------------------------------

---- % 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;


%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('-------------');


%---------------------------------------------------------------------




% Data Analysis Script %---------------------------------------------------------------------

----


%---------------------------------------------------------------------

---- %Declaring variables used in the code


TimeNumber = 12; %Time divided into 10

parts:120(s)/10=12





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


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')


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


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('-------------');


%---------------------------------------------------------------------




% Data Representation Script %---------------------------------------------------------------------

----


%---------------------------------------------------------------------

---- %Declaring variables used in the code


TimeNumber = 12; %Time divided into 10

parts:120(s)/10=12





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;


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);


Skewness_Data(j,:) = skewness(Filtered_Data) Kurtosis_Data(j,:)= kurtosis(Filtered_Data) %---------------------------------------------------------------------

----- end Theta=[0:30:330]'; plot(Theta,RMS_Data)


Appendix C: Manufacturing Drawings


Appendix D: Project Snapshots


A Circular Cylinder with a Microphone inside


The Experimental Rig


The Experimental Rig placed in a Wind Tunnel


The Experimental Setup with the Rig, a Single Channel

DAQ, Power Source and a Computer