Investigation into Streamwise Vortices Occurring from Flow Instabilities over an Unswept Cylindrical Body Nuffield Research Project 08/2015

Lucy Bennett

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Table of Contents Abstract ................................................................................................................................................ 3

Introduction .......................................................................................................................................... 3

Methodology ........................................................................................................................................ 6

Apparatus ......................................................................................................................................... 6

Charles Wilson Wind Tunnel ......................................................................................................... 6

Traverse ........................................................................................................................................ 7

Elliptical Sideboards ...................................................................................................................... 7

Trailing Edge L-plate ...................................................................................................................... 8

Simple Pitot Anemometers ........................................................................................................... 9

Pitot-Static Anemometer ............................................................................................................ 10

Calculation of the Height of the Boundary Layer ............................................................................ 12

Differential Pressure Transducers ............................................................................................... 12

Calibration ...................................................................................................................................... 12

Calibration of Differential Pressure Transducers ........................................................................ 12

Calibration of Pitot Anemometers .............................................................................................. 13

Conditions ....................................................................................................................................... 15

Reynolds Number ....................................................................................................................... 15

Signal Acquisition ............................................................................................................................ 16

Acquisition Rate .......................................................................................................................... 16

Station Spacing ........................................................................................................................... 16

Probe Position Reference............................................................................................................ 17

Results and Discussion ........................................................................................................................ 18

Post Processing and Analysis Techniques ....................................................................................... 18

Results ............................................................................................................................................ 19

Error ................................................................................................................................................ 22

Conclusion ...................................................................................................................................... 23

Evaluation ........................................................................................................................................... 24

References .......................................................................................................................................... 24

Bibliography ........................................................................................................................................ 25

Acknowledgements ............................................................................................................................ 25

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Figure 1: Surface oil visualisations recorded by Durham University at a wind

velocity of 30m/s and sweep angle of 60

Abstract

The research set out to investigate the existence of Grtler type vortices formed on the leading edge

of an unswept cylinder through measuring the near-wall pressure using Pitot anemometers. It was

decided to revert to a more traditional way of measuring pressure because it was felt that the

previous method of using hot wire anemometry, although sensitive, gave readings over a sample

area which was too great to detect the very small vortices. It was found that there is strong evidence

of the intermittency of streamwise, Grtler type vortices on the leading edge of unswept cylinders at

a Reynolds number of 140,000.

Intermittency

Introduction

It is thought that the streamwise boundary layer vortices forming at the leading edge of rotating

turbine blades in an engine add up to 10% inefficiency to a system when considered over all blades.

This is due to the mixing of flows it creates, leading to an enhanced rate of boundary layer growth.

Boundary layer instabilities therefore increase the rate of heat transfer and drag, whilst decreasing

lift and overall efficiency. A better understanding of their nature, as well as how, when and why they

form may lead us to a way of controlling the instabilities and potentially reducing fuel consumption,

heating effects and drag. This could have a dramatic impact on engines, aerofoils and wind turbines,

as well as wider applications such as in bioengineering where aerodynamics and research into

boundary layer instability is being used to determine illness through looking at the flow patterns in

the lungs otherwise undetectable through conventional scans.

Streamwise striations consistent with pairs of counter rotating vortices on the leading edge of a

cylindrical body, normal to the direction of flow, , were first observed by Grtler [1] in 1940

through oil surface visualisations similar to those found by Durham university. These vortices can be

seen in figure 1 by the streaks that they leave behind in the oil, created by up-wells scraping at the

surface, and down-wells depositing on the surface. Grtler developed a way of categorising these

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vortices based on their Grtler number; however, we are still unsure today as to what causes the

vortices to form, and much about their behaviour.

There are two main theories on their formation:

Grtler found that if the boundary layer (figure 3) was relatively large in comparison to the radius of

the cylinder, a pressure difference would occur over the boundary layer, leading to the flow

undergoing centripetal acceleration, caused by the resultant transfer of momentum. This produces

areas of low and high shear in the boundary layer, resulting in the formation of vortex structures

(figure 2).

The other theory is that the centripetal instabilities occur as the flow accelerates over the convex

surface of the cylinder in order to circumvent the obstacle (figure 4).

Our hypothesis was based on the fact that the two current theories revolve around the same

principles, and so it would not be unreasonable to predict that the vortices would form in both the

boundary layer of the flow, and further out where the negative pressure gradient occurs through the

placement of the cylinder.

Figure 2: Boundary layer vortex formation [3] Figure 3: Velocity vectors showing the boundary layer.

Figure.4: Negative pressure gradient vortex formation.

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Figure 5: Measurements of spanwise wavelength on circular

cylinders against increasing Reynolds number.

Previous computational and experimental research by Kestin and Wood [2] on the effects of changing Reynolds number and sweep angle found an equation for the wavelength, , of the vortices:

= 1.790.5

= Diameter of the unswept cylinder = Reynolds number

Kestin and Woods research has been further confirmed by similar experiments on the relationship

between Reynolds number and vortex wavelength (figure 5) by A Rona & J.P Gostelow [4],Myriam

de Saint Jean [5], as well as research by Poll [6] and Kohama [7]. In addition, work by Alexandra

Mailleur [8] using hot-wire anemometry found that the vortices she detected had a characteristic

wavelength of 2.2mm, which is in agreement with Kestin and Woods widely accepted model for

these vortices.

One of our aims was to see if our

readings, at a lower Reynolds

number, would indeed support this

research. In addition, detecting the

structures had proved difficult in

previous experiments conducted on

the leading edge of an unswept

cylinder at a similar Reynolds

number, so we wanted to

investigate whether our results

would shed light on the

intermittency the pattern seemed

to show. We also wanted to

investigate further into the

wavelength of the vortices to see if

our results would be consistent with

previous estimations.

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Methodology

Apparatus

Charles Wilson Wind Tunnel

For all of our readings, we used the Charles Wilson wind tunnel; a low-speed closed circuit wind tunnel, located at the University of Leicester. The tunnel has a wooden frame structure, with 13mm birch-faced ply lining it. There are two main test sections to the tunnel; for our investigation, we used the smaller one, detailed below, to achieve a higher velocity and therefore Reynolds number. Charles Wilson wind tunnel specification:

Overall length: 20.4m

Overall width: 6.4m

Maximum height: 1.9m

Power supply: 24kW Ward Leonard set

Fan unit: single 1.5m eight bladed true aerofoil section axial belt-driven fan Aerodynamic test area:

Length: 4.8m

Width: 1.15m

Height: 0.84m

Maximum air velocity: 20ms-1

Typical turbulence intensity: 0.2%

Figure 6: The Charles Wilson wind tunnel

Figure 8: The work space Figure 9: The 1.5m eight bladed true aerofoil section fan belt-driven fan

Figure 7: Lauren and I in the tunnel

Cylinder

Turbine

Entrance

Work space

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Traverse

On the roof of the test section, a two-axis LabVIEW controlled traverse system was mounted to

move the probes along the span of the cylinder (figure 10). The stepper motor (figure 11) and gears

mean that it has a vertical precision of 0.1mm and horizontal precision of 0.01mm. However, due to

the nature of the drive train, the system does have around 1mm of backlash.

Elliptical Sideboards

The wind tunnel has two elliptical sideboards (figure 12) designed to part the turbulent boundary

layer flow accumulating on the walls of the tunnel from the laminar flow in the centre. This should

prevent the side-wall boundary layer interfering with the streamwise vortices. However, the plates

unfortunately oscillate when the air is at a high velocity, meaning that they may themselves cause

other forms of interference.

Figure 11: The inside of a stepper

motor Figure 10: The traverse

Figure 12: The test section, with elliptical sideboards

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Figure 14: 0.5 < Re < 70 boundary layer

separation of a cylinder [9]

Figure 13: Re < 0.5 boundary

layer flow over a cylinder [9]

Trailing Edge L-plate

At very low Reynolds number (Re < 0.5) the boundary layer will move around a cylindrical body

happily due to only slight pressure changes (figure 13). At a slightly higher Reynolds number

(0.5 < Re < 70) the boundary layers separate symmetrically on either side of the trailing edge of the

cylinder (figure 14).

However, at Re > 70 the flows curl up and detach alternately from the cylinder in a von Krmn

vortex sheet (figure 15).

A von Krmn vortex sheet is caused by the unsteady separation of air around a blunt trailing edge,

and generates heavy turbulence in the flow. We used a Reynold number of 140,000, meaning that

this effect would be present in our experiment.

The flow interferes with the vortices that we are measuring and may hinder their formation. To

prevent von Krmn vortex shedding taking place, we fitted an aluminium L plate (figure 16) to the

trailing edge of our cylinder, stopping the two flows from interacting at the point of measurement.

Figure 15: Von Krmn vortex street caused by the unsteady

separation flow of a fluid around blunt bodies.

Figure 16: The aluminium L-plate

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Figure 17: Simple Pitot tube

Simple Pitot Anemometers

Simple Pitot tubes (figure 17) act as a way of sampling air from a

specific area and measuring the pressure that it is under at that point.

Figures 18 and 19 show the specifications for the pitot probes which

we designed on Solidworks. We ordered the thin wall stainless steel

tubing at a gauge size 24 (0.381mm). We chose such a small tube so

that our sample area was as small as possible, allowing us to detect the

localised pressure changes along the cylinder caused by the vortices.

We used a fully circular head (figure 20) because an elliptical head would have only be advantageous

if we were aiming to get as close to the surface as possible; as this was not the case, and because it

would have increased the chances of the probes being non-identical, we decided to use circular

heads.

Figure 18: CAD drawing of the Pitot probe used to

measure the near wall velocity at the cylinder. Figure 19: CAD drawing of the probe head.

Figure 20: A circular head probe and an elliptical head probe

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Figure 21: CAD model of our three probes in relation to the cylinder;

the two traversing probes (right) are so close, the look as one.

Figure 22: Pitot-static tube

We used three identical probes; one reference probe, which was in a fixed position, and two

traversing probes that took measurements along the span of the cylinder (figure 21).

Pitot-Static Anemometer

We used one Pitot-static tube (figure 22) located in front of the apparatus to

measure the pressure, from which we calculated the flow velocity in the test

section.

A Pitot-static probe has an inner tube and an outer tube (figure 23); this allows it to measure both

the total and static pressure.

Figure 23: Pitot-static probe

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The static pressure can be connected to each of the reference inputs on the differential pressure

transducers, so that the dynamic pressure of each probe can be found using Bernoullis equation,

which is derived from Newtons 2nd Law:

+1

22 = 0

P =Static Pressure /Pa 1

22= Dynamic Pressure /Pa

P0 = Total Pressure /Pa = Air Density /kgm-3 u = Flow velocity /ms-1

Meaning basically that the dynamic pressure is equal to the total pressure minus the static pressure. The larger Pitot anemometer was also used in our experiment to calculate the velocity of the wind.

Because the density of the air, , is defined as:

=

p = Absolute pressure /Pa R = Specific gas constant (287.05) /Jkg-1K-1 T = Temperature /K

The velocity, u, is calculated by rearranging Bernoullis equation:

= 2(0 )

The LabVIEW program installed on the computers in the wind tunnel interprets the pressure

received and then applies the rearranged Bernoullis equation to find the velocity, giving the output

data in m/s.

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Tota

l pre

ssu

re

Static pressu

re

(0 5)V

Figure 24: Diagram of a differential pressure transducer.

Calculation of the Height of the Boundary Layer We estimated that the boundary layer extended to around 1-1.5 mm. However, we conducted a

short experiment where we changed the vertical positions of the probes and then compared the

pressure at each height. This told us that the boundary layer extended to roughly 0.8-1.2 mm from

the cylinder. This allowed us to confidently exit the boundary layer when we took readings at

1.4mm.

Differential Pressure Transducers

We used 4 differential pressure transducers to

determine dynamic pressure at each probe. The

instruments work by having a diaphragm that is

pushed one way by the total pressure input, and

then pushed the other way by the static pressure

input, giving the differential pressure (figure 24). The

total displacement of the membrane of the

diaphragm is measured by a capacitive sensor. This

then generates a voltage output of 0-5V, which is

read by the computer.

The differential pressure transducers have four

different settings: velocity, pressures 0-200 Pa,

pressures 0-2000 Pa, and pressures 0-7000 Pa. We

decided to use the 0-200 Pa setting so that the

complete range of 0 to 5 volts would be used, giving us

much better digital resolution.

Calibration

Calibration of Differential Pressure Transducers

When we took wind-off readings we found that the differential pressure transducers were calibrated

slightly differently, so did not give the same outputs for identical inputs.

We decided to use the differential pressure transducer that had the most recent calibration as the

most accurate one, and then cross calibrate from that one. To do this, we measured the output

voltage of the instrument at different pressures by adjusting the wind velocity in the tunnel.

This allowed us to plot a graph of pressure (Pa) against voltage (V) to measure the gradient (105.68,

the voltage coefficient) and y-intercept (-0.18, the gain). We inputted this into the LabVIEW program

so that for each voltage received by the computer, it would multiply it by 105.68, then minus 0.18 to

give us an accurate pressure reading. This was done for each pressure transducer, and then checked

at different pressures to ensure that all instruments were giving correct readings.

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Calibration of Pitot Anemometers

To test that the Pitot probes were detecting the correct pressure at the correct time, we positioned

them all in the test section at the same height above the cylinder (clear of the boundary layer). We

then measured their outputs over a changing velocity from 0m/s to 20m/s. We plotted this and

found that there was a lead and lag pattern to the data (figure 25). The reference probe and probe 2

seemed to lead, with probe 1 lagging behind.

We thought that this could have caused by one of two problems: either the bend in one of the Pitot

probes was narrower so that it would take longer for the volume to fill or that one of the tubes

was longer, meaning there was a larger volume to fill. To overcome this, we switched the tubes at

the probe end; this solved the problem meaning that as soon as the pressure changed, the Pitot

probes would detect it at the same time, allowing us to compare between probes at similar times

(figure 26).

Ref

Figure 25: Graph showing the lead/lag in readings.

Figure 26: Graph showing the corrected lead/lag in readings.

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We then did some runs at a constant velocity to check that the probes were measuring similar

pressures. At first we found that the reference probe was measuring a lower pressure which

fluctuated much more than the other two; we interpreted this as the probe being slightly below the

other two, meaning that it was just inside a turbulent boundary layer (figure 27).

We then realigned the probes so that they all were at the lower height, and found that they all

detected the highly fluctuating boundary layer trace (figure 28). This meant that all probes gave

readings within a range of 4 Pa.

Figure 27: Graph showing the difference in pressure readings between probes.

Figure 28: Graph showing the final range of pressure readings of probes

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Conditions

Reynolds Number

We firstly considered at what Reynolds number we wanted to run the experiment. A Reynolds

number is the ratio of inertial forces to viscose forces in a fluid, and is a good way of comparing the

conditions affecting the flow. It is often used as a way of keeping conditions constant when

conducting experiments on scaled down aeroplanes and wing sections. This is because if you were to

simply scale down the wind velocity in the same ratio of the model, then if would be like testing the

model in honey, and thinking the effects would be the same.

Reynolds number, , is defined as:

=

Re = Reynolds number air = Density (of air) /kgm

-3 Vair = Flow velocity (of air) /ms

-1 = Cylinder diameter /m (=0.152 for our cylinder) air= Air viscosity (of air) /kgm

-1s-1

Previous studies by various researchers show that the wavelength, , of the vortices reduce with

Reynolds number (see figure 5). In addition, in experiments on a yawed cylinder, Tokugawa, Takagi &

Itoh [10] found that at higher Reynolds number the vortices could be identified more clearly because

of the larger pressure difference across them.

As mentioned earlier, we decided to use the differential pressure transducers on their 0-200 Pa

setting for a better resolution. This therefore limited the maximum velocity, Vair, we could use to

17.5m/s, because above this velocity the pressure was greater than 200 Pa.

In addition, the diameter, , of the cylinder was fixed at 0.152m.

The density of air, , cannot easily be manipulated because it is based on the absolute pressure

and temperature, ( =

) which we cannot control.

The viscosity of air, air, is defined as:

= 1.458 106

1.5

+ 110.4

Tair = temperature of air/K

This therefore is dependent on the temperature of the room, so is also difficult to change.

This left us with a maximum achievable Reynold number of 140,000 for our tunnel and conditions.

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Distance between traversing probes (5mm)

~ 2mm

Distance between stations (0.25mm)

Figure 29: Scale diagram showing the vortices (black), distance between probes (blue) and the distance

between stations (green).

Signal Acquisition

Acquisition Rate

We wanted to take readings at a high acquisition rate so that we could then take averages over the

same flow conditions. The fastest acquisition rate without altering the LabVIEW program was

8000 Hz, which would allow us to take 30,000 readings in fewer than 4 seconds. With these 30,000

readings, we set the LabVIEW program so that it would calculate an average over every 100

readings; giving us 300 averages per station. This high number of acquisitions per station allowed us

to reduce the percentage error in each reading and therefore have a more informed picture of the

flow pattern.

We felt that at each station we wanted the air to have travelled for a reasonable length of time so

that it could settle and we could measure the true pressure, and not random eddies. The flow

roughly travelled at 20 m/s, so if the exposure at each station was 40s, this allowed the flow to have

travelled around 800m; a suitably long distance for us to be able to separate minor fluctuations from

trends.

With these two parameters set, we knew that we were going to take 300 averages (30,000 raw

samples) over an exposure time of 40s at each station.

Station Spacing

We knew that the wavelength, , of the vortices we were looking for were approximately 2mm. The

traverse system was specified to have a horizontal resolution of 0.01mm, which we confirmed by

measuring the teeth on the screw thread and the movement of the stepper motor.

We originally planned to traverse the two probes side by side, however this proved too difficult due

to the 2.98mm collar each probe had around it. Various methods were brainstormed, including

having a swanned necked probe so that the opening of the Pitot could sit alongside the other one;

however, this would make manufacturing a consistent bend on all three probes very difficult. In the

end we settled to hold the probes 5mm apart a distance far enough so that they would not

interfere with each other, yet close enough so that they could overtrack if we traversed far enough.

The spacing between each station was decided on by the fact that we wanted a minimum of 4

stations per individual vortex (8 per ) and it would be beneficial if the second probe could re-

measure the pressure the first probe measured previously, giving us an offset of time, but not

displacement. Therefore, we moved in increments divisible by the 5mm separation between probes.

A station distance of 0.25mm allowed us to have 8 stations per wavelength, and an overlap in probe

positions of 1.5 . This means that we collected 960,000 raw data points in each run over 21

minutes. Figure 29 shows a scale diagram of this set up with the vortices pictured as rotating circles.

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Probe Position Reference

We positioned the simple Pitot probes so that they would lie normal to the 60 azimuth angle, and

so that they would all measure air at the height of the 60 line (figure 30) as this is where the

vortices are thought to be most organised and defined.

In practice, positioning the probes proved to be quite complex due to it being difficult to find a

reference point to work from; the floor of the test section was neither perpendicular to the wall, nor

was it parallel to the cylinder or roof. In addition, we had no reference on the cylinder itself. We took

the direction of wind flow to be , the centreline of the cylinder to be , and the upright height of

the probes to be . With this coordinate system we could calculate the height of the line (from the

floor) on the cylinder that would be at 60, and then align the probes with this information (figure

33). We used feeler gauges to ensure that the probes were not touching the cylinder surface, and

then used the traverse to accurately position the height of the probes.

Figure 31: The reference and traversing

probes on the cylinder.

Figure 32: The two traversing probes in

position.

Figure 30: The probes at 60to the

horizontal on the cylinder.

Z

Y

Figure 33: The cylinder and probes with the axes labelled

and 60 line shown.

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Figure 36: Graph showing the changes in

pressure independent of the changes in tunnel

velocity.

Probe 1 Probe 2

Results and Discussion We conducted runs of the experiment over 11 separate days; conducting 28 tests in total, 20 of

which were complete runs. In each run, we gathered 960,000 pieces of raw data.

Post Processing and Analysis Techniques To process and analyse the data we used MATLAB, a high-level technical computing language and

interactive environment for algorithm development, data visualization, data analysis, and numerical

computation.[11]. Using MATLAB, we wrote a script that allowed us to process all the data in the

following steps, producing a graph at each stage:

1 Average temperature data at each station (giving 32 averages with error bars)

2 Average velocity data at each station (with error bars)

3 Produce one average for pressure over each 300 results at each station (giving us 32

averages in total), for each probe

4 Divide the average for each traversing probe pressure by the average for reference probe

pressure at each point.

5 De-trend the graph

When the average pressure at each station was plotted for each probe, we found that it was difficult

to distinguish changes in pressure due to the presence of vortices from changes in pressure because

of fluctuations in the velocity of the tunnel (figure 34).

Keeping the velocity constant was difficult because

even with constant manual correction, the fan speed

varied from 548rpm to 550rpm. However, you can

see by comparing figures 34 and 35, that changes in

the velocity affected all probes equally. Therefore,

we were able to identify changes in pressure

independent of changes in velocity by dividing the

pressure measured in the traversing probe by the

pressure measured in the reference probe( /).

Figure 34: Graph showing the velocity at

each station

Figure 35: Graph showing the pressure at

each station

This gave us figure 36, which is a true reflection of

localised pressure change.

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Figure 38: Graph showing signs of vortices in both probe 1 and

probe 2, with a wavelength of around 1.8mm

Figure 37: Graph showing the / over the 32 stations,

with signs of vortices with a wavelength of around 1.5mm

being present

Probe 1 Probe 2

Probe 1 Probe 2

Figure 39: Graph showing more vortex structure with a

short wavelength of 1mm (probe 1)

Probe 1 Probe 2

Results We found some supporting evidence for the presence of streamwise vorticity in the boundary layer;

figure 37 shows one of our results which seems to indicate pressure changes consistent with vortex

structures in the boundary layer.

Arrows on figure 37 have been added to highlight where we think vortices appear. Regarding probe

2, a pattern at stations 3 to 15 seems to show the formation of vortex structures along the cylinder.

Moreover, this pattern can be seen further along the cylinder at stations 23 to 34. This suggests that

there is indeed a vortex structure present that occurs on and off along the span of the cylinder. From

figure 37, you could estimate the wavelength of the pairs of vortices to be around 1.5mm (four

vortex structures spanning 12 stations, spaced 0.25mm apart, would give 1.5mm for every two

vortices).

Figure 38 shows more evidence of vortices, recorded on the same day as figure 37. Probe 2 detects a

vortex pattern with wavelength of around 1.8mm; however, this is only present in later stations,

with almost no vortices detected at the start of the experiment.

Probe 1 also detects changes in pressure;

however, these are less clear and again they

appear more prominent from station 20

onwards. The wavelength of these vortices

seems to be around 1mm.

Figure 39 gives more evidence of areas of higher

and lower pressure in the boundary layer, but

the vortices do not seem to be in an organised

pattern like the surface oil visualisations suggest.

Furthermore, in figure 39 large gaps between

pairs of or single vortices can be seen that do not

correspond to previous research such as Kestin

and Woods [2].

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Some of our results did not show vortex structures. It is hard to distinguish any clear vortices in

figure 40; the pressure did seem to fluctuate a lot, but not in a way that reflects the presence of

vortices.

Furthermore, with the de-trend function applied (figure 41) it shows that in there are no obvious

pressure changes when the general downward drift of figure 40 is straightened. If vortices were

present during these runs, we did not detect them.

We found that on certain days, all of our results reflected figures 40 and 41: on 4 separate runs on

one day, each set of results was just as inconclusive as the next, with the implication being that the

vortices were not present that day. However, on other days we would collect many sets of results

which showed clear signs of streamwise vorticity in the boundary layer, compatible with previous

research by Kestin and Wood [2] and Grtler [1].

This gives a strong indication that the vortex structures in the boundary layer are an intermittent

pattern, present on some days in certain conditions, and not on others. However, it is not clear what

conditions effect the formation of the vortices, and allow them to form on some days but not on

others.

Figure 40: Graph showing / over the 32

stations with no obvious signs of vortices.

Figure 41: Graph showing / detrend, with no

clear vortices detected.

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Lastly, we changed the height of the probes so that they were 1.4mm above the surface of the

cylinder, and thus out of the boundary layer. Figure 42 shows that there are a few pressure rainbows

that could be vortex structures out of the boundary layer. As we were 1.4mm above the cylinder, the

pressure was more uniform than at the lower height, and therefore any changes detected are more

reliably as a result of streamwise vorticity as opposed to minor changes in the height of the

boundary layer. However, there is no clear pattern of vortices present, and we do not know if we are

merely detecting the top of vortices that formed in the boundary layer or vortices that formed due

to the flow undergoing centripetal acceleration when circumventing the cylinder.

Kestin and Woods theory that the vortices stretch and adapt their wavelength depending on the conditions [2] would give us a wavelength, , of:

= 1.790.5 = Diameter of the unswept cylinder = 0.152

= Reynolds number = 140,000

= 1.79 ( 0.152 140,0000.5)

= 2.28

Our results did not support this estimate; we found that the vortices (we detected) had a

characteristic wavelength of 1.6mm-1.8mm. However, we would need more evidence of a repeating

pattern before making a valid estimate of wavelength.

Probe 1

Probe 2

Figure42: Graph showing vortices above the boundary layer

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Figure 43: Backlash in a gear system

Error

Averaging

We took averages over each 100 raw data points, to record one reading, and then took an average

over the 300 readings collected at each station. This allowed us to take the mean value, rather than

record any eddies in the flow as vortices. Nevertheless, taking an average at each station would have

only been beneficial if the conditions stayed the same throughout the exposure. To check that our

averages reflected the true measurements, we took the standard deviation calculated by the

LabVIEW program at the point of measurement, and plotted it as error bars on our graphs

By including error bars in our graphs, we could see the uncertainty in our measurements and

therefore assess reliability of them. The standard deviation in each reading was typically 0.01 to 0.02

and the error bars over the average of 300 readings were typically around 0.15 Pa for a typical

reading of 180 Pa. This confirms that the averages we took were reflective of the data and that the

conditions stayed constant over the 40 second exposure.

Traverse

Because the traverse has a gear system, backlash may occur (figure 43). We calculated that the

backlash was around 1mm. To reduce the impact of this on our probe positioning, would take the

traverse to -1.5mm from our datum, then move it back to our 0 point. This took out any play in the

gears and meant that the system was moving

in the direction the traverse would then

travel in. We were unable to measure the

backlash in the vertical (z) direction, however

we mostly manually adjusted the height of

the probes using the grub screws holding

them.

When we first started collecting results, we

found that the two traversing probes would

measure gradually increasing pressures as

they moved along the cylinder. We found that this was because the cylinder sloped away from the

traverse at a gradient of roughly 1.3mm per metre which could be considered negligible; however,

since the boundary layer gradient is so steep, microns difference in height equates to a sharp change

in pressure. This meant that as we traversed along the cylinder, we found that the pressure for the

two traversing probes increased at the same rate, as can been seen in the results. This could mean

that some of the structures we identified as vortices were merely steps in pressure due to a change

in height.

Velocity Control

In the post-processing section it was mentioned that the speed of the tunnel had to be manually

controlled using a rotary potentiometer switch, which led to an non-constant flow velocity. We

managed to reduce this effect dramatically by plotting /, explained previously. However, it is

possible that errors may have crept in through this process, and that the changing velocity may have

somehow affected the probes differently.

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Electronics

We were concerned that as the electrical equipment gradually heated up when first switched on, it

may impact on the digital output from the manometers. This could mean that readings would

change until the electrical equipment was at a constant temperature. We therefore ensured that all

of the equipment was turned on for a minimum of 30 minutes before taking readings to bake it.

Furthermore, the differential pressure transducers were a little temperamental at times and had

outdated calibrations. This may have affected the outputs they gave, leading to errors.

Temperature

The temperature in the tunnel would increase from around 20C at the start of each run, to around

22C at the end with the heating effect from the fan (and heaters!). This obviously made the air less

dense and therefore affected the Reynolds number and other variables. However, at a temperature

rise of 0.09C per minute, we felt that the effect of this would be insignificant, especially since we

were reducing the effect of changing conditions by plotting /.

Positioning Of Probes

We used feeler gauges to position the height of the probes. However, it was very difficult to get

them all in the same place, at the same height, and at the same angle. Therefore, we could not be

certain that the probes were all recording at the same height or at the 60 angle. Hopefully, if there

were some differences in the placement of the probes, the effect would be an offset in reading; this

therefore would not affect out conclusions.

Human Error

The probes were made by hand, and therefore they may not be identical to one another. In addition,

we specified that the ends be smoothed with a very fine diamond edged grinder but if a more coarse

or blunt grinder was used, this may have torn the edges of the probes resulting in slight differences

between them.

For the LabVIEW program algorithms, we manually entered the atmospheric pressure from a

mercury barometer in the tunnel at the start of each test. The manual entry automatically allows for

human error, parallax reading issues and inputting incorrect figures into the system.

Conclusion We concluded that there is strong evidence of the intermittency of streamwise, Grtler type vortices

on the leading edge of unswept cylinders at a Reynolds number of 140,000. Suitable confirmation of

the structures has been recorded on multiple runs, whilst other runs did imply that no vortex

structures had formed.

We have gathered some evidence that the wavelength of these vortices is around 1.4mm 1.6mm

under our conditions, however we do not feel that enough data was gathered to draw valid

conclusions on wavelength from this investigation.

Our research builds on, and provides more evidence for, preceding experiments in this field

including other Nuffield Research Placements and previous experiments conducted in the Charles

Wilson Wind Tunnel. Although we have found some evidence of patterns in the pressure that are

consistent with streamwise vortices in the boundary layer, more research in this field is needed to

look at the intermittency and possible causes for this, before work can be done in looking at

prevention techniques for the vortices.

24

Evaluation We felt that using Pitot probes was a good method of measuring the pressure differences caused by

the vortices; they were suitably small enough to measure the pressure over a localised area, and

provided enough sensitivity for the reading we were taking.

However, the differential pressure transducers may have introduced unnecessary error and would

benefit from a re-calibration.

We found it difficult to position the probes accurately, so an improved method of doing this would

definitely reduce the error in the results.

If the work was to continue, we feel that it would benefit from focusing on collecting repeatable

evidence for the wavelength of the vortices, in addition to looking at possible reasons behind the

intermittency of the pattern.

References [1] (Grtler, 1940). Naca Tech. Memo No.1375, 1940.

[2] J. Kestin and R.T. Wood. On the stability of two-dimensional stagnation flow. Journal of fluid

mechanics, Vol. 44, pp. 461-479, 1970

[3] J.M. Floryan, On the Grtler instability of boundary layers. J. Aerosp. Sci. 28 (1991) 235

[4] Aldo Rona and J.P. Gostelow. Streamwise and Crossflow Vortical Structures on Turbine Blades

and Swept Cylinders. Paper ASME GT 2014-27009, Dsseldorf, June 2014

[5] M. De Saint-Jean. An experimental investigation into vortical structures over a circular cylinder in

cross-flow. Engineer internship report, University of Leicester, Department of Engineering, 2011.

[6] Poll, D. I. A., 1985, Some Observations of the Transition Process on the Windward Face of a Long

Yawed Cylinder, Journal of Fluid Mechanics, Vol.150m p. 329-356

[7] Kohama, Y.P., 2000, Three-Dimensional Boundary Layer Transition Study, Current Science, Vol.

79, No. 6, pp.800-807

[8] Alexandra Mailleur. Hot-Wire Measurements Of Streamwise Vorticity Over The Surface Of A

Circular Cylinder In A Laminar Boundary Layer. Internship Report, August 2012

[9] https://upload.wikimedia.org/wikipedia/commons/f/f6/Backlash.svg [10] N. Tokugawa, S. Takagi and N. Itoh. Experiments on Streamline-Curvature Instability in Boundary

Layers on a Yawed Cylinder. AIAA Journal. Vol. 43, No. 6, June 2005. P.1156 Fig. 6.

[11] http://uk.mathworks.com/products/matlab/

25

Bibliography The following unreferenced research materials were also used to enhance my understanding on this

interesting topic:

John F. Douglas, Janusz M. Gasiorek, John A. Swaffield, Lynne B. Jack, Fluid Mechanics (fifth

edition), Pearson a brilliant book kindly given to me by Paul Gostelow for my future as an

engineer!

J.P. Gostelow, A. Rona, S.J. Garrett, W.A. McMullan and M. De Saint-Jean. Investigation Of

Streamwise And Transverse Instabilities On Swept Cylinders And Implications For Turbine

Blading. Paper GT2012-69055, Copenhagen, June 2012.

2 brilliant seminars given by Professor J. Paul Gostelow at the University of Leicester on what

we currently know about flow behaviours and characteristics, and the impact of these.

S. Takagi and N. Itoh. Observation of Travelling Waves in the Three-Dimensional Boundary

Layer along a Yawed Cylinder. Fluid Dynamics Research 14 (1994) 167-189. 5th February 1994

Acknowledgements There are many people that I would like to thank for their invaluable input of time, knowledge,

guidance, resources and general helpfulness on this project. Dr. Aldo Rona has been a great

supervisor, open to new ideas and suggestions and willing to impart his knowledge on a range of

interesting subjects (I particularly remember learning how to pick a lock one morning!). Paul

Williams made the project practically feasible at every step, never failing to come up with a solution

to yet another difficult problem! He too was more than willing to answer our questions and was able

to explain some difficult concepts in a digestible manner. Prof. Paul Gostelow followed the project as

it progressed imparting his incredible experience and useful advice delivering two really

interesting talks to us on flow behaviours.

Overall, the project has been a fantastic experience for which I have the people at Leicester

University who made it possible to thank, as well as Danielle Wright from the Nuffield Foundation.