1

Final Report

Hot-wire anemometry of the streamwise vorticity on the

windward surface of a swept-back cylinder

Andrew Mirzai

119025545

EG3005 3rd Year Project

Department of Engineering

University Of Leicester

Supervisor: Dr Aldo Rona & Dr Audrius Bagdanavicius

Technician: Mr Paul Williams

Submission date: 9th May 2014

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Contents Page

Summary..3

1. Introduction...4

1.1 Background....4

1.2 Objectives...6

2. Experimental set up....7

2.1 Charles Wilson wind tunnel....7

2.2 Cylinder..7

2.3 Mesh turbulent screen...9

2.4 Traverse...10

2.5 Hot-wire probe...11

2.6 Reynolds number and fluid velocity11

3. Procedure...13

3.1 Hot-wire calibration.13

3.2 Experimentation.15

4. Results and Discussion..17

4.1 Temperature corrections of CTA voltages...18

4.2 Processing results..19

4.3 Correlation.20

4.4 Improvements.23

4.5 Error Analysis24

5. Conclusion..25

5.1 Divergence from project proposal.25

Appendix.26

3

Summary

Grtler vortices are secondary flows that appear in a boundary layer flow along a concave wall. This can make heat transfer and flow hard to predict, which is why this research of is of interest to the fluids research community, mainly in the design of propellers and aircraft wings. By being able to control these structures, drag can be reduced and heat transfer can be minimized. To gain evidence of these structures, hot-wire anemometry was used to measure the surface of a circular cylinder that was subject to a free-stream velocity with a Reynolds number of 150000. Two constant temperature anemometer hot-wire probes were used to collect data over a spanwise 10mm section of the circular cylinder, with one of the probes acting as a reference. This procedure was consistent with a previous students experiment to allow comparison. The results obtained were used to confirm the presence of these streamwise vortical structures. This experiment improves on a previous experiment, run by Sakthitharan Srinamasivayam, by moving the probes closer to the surface of the cylinder. From 1.5mm to 1mm. Overall, this experiment provides evidence for the existence of streamwise vortices on the surface of convexity, which have a spanwise wavelength approximately equal to 1.8-2.4mm. It was also concluded that the experiment is repeatable.

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1. Introduction

1.1 Background

This project involves using hot-wire anemometry to measure the flow over a circular cylinder in the

low-speed closed-circuit Charles Wilson wind tunnel, University of Leicester.

Previous work on surface flow visualization on the suction surface of turbine blades at subsonic

and transonic speeds showed robust streamwise streaks on a lengthy time-averaged basis1. The

study of boundary-layer stability over concave surfaces, started by Grtler (1940), has attracted the

attention of several scientists. The centrifugal instability mechanism is responsible for the

development of counter-rotating vortices aligned in the streamwise direction, known as Grtler

Vortices2. As shown in [Figure 1].

[Figure 1]: Vortices in the boundary layer of a concave wall3

Grtler vortices are secondary flows that appear in a boundary layer flow along a concave wall. If the

boundary layer is thin compared to the radius of curvature of the wall, the pressure remains

constant across the boundary layer. On the other hand, if the boundary layer thickness is

comparable to the radius of curvature, the centrifugal action creates pressure variation across the

boundary layer. This leads to centrifugal instability (Grtler instability) of the boundary layer and

consequent formation of Grtler vortices4. This can make heat transfer and flow difficult to predict.

The spanwise length of streamwise vortices had been predicted hypothetically by Kestin and

Wood5. J.P. Gostelow later confirmed this hypothesis by visualising the vertical structure

development of a bluff body6.

Vorticity is defined as a measure of the circulation of a fluid7. More precisely, the vorticity of a flow is

a pseudovector field , equal to the curl of its velocity field v. It can be expressed by the vector

analysis formula8:

=

1 https://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/sjg50/aiaa-2013 2 http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782004000300003 3 http://www.thermopedia.com/content/817/?tid=104&sn=1412 4 http://en.wikipedia.org/wiki/G%C3%B6rtler_vortices 5 J. Kestin & R.T. Wood. Enhancement of stagnation-line heat transfer by turbulence. Progress in heat and mass transfer, Vol. 2, pp. 249-253, 1969. 6 J.P Gostelow, W.A Mc Mullan, S.J Garrett, M. De Saint Jean. The Influence of Streamwise Vorticity on Transition in the Presence of Sweep. Paper AIAA 2011-3878, Honolulu, 30 June 2011. 7 http://dictionary.reference.com/browse/vorticity 8 http://en.wikipedia.org/wiki/Vorticity

5

This project is of a lot of interest because of the limited information on streamwise vortices. It is

particularly of interest to the aerospace industry as streamwise vortices decrease the performance

of smooth surfaces such as blades and wings by increasing the boundary layer growth and the rate

of heat transfer. Consequently, this reduces lift and increases drag. A good understanding of vortical

structures is essential for controlling these aerodynamic structures as it can help reduce fuel

consumption and other properties9.

A hot-wire probe is an electrically heated cylinder which is stretched across a pair of supports and

held in a flow which cools it down by forced convection. The supports connect the wire to a bridge

circuit which provides the heating for the wire. Tungsten or platinum are popular choices of metal

for hot-wires. Generally, the sensors are made out of tungsten but have a platinum coating. As the

electrical resistance of most metals is dependent upon the temperature of the metal, a relationship

can be obtained between the resistance of the wire, and the flow speed. There are 2 types of hot-

wire anemometers. They both use the same type of probe but differ in how the bridge receives its

supply:

1. CCA (constant current anemometer): The simpler of the 2. Effectively a passive Wheatstone

bridge with the wire as one of the four arms. The bridge output provides a signal

proportional to velocity.

2. CTA (constant temp. anemometer): The most common type. The bridge output feeds a

differential amplifier able to supply power rather than just voltage.

[Figure 2]: Probe Types10

Wire temperature is normally 220C. Below this the wire loses sensitivity but above this, there is risk of the wire burning out. Probes are available in one-, two- and three-dimensional versions as single-, dual and triple sensor probes referring to the number of sensors. Since the sensors (wires) respond to both magnitude and direction of the velocity vector, information about both can be obtained only when two or more sensors are placed under different angles to the flow vector11.

9 Measuring streamwise vortices over a circular cylinder using hot-wire anemometry Sakthitharan Srinamasivayam 10 http://www.leb.eei.uni-erlangen.de/winterakademie/2008/report/content/course01/pdf/0107.pdf 11 Dantec Dynamics How to measure turbulence with hot-wire anemometers a practical guide

6

1.2 Objectives The aim of this project is to confirm the hypothesis, 'Oil surface flow visualization shows streamwise streaks that are thought to result from Grtler type vortices' by measuring the near-wall velocity using a hot-wire anemometer.

This project is a follow-up from successful Nuffield Science Bursary placements in 2012 and 2013 as well as two Erasmus placements from France. This work improves on research done by Sakthitharan Srinamasivayam by lowering the two hot-wires to a height of 1mm above the cylinder using a vertical traverse. In order to achieve this, the following needs to be done:

Restore the computer based probe height control by using the vertical traverse.

Install turbulence screens to elevate the free stream turbulence level.

Calibrate both hot-wires.

Measure and record the near wall velocity at two points over the cylinder surface, at a fixed point and at a second position that is moved in the spanwise direction.

7

2. Experimental set-up

[Figure 3]: Experimental set up

A 10mm section of the laminar boundary layer 1mm from the surface of the cylinder is measured using two hot-wire probes in divisions of 0.2mm at 51 stations. Data on temperature, free stream velocity within the aerodynamic test section and the hot-wire voltage outputs were gathered using a computer running Labview.

2.1 Charles Wilson Wind Tunnel The Aerodynamic test section has the following dimensions:

Length: 4.8m

Height: 0.84m

Width: 1.15m There is a 1.5 meter fan unit, which is powered by a 24kW Ward Leonard set and is capable of producing air velocity up to 30 m/s with a typical turbulence intensity of 0.2%12.

2.2 Cylinder The cylinder acting as the smooth surface has the following dimensions:

Length: 2.5m

Diameter: 0.152m The hot-wire probes were placed at an angle of 30 from the centerline of the cylinder face (see [Figure 9]). The cylinder is made out of aluminum. The reason behind this choice of body rather than an aerodynamic body was to start the experiment from a simple basic model. The angle between the axis of the cylinder and the lateral wall is equal to zero in this experiment, which means the cylinder is unswept13. An image of the cylinder used is shown in [Figure 4].

12 http://www2.le.ac.uk/departments/engineering/research/thermofluids/facilities/charles-wilson-wind-tunnel 13 Measuring streamwise vortices over a circular cylinder using hot-wire anemometry Sakthitharan Srinamasivayam

8

[Figure 4]: Cylinder in aerodynamic test section14

A von Krmn vortex sheet is a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid around blunt bodies. A vortex street will only form at a certain range of flow velocities, specified by a range of Reynolds numbers. The range of Reynolds values will vary with the size and shape of the body from which eddies are being shed, as well as with the kinematic viscosity of the fluid. The range for circular cylinders is 47

9

[Figure 6]: L-Plate to prevent vortex shedding

Elliptical side plates were attached next to each wall of the wind tunnel, as shown in [Figure 7], in

order to eradicate the side wall boundary. These sidewall boundary layers are likely to disturb the

settling down of streamwise streak spacing. The elliptical sideboards used in this experiment were

designed by Dr Aldo Rona from the University of Leicester.

[Figure 7]: Elliptical sideboards

10

2.3 Mesh Turbulence Screen The Mesh Screen used is a woven stainless wire cloth with an 11mm aperture and 1.6mm bar diameter. It is welded onto the far left hand side of the aerodynamic test section which is 1450mm from the centreline of the circular cylinder, as show in [Figure 8]. The mesh screen provides a 0.86% turbulence intensity.

[Figure 8]: Mesh screen position

The mesh screen was designed by myself, using references from Cascade Aerodynamics by J. P.

Gostelow17, with a target of achieving 1% turbulence intensity (see appendix 4). However, due to

manufacturing constraints, a tolerance of 0.25% was agreed.

2.4 Traverse

The wind tunnel has a two-axis traverse attached to its roof, which is aligned at a 30 angle from the centreline of the circular cylinder, as shown in [Figure 9]. The traverse is controlled by Labview which moves it in the spanwise direction using a motor according to an array of previously specified distances. The traverse was also designed to allow vertical movement, also controlled by Labview. This enabled the traverse to be moved to any desired height. In the case of this experiment, we wanted the hot-wire probes to be 1mm away from the surface of convexity.

[Figure 9]: Traverse Position [Figure 10]: Traverse

17 http://books.google.co.uk/books/about/Cascade_aerodynamics.html?id=MdxSAAAAMAAJ&redir_esc=y

11

2.5 Hot-wire Probe Hot-wire anemometers measure the instantaneous velocities and temperature at a point in a flow. A very fine wire is used, which is electrically heated up to a temperature above ambient18. It is an invasive technique as the probe has to be placed which will disturb the flow. These effects are relatively small. It has a quick response time which allows it to measure small rapid changes in velocity. The most common type of probe is a constant temperature anemometer (CTA). They have an extremely thin wire sensor, made from tungsten, mounted on two supports which hold and direct electricity to the wire. Two CTA single sensor (wire) probes are used in this experiment. A probes resistance is proportional to the temperature of the hot-wire. Thermal anemometry uses this fact, as the cooling effect of the flow causes the hot-wire temperature to steadily drop, thus, changing the resistance of the hot-wire. CTA works by connecting the probe to a Wheatstone bridge ([Figure 11]) with a chosen resistance as an offset. As the resistance of the probe differs due to the cooling effect caused by the wind, a servo amplifier keeps the bridge in balance by controlling the current so that the resistance is kept constant. Hence, the temperature through the wire will be kept constant and the difference in the bridge voltage will represent heat loss which is a direct measure of velocity fluctuations in the area being investigated19.

[Figure 11]: Wheatstone bridge circuit

2.6 Reynolds Equation

Reynolds number is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions20.

Re = air uflow D

air

Re = Reynolds number = Density (kg/m) u = free-stream velocity (m/s) D = diameter of cylinder (m) = dynamic viscosity (kg/ms)

18 http://en.wikipedia.org/wiki/Anemometer 19 Measuring streamwise vortices over a circular cylinder using hot-wire anemometry Sakthitharan Srinamasivayam 20 http://en.wikipedia.org/wiki/Reynolds_number

12

In this experiment the Reynolds number is will be 150000. The diameter of the cylinder is constant

and the density and dynamic viscosity of the fluid are dependent on uncontrollable atmospheric

conditions. Therefore, the only controllable variable in the Reynolds number equation is the free-

stream velocity which, can be calculated by rearranging the equation:

uflow = Re airair D

Where:

air = Patm

Rair Tatm

Patm = laboratory ambient pressure (Pa) Tatm = laboratory ambient temperature (K) Rair = universal gas constant for air = 287.058 (J/kgK) Ambient pressure is measured using a barometer. Ambient temperature is measured using a thermometer in the wind tunnel aerodynamic test section. The dynamic viscosity of air can be calculated using Sutherlands law:

air =A Tatm

32

Tatm + B

Where Sutherlands constants A = 0.000001458 and B = 110.4. The free-stream velocity was determined before the experiment (described in section 3.2) due to the changing environmental conditions.

13

3. Procedure 3.1 Hot-wire Calibration

In order for the hot-wire probe to be used for calculating changes in air velocity, the voltage change with respect to velocity must be identified. This is why both hot-wires were calibrated. The calibration device which is used to calibrate both hot-wires is shown in [Figure 12] and [Figure 13]. Hot-wires are placed into the device (one at a time). It uses a variac to produce variable fan speed and a manometer to measure the pressure. These are linked to a computer that gathers data using Labview. Both hot-wires were calibrated using separate anemometers. These are the same anemometers that are used in the wind tunnel experiment (section 3.2). [Figure 14] shows one of the anemometers used in the experiment. Anemometers contain the power supply and bridge circuit for heating the probe and producing a signal. It has a meter for visually measuring the output voltage.

[Figure 12]: TSI hot-wire calibration device [Figure 13]: Hot-wire instalment

[Figure 14]: TSI 1040 anemometer

Shorting probe Before calibration can begin, a shorting-probe must be used in order to short-circuit the probe cable. This will remove errors in the calibration experiment.

14

Procedure for short-circuiting probe cables:

1. Set bridge output to 0-3 2. Move the dial on the voltage meter to a reference voltage on the bottom scale 3. Place shorting probe in position 4. Turn screw on zero ohms until the reference setting remains stationary on the scale 5. Replace shorting probe with hot-wire probe 6. Find out hot-wire resistance by turning variable decade and pressing zero ohms until the

dial on the voltage meter remains stationary 7. Record the reading on the variable decade 8. Use the temperature ratio (1.8) to find out the resistance by multiplying this by the reading

on the variable decade 9. Change the variable decade to the calculated hot-wire resistance 10. Set bridge output to 0-30 and give the anemometer 15V on the top scale of the voltage

meter 11. Switch to run

The measured hot-wire resistances were:

Moving hot-wire: 6.41

Reference hot-wire: 7.20 Once this is done, calibration of hot-wires can begin. The calibration procedure is achieved by steadily increasing a known turbulent velocity, using the variac. Labview then records the corresponding voltage change. Data can be seen in [Figure 15].

[Figure 15]: Graphs displaying calibration results. Top: Reference probe. Bottom: Moving probe

15

These graphs show that hot-wires respond to a non-linear equation known as Kings Law:

E2 = A + Bun Where E = voltage across the wire (V)

u = velocity of the flow being measured (m/s). A, B and n are constants determined by calibration of the hot-wires. Each hot-wire produced a gradient with an equation equal to a polynomial. It is this polynomial which is used to convert voltage readings into velocity. The following polynomials were produced:

Reference Probe: -130.476 + 128.179E - 43.24E + 4.989E

Moving Probe: -168.404 + 166.472E - 55.84E + 6.412E

3.2 Experimentation Labview was programmed to measure a spanwise 10mm section of the cylinder at 51 stations, 0.2mm apart. The height of both hot-wires from the surface will be 1mm. The moving hot-wire stayed at each station for 300 seconds and gathered data at a sampling rate of 0.556Hz. This gives 167 samples per point. Labview would record free-stream velocity, ambient temperature, reference probe voltage and moving probe voltage. Data was gathered over a period of 4 hours and 15 minutes. The experiment was run on the 12th of March 2014. The atmospheric conditions on the day were:

Tatm = 295.15K Patm = 102547.69Pa

Therefore:

air = Patm

Rair Tatm=

102547.69

(287.058 295.15)= 1.21036 kg/m

air =A Tatm

32

Tatm + B=

1.458x106 + (295.15)32

295.15 + 110.4= 1.82296x105 m2/s

uflow = Re airair D

= 150000 1.822965

1.21036 0.152= 14.86 m/s

Experimental Parameters Due to circulating fluid around the aerodynamic test section, variations in environmental conditions during the experiment are unavoidable. This forces the fluid properties to alter, due to changes in atmospheric pressure and room temperature. Also, work is done on the fluid by the fan inside the aerodynamic test section. This causes an increase in temperature of the fluid and therefore, a decrease in density and an increase in velocity of the fluid. Free-steam velocity was controlled manually during the experiment due to the lack of a working feedback system. Keeping free-stream velocity constant meant Reynolds number was kept constant during the experiment. This was important as changing a fluids characteristics can affect the behaviour of vortical structures.

16

4. Results and Discussion Raw data containing information on hot-wire voltages, temperature and free-stream velocity was acquired from the experiment. It can be seen from [Figure 16], that the voltage recorded dropped in proportion with time.

[Figure 16]: Graph displaying voltages of reference probe from experiment

Possible reasons for the decrease in voltage are due to changes in free-stream velocity and temperature with respect to time. Since free-stream velocity was kept constant during the experiment and we know that temperature increased over time, then errors must be due to the increases in temperature. Graphs representing how free-stream velocity and air temperature varied over time are shown in [Figure 17] and [Figure 18] respectively.

[Figure 17]: Graph displaying free-steam velocity of wind in experiment

4.02

4.03

4.04

4.05

4.06

4.07

4.08

4.09

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Vo

ltag

e (V

)

Probe Position

Reference probe voltages

14.00

14.20

14.40

14.60

14.80

15.00

15.20

15.40

15.60

15.80

16.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Vel

oci

ty (

m/s

)

Probe position

Free-stream velocity

17

[Figure 18]: Graph displaying ambient temperature during experiment

4.1 Temperature Correction of CTA voltages

In order to properly process the results, temperature corrections of the CTA voltages must first be calculated. Temperature correction is only valid if the sensor temperature has been kept constant during the experiment and can only be used for moderate temperature changes in air (5C), which is true in this experiment. Voltages can be corrected using the following formula

Ecorr = (Tw ToTw Ta

) 0.5 Ea

Ea = acquired voltage Tw = sensor hot temperature To = ambient reference temperature before calibration Ta = ambient temperature during acquisition Ta and Ea are variables which were recorded during the experiment. To is a constant and was recorded before calibration, and has a value of 19C. Tw is also a constant. The box provided by the hot-wire probes suggested Tsensor < 300C. With this information and through research to find the average hot-wire temperatures a value of 220C was chosen. All Information on temperature correction was provided by chapter 8 from Dantec Dynamics How to measure turbulence with hot-wire anemometers21 With this information each recorded voltage in each probe position was corrected to remove any errors caused by temperature variation. The results are displayed in [Figure 19].

21 http://www.dantecdynamics.com/docs/support-and-download/research-and-education/practicalguide.pdf

12.0

12.5

13.0

13.5

14.0

14.5

15.0

15.5

16.0

16.5

17.0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Term

pat

ure

(C

)

Probe Position

Ambient temperature

18

[Figure 19]: Graph displaying Reference probe voltages after temperature corrections

This same method was also used to correct the moving hot-wire voltages.

4.2 Processing results Voltage recordings were then converted into velocity, using the polynomials produced by each hot-wire during calibration (See section 3.1: Hot-wire calibration). Once they were converted into velocity, results were normalised in order for the results to be understood better. This was achieved by dividing each point by its average velocity. Normalised velocity results are displayed in [Figure 20].

[Figure 20]: Graph displaying the normalised velocity values

It can be seen that both hot-wire probes produced similar results with the exception of position 48 on the reference probe. The reason for this is unknown and can be seen as an anomaly.

3.99

4.00

4.00

4.01

4.01

4.02

4.02

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Vo

ltag

e (V

)

Probe position

Reference probe voltages after temperature corrections

0.965

0.970

0.975

0.980

0.985

0.990

0.995

1.000

1.005

1.010

1.015

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Probe Position

Normalised velocity values

Reference Probe Moving Probe

48

19

Root-mean-square (rms) velocity of each point was also acquired. This gives the average intensity of turbulence. Rms was calculated using the formula:

urms = u

Where u = turbulence = u u

u = average turbulence Velocity rms results are displayed in [Figure 21], shown below.

[Figure 21]: Graph displaying velocity rms values

Again, the two probes show very similar readings for turbulence intensity. This shows evidence towards streamwise vortices exist on the surface of the cylinder.

4.3 Cross-correlation Cross-correlation is a standard method of estimating the degree to which two series are correlated. It has applications in pattern recognition in long signals, which is why it is used here22. Cross-correlation can be calculated using the following formula:

(, ) = ( )( )

=1

( )2 ( )2=1

=1

23

Where x and y are two arrays of values. In this experiment, cross-correlation was done between the moving hot-wire voltage and the reference hot-wire voltage. [Figure 22] displays the cross-correlation between the two voltages. The numbered arrows point to significant peaks.

22 http://paulbourke.net/miscellaneous/correlate/ 23 http://www.mathsisfun.com/data/correlation.html

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

velo

city

rm

s (m

/s)

Probe position

Graph showing velocity rms values

Ref u rms Mov u rms

20

[Figure 22]: cross-correlation between moving probe voltage and reference probe voltage

[Figure 23] shows the graph pattern over a spanwise area of interest from a previous experiment by Sakthitharan Srinamasivayam.

[Figure 23]: Sakthitharan Srinamasivayams cross-correlation pattern24

The two graphs both display peaks and troughs as well as turbulent fluctuations. Peaks seem to be in similar positions on both graphs, particularly in between probe positions 24 and 51. When my graph is compared with Kestin & Woods graph (shown in appendix 1) and with Sakthitharan Srinamasivayams graph (shown in [figure 24]) the shape is similar to both. Although,

24 Measuring streamwise vortices over a circular cylinder using hot-wire anemometry Sakthitharan Srinamasivayam

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Co

rrel

atio

n c

oef

fici

ent

Probe position

Cross-correlation between the two voltages

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0.050.1

0.150.2

0.250.3

0.35

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

Co

rrel

atio

n c

oef

fici

ent

Probe position

Previous cross-correlation pattern

6

38

15 32

27

44

21

there are varying levels of correlation coefficient with Kestin & Woods graph. The reason for the varying levels of correlation coefficient is unknown so far, however, they all agree on the shape produced.

[Figure 24]: Comparison of experiments

[Figure 24] shows the graph produced form my experiment superimposed onto the graph produced by Sakthitharan Srinamasivayams experiment. As discussed above, these graphs are similar to one another. Particularly, at points labelled [A], [B], [C] and [D] where the similarity is extremely clear. Both experiments were run at the same Reynolds number. The difference between the two experiments was that the free-stream velocity which was approximately 4.86m/s in my experiment and 5.7m/s in Sakthitharan Srinamasivayams experiment. Another difference was that both hot-wires were lowered to 1mm above the surface of convexity in my experiment. Hot-wires were 1.5mm away from the surface of convexity in Sakthitharan Srinamasivayams experiment. Since there are similar peaks in between probe position 24 to 51, this provides evidence to the repeatability of the experiment as random turbulent fluctuations would not produce such an evidently repeating pattern. The reason for this lack of similarity in the first half of the experiment may be due to the fact that vortical structures had not yet been fully developed. Surface patterns form spontaneously in a laminar or turbulent flow. In the previous experiment, data gathering had started 40 minutes after the flow had started to allow patterns and vortical structures to form and fully establish themselves. Despite the several points of correspondence, both graphs still agree in a lot of positions with turbulent fluctuations. By repeating the experiment, we can reduce the effect of turbulence on this research and further analyse for more substantial patterns. My experiment shows that the average wavelength of the vortices is approximately within the range of = 1.8mm - 2.4mm. In the experiment run by Sakthitharan Srinamasivayam, the average wavelength wavelength was within the range of = 2.0mm 2.6mm. This is very similar to my experiment. Therefore, this provides further evidence for the experiment being repeatable. An experiment by Myriam De Saint-Jean, Aldo Rona and J.P Gostelow25 found wavelengths equal to 2.14mm and 2.31mm under the same conditions as this experiment. This advocates that the wavelength of the vortices changes marginally from each experiment.

25 http://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/sjg50/turbomachin

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Co

rrel

atio

n c

oef

fici

ent

Probe position

Chart Title

A B C

D

22

According to Kestin and Wood26, the theoretical spanwise wavelength between vortex pairs for a cylinder is given by:

= 1.79 2R

Re0.5

In this experiment: Re = 150000 R = 0.076 Therefore = 2.207mm This theoretical value lies within the range of wavelengths found through my own experiment.

4.4 Improvements By repeating the experiment, it would eliminate anomalies such as position 48 on the reference probe. It would also produce further comparable evidence to the presence of streamwise streaks and allow patterns to be further analysed. It would also significantly improve the results if streamwise vortices were given time to form before starting to take readings. In Sakthitharan Srinamasivayams experiment, 40 minutes was allowed for these structures to form before readings were taken. Another aspect of the experiment which could be improved is the potential use of a feedback system to control the free-stream velocity and therefore, keeping Reynolds number constant. Using a feedback system will help minimize fluctuations in the free-stream velocity when compared to a human input. The use of a slanted hot-wire probe would also improve the experiment. As can be seen in [Figure 25], a straight hot-wire probe creates and angle with the surface of the circular cylinder therefore, a large area is left which is not being measured. Since vortices are formed perpendicular to the surface, this causes a problem. A slanted probe would be considerably closer to the surface and it would be also parallel to the surface. It would be able to include the area not being measured which would lead to more accurate results.

[Figure 25]: Area not being surveyed

4.5 Error analysis Since a lot of digital devices were used in this experiment, it is inevitable that equipment error will occur and effect the results.

Free-stream velocity was measured using a device with an increment of 0.1m/s.

Temperature was measures using a digital thermometer with an increment of 0.1C.

The CTA had an increment of 0.1V.

26 J. Kestin & R.T. Wood. Enhancement of stagnation-line heat transfer by turbulence. Progress in heat and mass transfer, Vol. 2, pp. 249-253, 1969.

23

Systematic errors are due to a known cause and can be removed in practice. The absence of a feedback system to control free-stream velocity is a systematic error. Flow characteristics of the wind changes inside the wind tunnel due to the changing atmospheric conditions. The velocity of the wind is kept constant manually using a dial. This is much less accurate than an electronic feedback system which would be more beneficial.

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5. Conclusion The experiment confirms the objective by providing evidence for the existence of

streamwise vortices on the surface of convexity, which have a spanwise wavelength roughly equal to 1.8-2.4mm.

The experiment also confirms that Kestin & Woods zero-sweep theory can be used as a basis for predicting the spanwise wavelength of the streamwise vortices for bluff bodies such as the cylinder used. Because, the theoretical wavelengths lies in the range of experimental wavelengths.

The results attained also confirm that the experiment is repeatable as they agree with results attained by Sakthitharan Srinamasivayam after probe position 24. The reason for this lack of similarity before position 24 is explained in section 4.4.

Overall this experiment improved on Sakthitharan Srinamasivayams work by moving the probes closer to the surface of the cylinder. From 1.5mm to 1mm.

5.1 Divergence from project proposal A change from the original project proposal is the change in sampling frequency and time spent at each position. Initially, probes were supposed to remain in each position for 200 seconds and take 1000 samples per data point. This would give a sampling rate of 5Hz (5 samples per second). However, the circuit within Labview was only able to complete a loop approximately once per second and two loops needed to be completed to record a data point. This lead to an alteration in time spent at each position which would be 300s and we would take 167 samples per point. This gives a sampling rate of 0.556Hz.

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Appendix Appendix 1: Kestin and Woods theory The traverse was at an angle of 30 from the centre of the cylinder. This traverse was taken on a

cylinder of D=107.2 mm in diameter giving, =1.5 mm.

Hot-wire measurements produced a spatial correlation curve taken with one hot-wire stationary and

one traversing along a line parallel to the axis of the cylinder. Both hot wire probes were placed at a

distance of about half a boundary layer thickness away from the cylinder. In all cases there resulted a

periodic pattern of correlation signals.

[Figure 27]: Kestin and Woods correlation

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Appendix 2: Labview Interface

[Figure 28]: Labview interface

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Appendix 3: Calibration results

Moving hot-wire probe

anemometer voltage (V) contraction pressure (Pa)

0.000 2.555 0.009

5.213 3.459 16.415

13.386 3.909 108.252

20.936 4.168 264.795

26.123 4.309 412.249

31.709 4.432 607.437

37.790 4.558 862.745

43.294 4.638 1132.347

48.668 4.715 1430.903

54.300 4.796 1781.235

55.938 4.822 1890.361

Reference hot-wire probe

anemometer voltage (V) contraction pressure (Pa)

0.000 2.592 0.034

4.142 3.459 10.294

12.270 3.976 90.339

18.429 4.217 203.789

24.483 4.398 359.671

30.417 4.550 555.121

37.336 4.694 836.390

44.036 4.810 1163.540

50.313 4.908 1518.858

55.355 4.979 1838.565

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Appendix 4: Mesh Screen Calculations

[Figure 29]: Chosen mesh screen

Tu = 112 (x

b)

57

= 112 (1450

1.6)

57

= 0.86%

Where Tu = Turbuelnce intensity

b = wire diameter

x = distance of centre of cylinder to the position of the screen