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

Lucy Bennett

Table of ContentsAbstract.................................................................................................................................................4

Introduction...........................................................................................................................................4

Methodology.........................................................................................................................................7

Apparatus..........................................................................................................................................7

Charles Wilson Wind Tunnel..........................................................................................................7

Traverse.........................................................................................................................................8

Elliptical Sideboards.......................................................................................................................8

Trailing Edge L-plate......................................................................................................................9

Simple Pitot Anemometers..........................................................................................................10

Pitot-Static Anemometer.............................................................................................................11

Calculation of the Height of the Boundary Layer.............................................................................13

Differential Pressure Transducers................................................................................................13

Calibration.......................................................................................................................................13

Calibration of Differential Pressure Transducers.........................................................................13

Calibration of Pitot Anemometers...............................................................................................14

Conditions........................................................................................................................................16

Reynolds Number........................................................................................................................16

Signal Acquisition.............................................................................................................................17

Acquisition Rate...........................................................................................................................17

Station Spacing............................................................................................................................17

Probe Position Reference............................................................................................................18

Results and Discussion.........................................................................................................................19

Post Processing and Analysis Techniques........................................................................................19

Results.............................................................................................................................................20

Error................................................................................................................................................23

Conclusion.......................................................................................................................................24

Evaluation............................................................................................................................................25

References...........................................................................................................................................25

Bibliography.........................................................................................................................................26

Acknowledgements.............................................................................................................................26

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AbstractOur research set out to investigate the existence of Görtler type vortices formed on the leading edge of an unswept cylinder through measuring the near-wall pressure using Pitot anemometers. We 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. We found that there is strong evidence of the intermittency of streamwise, Görtler type vortices on the leading edge of unswept cylinders at a Reynolds number of 140,000.

IntroductionIt 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, x, were first observed by Görtler [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

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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 °

depositing on the surface. Görtler developed a way of categorising these vortices based on their Görtler 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:

Görtler 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).

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

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.

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, λ , of the vortices:

λ=1.79πDR e−0.5

D = Diameter of the unswept cylinderℜ = Reynolds number

Kestin and Wood’s 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 Wood’s 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

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Figure.4: Negative pressure gradient vortex formation.

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.

Methodology

Apparatus

Charles Wilson Wind TunnelFor 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%

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Direction of flow

Work space

Entrance

Turbine

Cylinder

Figure 7: Lauren and I in the tunnelFigure 6: The Charles Wilson wind tunnel

TraverseOn 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 SideboardsThe 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.

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Figure 10: The traverse Figure 11: The inside of a stepper motor

Y track

Z

Trailing Edge L-plateAt 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 Kármán vortex sheet (figure 15).

A von Kármán 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 Kármán 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.

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Figure 13: Re < 0.5 boundary layer flow over a cylinder [9]

Figure 14: 0.5 < Re < 70 boundary layer separation of a cylinder [9]

Figure 15: Von Kármán vortex street caused by the unsteady separation flow of a fluid around blunt bodies.

Simple Pitot AnemometersSimple 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.

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Figure 19: CAD drawing of the probe head.Figure 18: CAD drawing of the Pitot probe used to measure the near wall velocity at the cylinder.

Figure 17: Simple Pitot tube

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.

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 AnemometerWe 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.

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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 23: Pitot-static probe

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.

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 Bernoulli’s equation, which is derived from Newton’s 2nd Law:

P+ 12ρu2=P0

P =Static Pressure /Pa12ρ u2

= Dynamic Pressure /Pa

P0 = Total Pressure /Paρ= 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, ρ, is defined as:

ρ= pRT

p = Absolute pressure /PaR = Specific gas constant (287.05) /Jkg-1K-1

T = Temperature /K

The velocity, u, is calculated by rearranging Bernoulli’s equation:

u=√ 2 (P0−P )ρ

The LabVIEW program installed on the computers in the wind tunnel interprets the pressure received and then applies the rearranged Bernoulli’s equation to find the velocity, giving the output data in m/s.

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Calculation of the Height of the Boundary LayerWe 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 TransducersWhen 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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Figure 24: Diagram of a differential pressure transducer.

(0 – 5)V

Static pressureTotal pressure

Calibration of Pitot AnemometersTo 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

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

Ref

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

probes would detect it at the same time, allowing us to compare between probes at similar times (figure 26).

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.

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

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

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

Conditions

Reynolds NumberWe 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, ℜ, is defined as:

ℜ=ρairV air D

µair

Re = Reynolds number ρair = Density (of air) /kgm-3

Vair = Flow velocity (of air) /ms-1

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

Previous studies by various researchers show that the wavelength, λ, 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, D, of the cylinder was fixed at 0.152m.

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

and temperature, (ρ=pRT

) which we cannot control.

The viscosity of air, µair, is defined as:

μair=1.458×10−6 Tair1.5

T air+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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Signal Acquisition

Acquisition RateWe 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 SpacingWe knew that the wavelength,λ , 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 λ) 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 1.5λ . 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.

16Figure 29: Scale diagram showing the vortices (black), distance between probes (blue) and the distance between stations (green).

Distance between stations (0.25mm)

λ 2mm

Distance between traversing probes (5mm)

Probe Position ReferenceWe 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 x, the centreline of the cylinder to be y , and the upright height of the probes to be z. 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.

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Figure 30: The probes at 60°to the horizontal on the cylinder.

Figure 32: The two traversing probes in position.

Figure 31: The reference and traversing probes on the cylinder.

Figure 33: The cylinder and probes with the axes labelled and 60° line shown.

Y

Z60°

Direction of flow, x

60° line

Results and DiscussionWe 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 TechniquesTo 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 probe4 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( P/Pref ).

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Figure 35: Graph showing the pressure at each station

Figure 34: Graph showing the velocity at each station

ResultsWe 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

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Probe 2

Probe 1

Probe 2

Probe 1

Figure 37: Graph showing the P/Pref over the 32

stations, with signs of vortices with a wavelength of around 1.5mm being present

Figure 38: Graph showing signs of vortices in both probe 1 and probe 2, with a wavelength of around 1.8mm

Probe 2

Probe 1

Figure 39: Graph showing more vortex structure with a short wavelength of 1mm (probe 1)

correspond to previous research such as Kestin and Wood’s [2].

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 Görtler [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.

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

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Figure 41: Graph showing P/Pref detrend,

with no clear vortices detected.

Figure 40: Graph showing P/Pref over the 32

stations with no obvious signs of vortices.

Probe 1

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 Wood’s theory that the vortices ‘stretch’ and adapt their wavelength depending on the conditions [2] would give us a wavelength, λ, of:

λ=1.79πDR e−0.5

D = Diameter of the unswept cylinder = 0.152ℜ = Reynolds number = 140,000

λ=1.79(π∗0.152∗140,000−0.5)λ=2.28mm

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.

Error

AveragingWe 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.

TraverseBecause 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

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Figure 43: Backlash in a gear system

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 ControlIn 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 P/Pref , 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.

ElectronicsWe 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.

TemperatureThe temperature in the tunnel would increase from around 20°C at the start of each run, to around 22°C 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 0.09°C per minute, we felt that the effect of this would be insignificant, especially since we were reducing the effect of changing conditions by plotting P/Pref .

Positioning Of ProbesWe 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 ErrorThe 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.

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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.

ConclusionWe concluded that there is strong evidence of the intermittency of streamwise, Görtler 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

EvaluationWe 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] (Görtler, 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 Görtler 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, Düsseldorf, 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.

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

[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/

BibliographyThe 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.

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