DEVELOPMENT OF A WIND TUNNEL FORCE
BALANCE AND RELATED PRACTICAL
EXERCISE MANUAL
A Thesis Part B report submitted in partial fulfilment of the requirements
for
the degree of Bachelor of Engineering
in
Mechanical Engineering
By
Gethin Barden
Student No. s203897
Supervisor:
Dr. Daria Surovtseva and Micah Thorbjornsen
Thesis coordinator:
Kamal Debnath
School of Engineering & Information Technology
Faculty of Engineering, Health, Science and the Environment
Charles Darwin University
Darwin
May 2014
2
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ABSTRACT
DEVELOPMENT OF A WIND TUNNEL FORCE BALANCE AND RELATED
PRACTICAL EXERCISE MANUAL
Keywords: Wind tunnel, two-component force balance, load cell, lift, drag, pressure
distribution
A two-component force balance has been constructed and installed in the Charles Darwin
University (CDU) wind tunnel to increase the capability of experimental investigation into fluid
flow around submerged bodies. The balance consists of a series of struts that transfer forces to
two load cells orientated perpendicularly in order to separately measure horizontal (drag) and
vertical (lift) forces. Various attachments have been manufactured for various model types. The
mechanism has been tested over a range of air velocities from 0-40m/s with the various
attachments and suitable models. Comparison of the experimental results with the results of
theoretical modelling using a CFD software package revealed an excellent agreement between
theoretical and experimental interpretation of fluid forces. A detailed practical exercise manual
was developed to assist future students and researchers in conducting experiments involving
investigation of fluid flow over submerged bodies. One of the major practical benefits resulted
from this project is that the created setup allows for the direct measurement of fluid forces
which was not available previously.
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ACKNOWLEGEMENTS
The author is grateful to and would like to thank Dr. Daria Surovtseva and Micah
Thorbjornsen for their insight and supervision throughout this thesis. He would also like to
thank the Stone family and Brendan von Gerhardt for their assistance in construction of the
apparatus and their ongoing support. A final thanks is to the author’s family who have
supported him throughout this thesis.
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Table of Contents
SYMBOLS AND ABBREVIATIONS ...................................................................................... 7
LIST OF TABLES ..................................................................................................................... 8
LIST OF FIGURES .................................................................................................................... 9
1.
PROJECT INTRODUCTION ........................................................................................... 10
2.
LITERATURE SURVEY ................................................................................................. 11
2.1.
Existing Force Balance System Designs ....................................................................... 11
2.1.1.
Model Mounting ........................................................................................................ 11
2.1.2.
Force Measurement .................................................................................................... 13
2.2.
Balance Effects on Air Flow and Fluid Forces.............................................................. 14
2.3.
Force Balances ............................................................................................................... 14
2.3.1.
2.4.
External Force Balances ............................................................................................ 14
Testing And Calibration Techniques ............................................................................. 15
2.4.1.
Methodology .............................................................................................................. 15
2.4.2.
Comparative Results .................................................................................................. 16
2.4.2.1.
Pressure Distribution Analysis ............................................................................... 16
2.4.2.2.
Computational Fluid Dynamics Software .............................................................. 17
2.4.2.3.
Coefficients Method ............................................................................................... 17
2.5.
Model Selection ............................................................................................................. 18
2.5.1.
Model Construction and Installation Details ............................................................. 18
2.5.2.
Model Coefficient Data ............................................................................................. 19
3.
PROJECT SCOPE ............................................................................................................ 21
4.
DESIGN STUDY .............................................................................................................. 22
4.1.
Apparatus Constraints ................................................................................................... 22
4.2.
Force Measurement Setup ............................................................................................. 22
4.2.1.
Selected Measurement Devices and Setup ................................................................ 22
4.2.2.
Force Balance Software ............................................................................................. 22
4.2.3.
Initial Design & Testing ............................................................................................ 24
4.2.4.
Improved Design & Testing ...................................................................................... 27
4.3.
Clark-Y Aerofoil on Flat Plate Mount Analysis ............................................................ 30
4.3.1.
Pressure Distribution Method .................................................................................... 31
4.3.2.
CFD Simulation Results ............................................................................................ 31
4.3.3.
Data Comparison ....................................................................................................... 32
4.4.
5.
5.1.
Flat Plate Model on Rear Plate Mount Analysis ........................................................... 34
PEER TESTING AND EVALUATION ........................................................................... 36
Effect of dimples on objects in air flow ........................................................................ 36
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5.1.1.
Cylinder ..................................................................................................................... 36
5.1.2.
Orgive ........................................................................................................................ 37
5.2.
ENG480 Projects ........................................................................................................... 39
5.2.1.
Aerofoils .................................................................................................................... 39
5.2.2.
Magnus Effect Demonstration ................................................................................... 40
5.2.3.
Wind Turbine ............................................................................................................. 41
5.3.
Peer Testing Summary .................................................................................................. 42
6.
PRACTICAL OUTLINE DESIGN ................................................................................... 44
7.
CONCLUSION ................................................................................................................. 45
8.
RECOMMENDATIONS .................................................................................................. 46
9.
APPENDIX ....................................................................................................................... 47
Appendix A: Practical Exercise Manual .................................................................................. 47
Appendix B: Design Calculations ............................................................................................ 59
Appendix C: Force Balance Drawing....................................................................................... 60
10.
REFERENCES .............................................................................................................. 61
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SYMBOLS AND ABBREVIATIONS
D
Drag
L
Lift
CD
Drag Coefficient
CL
Lift Coefficient
p
Pressure
pв€ћ
Atmospheric Pressure
U
Free stream Velocity
Оё
Angle normal to object surface
О±
Angle of attack
A
Area
ПЃ
Fluid density
П„w
Shear stress between fluid and object
F
Force
M
Moment
I
Moment of Inertia
Пѓy
Yield stress
Пѓb
Bending stress
П„avg
Average shear stress
E
Elastic Modulus
Оґ
Deflection
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LIST OF TABLES
Table 1 – Forces (N) at various wind tunnel speeds
Page 19
Table 2 – Test results for flat plate with preliminary design
Page 26
Table 3 – Preliminary test results
Page 26
Table 4 – Clark Y aerofoil wind tunnel testing
Page 30
Table 5 – Lift force calculated via pressure distribution
Page 30
Table 6 – COMSOL computational fluid analysis results
Page 31
Table 7 – Flat plate drag force measurements
Page 33
Table 8 – Flat plate drag force comparison
Page 34
Table 9 – Smooth cylinder results
Page 36
Table 10 – Smooth orgive results
Page 37
Table 11 – Data from supersonic aerofoil testing
Page 38
Table 12 – Wind turbine results
Page 41
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LIST OF FIGURES
Figure 1 – Sting and strut mounting methods
Page 11
Figure 2 – Half model mount of Bombardier Business Jet
Page 11
Figure 3 – Phidgets Micro Load Cell
Page 12
Figure 4 – 6-component platform balance
Page 14
Figure 5 – Diagram of small object and forces acting upon it
Page 15
Figure 6 – Clark Y profile
Page 18
Figure 7 – Force Balance Program Interface
Page 22
Figure 8- Support strut design created with 3D modelling software
Page 23
Figure 9 – Small pronged mount for smaller models.
Page 24
Figure 10 – Large pronged mount
Page 25
Figure 11 - Airfoil type model mount
Page 25
Figure 12 – Alternative Apparatus diagram
Page 27
Figure 13 – Installed apparatus
Page 28
Figure 14 – Model mounts
Page 29
Figure 15 – COMSOL image of Clark Y
Page 31
Figure 16 – Clark Y Lift force comparison
Page 32
Figure 17 – Smooth cylinder mounted in wind tunnel
Page 35
Figure 18 – Orgive mounted in wind tunnel
Page 36
Figure 19 – Supersonic aerofoil fitted with pressure taps
Page 38
Figure 20 – Magnus Effect
Page 39
Figure 21 – Magnus effect apparatus to demonstrate lift force
Page 40
Figure 22 – Wind turbine secured in tunnel
Page 41
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1. PROJECT INTRODUCTION
Fluid flow is involved in nearly any engineering application. It is an important consideration to
design for, or against. Fluid mechanics is especially important in mechanical engineering
applications. One of the primary tools used by engineers to design objects that are to encounter
fluid flows is a wind tunnel which draws air through a chamber and can be used to visualise
and measure the effects that the fluid imparts on the model. Charles Darwin University (CDU)
currently has a working wind tunnel with test section dimensions of 450mm x 450mm x
1000mm. The wind tunnel is primarily used in teaching the ENG480 Applied Fluid Mechanics
unit and for university displays to local senior school students. The fan is rated to provide
airflow of up to 40m/s, and the wind speed is measured by finding the stagnation pressure
through the use of a Pitot tube. Currently, a very basic setup for lift measurements has been
installed. Some features in which the CDU wind tunnel lacks include a method of displaying
the boundary layer, a method of taking pressure and temperature distributions along a surface
and, importantly for this thesis, a method of directly measuring drag and lift forces. This thesis
will primarily focus on providing an apparatus to measure lift and drag with the secondary focus
of producing a Practical Exercise Manual (Appendix A) for ENG480 students to utilise in their
studies.
In order to improve the wind tunnels functionality, a more accurate, stable and versatile method
of measuring the two major aerodynamic forces, lift and drag, is required. Previous students of
ENG480 created a device to roughly measure the drag force through springs and their extension.
Issues with this balance was that it was unstable, could be used at low velocities only and the
spring extension proved difficult to measure accurately. A force balance to measure drag, while
at the same time measuring lift, was highlighted as a necessary improvement to the wind tunnel
needed for the unit.
As the device is intended to be used primarily for ENG480 this thesis revolves around the design
of a practical or workshop for students to investigate the lift and drag properties of various
models. In the previous year, students designed models that would demonstrate lift, drag and
boundary layer. It is planned to continue to allow students to devise and create their own models
and, though these models will be constrained by the strut attachments, the force balance should
allow for various model designs to be built and tested.
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2. LITERATURE SURVEY
2.1. Existing Force Balance System Designs
There are a number of force balance designs available for lift and drag measurement in a wind
tunnel and the drawbacks and benefits are well described. Balances are categorized by
components, or the number of forces measured. For example, a one-component balance
measures only one force whereas a three-component balance measures three (typically lift, drag
and pitching moment). Pitching moment is vital for aerofoil testing but not so important for
regular wind tunnel use. Force balances comprise of two aspects that need to be considered, the
method of mounting the model and the method of measuring the forces. Two requirements that
any mount must comply with are being reasonably aerodynamically discrete and supply a
sufficient hold on the model (Onera, 2009).
2.1.1. Model Mounting
There are several methods of mounting models in wind tunnels which characterise the methods
used to calculate forces. One of the more common methods used is the sting, which is a strut
that rises typically from below to connect to the rear of the model. For example, the majority
(80%) of the wind tunnels at NASA’s Langley Research Centre’s in 1965 used sting supports
(Schaefer, 1965). The sting is most commonly fitted with internal strain gauges or load cells to
measure up to six component forces. To manufacture a sting is a complex process and available
stings are expensive to purchase1. A simpler method is to mount the model on supports, usually
called struts, which are then connected to an external balance system. An example of this is the
University of Washington Aeronautical Laboratory’s wind tunnel which typically uses a single
strut with a two or three pronged fork to better secure the model (University of Washington
Aeronautical Laboratory, n.d.). This method can be designed to be less complex to manufacture
than a sting though as the number of components increases so does the difficulty of design and
manufacture. These two mounting types, seen in Figure 1, can also be designed to be completely
removable from the wind tunnel. Stings generally allow for a greater range of angle of attack
than external balances (Barlow et al, 1999), it is however believed that the strut design can be
made to accommodate easy alteration of angle of attack. Both of these characteristics,
removability and the ability to alter the angle of attack, were desirables in the scope for this
project.
1
A quote for a sting without software and positioning system (force measuring component only) was in excess
of $50,000. With software and positioning system, price increased to over $120,000.
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Figure 1 – Sting and strut mounting methods (NASA, 2012)
Other methods often used in model mounting include making half models (Figure 2) and fixing
to an external balance through the sides or bottom of the tunnel. While this mounting and
balance system often produces good results due to the absence of the drag-inducing strut or
sting, it does not offer the same flexibility as a sting or strut, and interference with the tunnel
wall is an issue that needs to be recognised and accounted for. There are also issues with larger
than normal rolling moments with external balances and half models as only one side is present
(Barlow et al, 1999). Other types of model mounts do exist but these others are typically centred
on a certain design and, for example the half model side mount, do not offer the flexibility
desired by ENG480.
Figure 2 – Half model mount of Bombardier Business Jet (National Research Council of
Canada, 2009)
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2.1.2. Force Measurement
Measuring the forces produced by the fluid-model interaction is the purpose of a force balance
design. Purely mechanical methods exist such as the use of springs or counterweights (NASA,
2011). These methods are limited by generally having small operating force ranges. Springs are
governed by their spring constant and have a limited amount of extension before they stop
behaving linearly. They can also have a tendency to creep if the tolerable load is exceeded and
if a small load is applied it generally proves difficult to measure the spring’s extension. Though
counterweights would potentially have a larger range, it is still limited and, for high accuracy,
would require a large number of weights. It would also be difficult to design against a tedious
process of weight management. With the development of technology, data acquisition is
becoming more electronics based as these devices allow for the data to be sampled at higher
rates, be analysed and manipulated more easily and reduce sources of human error. As such,
electronic methods will be investigated.
Two electronic methods include the use of strain gauges and load cells. Strain gauges are an
alloy foil or set of wires with known resistance properties that are applied to a specimen. As the
foil or wires are stretched, the resistivity changes. The resistivity relies on the strain-sensitivity
of the alloy foil, the material of the carrier and the gage pattern though other characteristics can
also affect the performance (Vishay Precision Group, n.d.). From the extension of the foil (the
strain), a stress can be found by knowing the properties of the specimen. A load cell takes this
technology further and attaches gauges to a specimen of known material and dimensions (see
Figure 3). By doing this there is no requirement for calculating the stress-strain relationship of
the material. Load cells also come in a huge range with cells capable of measuring forces to a
high degree of accuracy.
Figure 3 – Phidgets Micro Load Cell (Phidgets Inc, 2012)
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2.2. Balance Effects on Air Flow and Fluid Forces
It is expected that a strut or sting will add some drag to the model. Whether this drag is
negligible or not needs to be investigated. There are three parts that make up the drag component
added due to the model support.
The first is the direct drag of the support. Part of the support is exposed directly to fluid flow
which causes drag as fluid impacts and flows over the support. The design of the strut may have
a significant effect on the magnitude of this drag and it needs to be taken into account during
the design. To reduce the effect, the support should be streamlined and the cross-sectional area
that encounters the fluid flow should be small.
The second component of the additional drag is the interference the support has on the fluid
flow around the model. Where the support meets the model there will be small gaps and vertices
at the edges of the support. The air flowing past the model must accelerate to pass through this
reduced area. This acceleration and disruption causes added turbulence and, in regards to a
sting, will affect the wake region behind the model.
The final part is the interference that the model has on the support. This will, in the same way
the supports affect the model, also add to the turbulence and effect the vortices in the wake
region (Barlow et al, 1999).
2.3. Force Balances
The next part of the system is the force balance. The measurement devices can be inside the
wind tunnel (internal) or outside the wind tunnel (external). If an internal measurement device
is used it needs to be discrete enough so that it will not disrupt the fluid flow and increase drag.
Internal devices are generally located inside the supports or the models themselves. As the
balance will be for multiple models, a measurement device on the inside of the model is not
suitable. External measurement devices are located outside the wind tunnel and so will not
directly influence the fluid flow. This allows for external balances to be as large as required.
2.3.1. External Force Balances
Two types of external balances exist. A single specimen fitted with strain gauges and more
complex linkage and member types which decouple the forces mechanically before being
measured by single force measurement devices. The single specimen balance offers the
advantages of being significantly smaller compared to the decoupling balances (Foss et al,
2007). There are four methods of decoupling that external balances typically use, the wire, the
platform, the yoke and the pyramidal (Barlow et al, 1999). The first of these, the wire balance,
is not used as often these days as other more robust and versatile alternatives exist. Issues with
Development of a Wind Tunnel Force Balance Practical
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wire breakage leading to model loss and calibrating difficulty are two of these reasons (Barlow
et al, 1999). The other three systems use members and linkages to decouple forces. The platform
balance (see Figure 4) is the most commonly used but not exceptionally accurate in measuring
moments (Barlow et al, 1999). As measuring moments are outside the scope of this thesis this
is not an issue. The other two types increase in complexity of design and calculation, especially
the pyramidal balance. As the measurement of moments is outside the scope of this project and
a two component balance is what is required the focus will be on either a single specimen type
or an external platform balance.
Figure 4 – 6-component platform balance (NASA, 2012)
2.4. Testing And Calibration Techniques
Testing and calibration will be a large part of the apparatus implementation part of this thesis.
Several methods have been proposed by different groups with differing levels of relevance
(Miranda, 2000; Reis et al, 2013; Gonzalez et al, 2011; Arney & Harter, 1964). In addition to
this, several numerical techniques are available in order to verify the reliability and accuracy of
the measurement device.
2.4.1. Methodology
In most wind tunnel balance calibrations, static loading is the first step towards calibration
(Gonzalez et al, 2011). Before calibration commences, the mount should be installed in its final
position and the direction of the fluid recognised. With this, the strut is loaded with known loads
and the reading on the sensor recorded. A known weight or load is applied and the load entered
into the software. A second load, preferably with a large range to reduce errors, is then applied
Development of a Wind Tunnel Force Balance Practical
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and that load entered into the software (Phidgets Inc, 2013). It is a simple matter to then
interpolate between or extrapolate the loads to calculate any subsequent load applied.
The second step is the dynamic calibration (Gonzalez et al, 2011; Arney & Harter, 1964) which
uses a reference model to make final adjustments. An aerofoil model with known lift and drag
forces at certain operating conditions is generally used to ensure sufficient decoupling of force
has occurred and any additional coupling requirements are resolved.
2.4.2. Comparative Results
The following techniques of acquiring forces caused by fluid flow over submerged bodies will
be used to ensure the apparatus is giving an accurate representation of the forces.
2.4.2.1. Pressure Distribution Analysis
One method that will be used for this investigation is the analysis of the pressure distribution
between the front and rear of the model and also between the top and bottom of the model in
cases of aerofoils (Smiadak, 2008; University of Iowa, 2002). These pressure distributions will
be obtained through the use of a manometer and specially manufactured models. The models
will then be tested in the wind tunnel at a range of air velocities. Fluid mechanics laws state
that drag is the force that is developed over an area by the difference in pressure between the
front and the back of the submerged object plus the friction force caused by friction between
the object surface and fluid. The following equation and figure shows this relationship.
Figure 5 – Diagram of small object and forces acting upon it in submerged fluid flow
(Munson et al, 2009)
Drag=D= ∫ 𝑝 𝑐𝑜𝑠𝜃 𝑑𝐴 + ∫ 𝜏𝑤 𝑠𝑖𝑛𝜃 𝑑𝐴
(1)
Experimentally, this integral can become a sum. If the intervals of an object with uniform width
are set as certain lengths and pressure measurements taken at these intervals, a pressure
Development of a Wind Tunnel Force Balance Practical
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distribution can be found and the interval areas used to find the equivalent force (University of
Iowa, n.d.). The following equation gives the force component due to the pressure difference,
Dp.
1
𝐷𝑝 ≈ ∑𝑖 2 [(𝑝∞ − 𝑝𝑖 ) + (𝑝∞ − 𝑝𝑖−1 )]𝑐𝑜𝑠𝜃𝑖−1,𝑖 ∆𝑠𝑖−1,𝑖
(2)
Where i represents the interval number, s is the interval element length and в€ћ represents the
submerged fluid. This method can also be used for lift by manipulating the equation. As this
only provides the pressure difference force component, it can be used, if done accurately, as a
close approximation for thin objects where friction drag will be negligible (a good example is
a flat plate perpendicular to the flow). This value will then give a force value that is occurring
experimentally and can be used to verify literature coefficient calculations.
2.4.2.2. Computational Fluid Dynamics Software
The next method that will be used to investigate the drag force effects that the balance and
support has on the drag force of the model is computational fluid dynamics (CFD) software.
This software models, using algorithms, the flow of fluids over objects. It has the capacity to
give values for forces such as drag and lift for various model types. The software does this by
finding the stress on opposing surfaces (ie. top and bottom or front and back) and calculating
the difference (Bychkov, 2013). This is similar to the pressure distribution method except with
an entirely theoretical model and more data points. The software, which has been selected is
COMSOL Multiphysics; one of the field’s leading programs.
Three-dimensional computer-aided design models will be created for each of the test models.
These will be examined at varying speeds and the forces produced from this will be compared
with literature coefficient calculations. Initial testing of the software show that the results from
COMSOL Multiphysics simulations and literature coefficients are similar.
2.4.2.3. Coefficients Method
The final method of calculating the drag, D, and lift, L, forces on a submerged object is by using
tabulated values for the lift coefficient, CL, and drag coefficient, CD, which have been derived
from experimentation for certain profiles and shapes. These coefficients can then be used in the
following formulae (Munson et al, 2009):1
рќђї = рќњЊрќ‘€ 2 рќђґрќђ¶рќђї
2
рќђ·=
1 2
рќњЊрќ‘€ рќђґрќђ¶рќђ·
2
Development of a Wind Tunnel Force Balance Practical
(3)
(4)
Gethin Barden
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Where U is the free stream air velocity, ПЃ is the air density and A is the frontal area of the object.
This method will give us the theoretical amount of drag force for the object only. This will
allow for comparison of how much extra drag the apparatus adds to the system and how the lift
force is affected.
2.5. Model Selection
The following models are proposed to be used:п‚·
Flat plate perpendicular to the flow
п‚·
Basic aerofoil shape with numerous coefficient sources available
The reasons for selecting these models is that they are simple in shape and should be able to
test the functionality of the apparatus. The plate will be used to test the pronged mounts in the
preliminary design and the flat rear plate mount of the secondary design to ensure they are
capable of supporting the models they are required to. They will only be used to test whether a
correct drag force is being obtained. The aerofoil will be used with the aerofoil mounts and will
test both lift and drag.
2.5.1. Model Construction and Installation Details
Flat Plate
The flat plate will be used to test the drag component. The model will have the dimensions
200mmx200mm and will be 10mm thick. The model will be installed perpendicular to the flow
so that a large pressure difference can be measured and used as comparison data. The flat plate
will be installed on the small or large model prong mount. Coefficient data for this model will
be gained using the data for a rectangular prism of width to thickness ratio of 0.05. Model will
be constructed from 3-ply plywood.
Aerofoil
The aerofoil that will be used for testing will be the Clark Y type aerofoil. This aerofoil has
been used and tested extensively since its creation with numerous designs spawning from it.
Due to its flat bottom and simple shape, this aerofoil is less complex to build compared to other
foils. Data regarding the aerofoil’s performance has been found and tabulated in the next
section. The model will be constructed of polystyrene and has a 250mm chord and is 230mm
wide. To manufacture, a profile of the aerofoil (downloaded from aerofoil construction site
AirfoilTools.com; Figure 6) will be printed and this profile used in the shaping of the
polystyrene. This manufacturing technique should allow for an accurate model to be produced.
Development of a Wind Tunnel Force Balance Practical
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Figure 6 - Clark Y profile (AirfoilTools.com, 2013)
2.5.2. Model Coefficient Data
Table 2 below details drag coefficient values found for each model, the respective source of
each coefficient and the drag forces experienced under 10m/s, 20m/s and 30m/s air velocities.
The air density that will be used will be 1.13kg/m3, a pressure that was calculated from the
Bureau of Meteorology website (2013). Drag and lift coefficients will be taken for a Reynolds
number of 100,000 though this can vary up to 200,000 for some of the models at 30m/s the
coefficients do not change excessively over this time. For the Clark-Y aerofoil, the angle of
attack will be set at its natural angle of 3.2o. The area of the aerofoil for lift is equal to the span
of the wing by the length of the chord which, for the aerofoil used, is 0.0575m2. The area for
drag is equal to the wing span by the height of the foil which is equal to 0.0067m2.
The two Clark Y aerofoil coefficients (Zimmerman, 1933; Silverstein, 1935) can be seen in
Table 1 to be very different. This is due to the Zimmerman coefficient taking into account the
aspect ratio whereas the Silverstein coefficient does not. The Silverstein coefficient has been
calculated for an aspect ratio of 6 whereas the aerofoil in question has an aspect ratio of only
0.9. Due to the aspect ratio being larger for the Silverstein coefficient, the vortices that would
be produced in this situation will have less of an impact due to the greater width. Vortices occur
on the outer edges of the wing and are caused by the high pressure air at the wing tips travelling
around the wing tips to the low pressure side on top of the aerofoil. These vortices create a
downwash which counteracts some of the lift being produced (Anderson, 2001).
Similarly, the aspect ratio also has an effect on the flat plate. A study by Fail et al (1959)
indicated that as the aspect ratio increased so did the drag coefficient. The generally accepted
drag coefficient for a flat plate perpendicular to the flow is about 1.98 (Munsen et al, 2009;
Engineering Toolbox, n.d.). This, however, is a general case and generally for a plate of infinite
size. For a plate with aspect ratio of 1 and an area of 25 square inches (5 inch x 5 inch which is
approximately equivalent to 200mm x 200mm), the drag coefficient was found to be equal to
1.17, generally due to a slightly higher base pressure behind the plate compared to the higher
Development of a Wind Tunnel Force Balance Practical
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aspect ratios. Table 1 displays the forces that are expected to be encountered in testing the flat
plate.
Table 1 - Forces (N) at various wind tunnel speeds
Object
Coefficient
Drag (Lift)
Flat Plate 1.97(0)
Clark Y
Source
10m/s
Drag (Lift)
4.45(0)
Munson et al,
2009
1.17(0)
Fail et al, 1959 2.64(0)
0.049(0.80) Silverstein,
0.02(2.60)
1935
0.045(0.28) Zimmerman,
0.02(0.91)
1933
Development of a Wind Tunnel Force Balance Practical
20m/s
Drag (Lift)
17.81(0)
30m/s
Drag (Lift)
40.07(0)
10.58(0)
0.08(10.40)
23.80(0)
0.17(23.39)
0.07(3.64)
0.16(8.19)
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3. PROJECT SCOPE
This thesis encompasses a large practical section. It aims to develop a working practical for
drag and lift measurement in the wind tunnel for ENG480 students. It is believed the thesis
results will greatly assist students in understanding fluid flow over submerged bodies and allow
comparison of theoretical methods. The primary objectives of this thesis are:п‚·
Construct and install an apparatus to directly measure lift and drag forces
п‚·
Test apparatus to ensure that measured results are similar to actual forces
п‚·
Develop a manual for the use of the apparatus, including installation and disassembly
п‚·
Develop a practical exercise document for use in the ENG480 unit
Secondary objectives include:п‚·
Build additional models for ENG480 unit examples
п‚·
Develop a method to record data over period of time and display both forces
concurrently
In order to progress the design, several constraints and requirements were put on the
development, these include:п‚·
Apparatus had to be built due to budget constraints and the unique nature of the CDU
wind tunnel.
п‚·
Design must be able to withstand a 300N drag force and a 50N lift force which have
been calculated to be the peak loads.
п‚·
Design must be capable of withstanding 40m/s air velocities while laden with model.
п‚·
Able to support and test a number of models of various shapes such as flat pates, spheres
and aerofoils.
п‚·
Lift and drag components need to be achieved through direct measurement.
п‚·
Be completely removable from the wind tunnel with no negative effect on airflow
Other additional design characteristics that are desirable, though may not be achievable in the
allotted time, include:п‚·
Design allowing the alteration of the angle of attack without removing the wind tunnel
test chamber from the diffuser.
п‚·
Angle of attack of the model made to be adjustable.
п‚·
A small access hole to access the chamber without having to detach the test chamber
from the diffuser or nozzle.
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4. DESIGN STUDY
4.1. Apparatus Constraints
Models used in conjunction with the force balance should be constrained to follow good
practice and the design limits. The width and height of the models should be kept to less than
0.8 times the width and height of the test chamber (Barlow et al, 1999). In this instance, that
limit is 360mm for both height and width. The reason for this constraint is that models that
exceed this limit may encounter effects from the walls of the wind tunnel. An aerofoil, for
example, may produce more lift than it would realistically due to vortices not being able to
move around the ends of the model.
Calculations should be completed to ensure that the design force limits are not exceeded. Lift
force should not exceed 50N or 5kg as this exceeds the operating range of the load cell.
Similarly, drag should not exceed 300N if the 30kg load cell is equipped. If the 5kg or 20kg
load cells are equipped then the limit should be 50N or 200N respectively.
4.2. Force Measurement Setup
An integral part of the apparatus is the force measurement devices. These devices take the forces
and convert them into data that can be easily interpreted.
4.2.1. Selected Measurement Devices and Setup
The selected method of measuring forces will be the use of load cells. The load cells that have
been selected for this apparatus are 5kg Phidgets load cells (Figure 3) With most models, it is
unlikely that 50N of drag force will be exceeded. However, if it is expected that the force will
be greater than this, a 20kg and 30kg load cell have also been procured. This type of cell was
selected as it is easily used and calibrated, programs for the data acquisition system can be
implemented on a variety of platforms including LabVIEW, delivery time is fast and the load
cells are inexpensive. In order to use the load cells, an electronic bridge is required and this was
also purchased. Initial testing of the load cells have shown them to work well and provide
accurate results. The load cells will be connected externally to the strut by threaded rod and
bolted to brackets which will support the entire apparatus.
4.2.2. Force Balance Software
Once data has been obtained by the load cells, it needs to be manipulated to give a reading that
is easily understood by the user. A software program is required for this step. LabVIEW was
chosen as the platform that would be used to write the program as it is more user friendly than
the other alternatives to people who are not experienced in programming. The program needs
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to be able to convert the load cell data from mV/V to newtons. As the load cells behave linearly,
the data can be converted by applying a linear equation to it. The program allows for two
equations, one for lift and one for drag, to be inputted and once done so will automatically
convert the data to a force value.
Calibration is conducted by applying a static force to the balance in the component directions
(ie horizontally or vertically). To produce this force, a precision digital force meter was
procured. Once the force is applied, the known force and the subsequent mV/V data value is
recorded. This is done for a second point in the same direction and from these two points the
linear equation can be derived and inputted into the program.
The interface of the program (Figure 7) needs to be suitable for ENG480 students to understand
with relative ease. As a result, the design is simplistic and detailed instructions are provided on
the interface for ease of use. In addition to this, there is further information regarding
procedures, including a calibration guide, in the Force Balance Practical Exercises Manual
(Appendix A).
Figure 7 – Force Balance Program Interface
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4.2.3. Initial Design & Testing
For the sake of simplicity, the following design was suggested to initially test the load cells.
The design involves a vertical strut, with which calculations on deflection could be easily
calculated by hand, with load cells orientated perpendicularly to measure each force. Doubts
existed whether this design would accurately measure the correct forces as the lift and drag
forces may be interfere with each other. This would be because the forces were not being
successfully decoupled. If this appeared to be the case, and no proportionality existed between
theoretical and measured results, then an alternative design would be implemented.
Figure 8- Support strut design with part details created with 3D modelling software
As can be seen in figure 8 above, the support design is relatively simple. Part 1 comprises of
two halves which are bolted to the main strut by two bolts to ensure rigidity. The initial design
had the part countersunk into the main strut but issues with the computer controlled milling
machines available at the university meant that this could not be completed and so the design
was modified to accommodate for this. Part 2 is clamped between the two halves of part 1 with
a nut and bolt (and spring or flat washers as required). The angle of attack is adjustable by
untightening the bolt holding part 2, changing the angle and then retightening.
The materials being used for the prototype attachment parts (parts 1 and 2) will be ABS plastic
for the model support fittings. This plastic, if laid axially, yields under tension at approximately
20MPa and a yield under compression of 38MPa (Ahn et al, 2002). The parts would generally
be under compression and the smallest cross-sectional area is 120mm2 and would be capable of
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supporting 4.56kN before compression failure. As, at this point of minimum cross sectional
area, the part is supported by the strut, this will reduce buckling and make destruction due to
the maximum force of 300N very improbable. The strut itself was be made from PlexiglasВ®,
which has a yield strength of 72MPa at 23oC and an elastic modulus of 3.3 GPa (Evonik
Industries, 2013). To reach the vertical centre of the tunnel from where the strut would be
secured, a span of approximately 300mm is required (y-component). The thickness of the
material is 10mm, though no significant load should be taken in this direction (z-component).
The last dimension is the horizontal component parallel with fluid flow (x-component) which
is the dimension that would have the most load applied to it. Calculations (see Appendix B)
have shown that, with a safety factor of 4, this x-component length needs to be 55mm.
Deflection calculations were then applied to these dimensions and it was found that at max load
a deflection of 5.8mm would occur. As a result, the x-component was increased to 70mm which
allowed for a maximum deflection of 2.9mm. This deflection calculation was tested by applying
a 15kg load to the strut which, under this load, should and did deflect by approximately 1.5mm.
Three model mounts were constructed to accommodate for models of various size and type.
The three mounts will be interchangeable with part 2 and images of each with a description can
be seen below in figures 9, 10 and 11.
Figure 9 – Small pronged mount for smaller models. Three prongs inserted into predrilled
holes in model.
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Figure 10 – Large pronged mount
Figure 11 - Aerofoil type model mount. Model placed atop mount and bolted into place using
a piece of thin wooden board as a washer
Testing for drag was undertaken with the initial apparatus in the wind tunnel. The design was
tested using the model of a flat plate loaded on the small model mount as the large model mount
had manufacturing flaws. To initially calibrate the device, a static load of known force is applied
in the drag component direction. This was then used to calibrate the load cells using the
software. A run without a model was completed to ensure vibrations or failure did not occur.
The wind tunnel was taken to its full speed of 50Hz (40m/s) with no ill effects noted. The model
was introduced and recalibrated using a 10 pound (45.3N) static weight. As the wind tunnel
increased the fluid velocity to 30m/s the model started to vibrate though not catastrophically.
The speed was increased to 40Hz (about 32m/s) without any additional vibration though the
speed was not increased after this point. It was expected that with the larger mount these
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vibrations would have been reduced as the model would be connected over a wider area. The
results from this testing can be seen below in Table 2.
Table 2 – Test results from Flat Plate with preliminary design
Fluid Velocity (m/s)
Horizontal Load Cell (N)
Vertical Load Cell (N)
10
0.6
1.5
20
9.1
7.6
30
15.0
17.7
As can be seen from Table 2, the apparatus measured significant forces in both the lift and drag
load cells. This indicates that the apparatus is not able to successfully decouple the forces. To
further illustrate this, a comparison with literature values and computational fluid simulations
can be seen in Table 3. The results immediately indicate that the forces, separately, are well
below the expected values of drag force for the flat plate. The sum of the two measured forces
however is similar, particularly at 20m/s, to the calculated forces. This indicates that the load
cells are successfully obtaining nearly all the force but are unable to split the force into its
components.
Table 3 - Preliminary test results
Fluid
Velocity Horizontal Load Vertical
Load Coefficient
COMSOL
(m/s)
Cell (N)
Cell (N)
Method (N)
Simulation (N)
10
0.6
1.5
4.4
4.2
20
9.1
7.6
17.8
17.0
30
15.0
17.7
40.1
38.5
In addition to the unsuccessful decoupling of the force, the vibrations apparent during testing
were also cause for concern. These vibrations, though they may be reduced with a larger mount,
will cause difficulty in reading the data and may cause damage to the wind tunnel. As a result,
the second design will be investigated and implemented.
4.2.4. Improved Design & Testing
In the case that the preliminary design did not decouple the forces, then an alternative design,
similar to Figure 12 below would be constructed and installed. This design was not completed
originally because of the potential need of extra space required underneath the tunnel, the
added complexity of design and a lack of time in the first semester to construct this system.
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This system would better decouple the lift and drag forces so they can be individually
measured. The strut is attached to members that are pinned and transfer forces along their
axes.
Figure 12 –Improved Apparatus
Figure 12 shows the secondary setup which has a support (1) that is located inside the wind
tunnel and connects to an external strut system outside. As lift and drag forces are applied to
the end of the support, they are transferred through the support where the drag component is
removed by the first (3) horizontal strut. This force is transmitted to the drag load cell (4). The
remaining lift force is then transmitted along the second (2) horizontal strut and down the
vertical lift strut (5) to the lift load cell (6). A counterbalance point (7) has been included in the
design though it is not necessary if load cells are being used instead of springs (which were
used in a previous design).
The support and strut system (Figure 13) have been made completely of lengths of aluminium
(25mm wide by 3mm thick). Aluminium was chosen as it will resist corrosion, it has sufficient
strength for low weight and is easily accessible. The main issue with using the aluminium was
finding a way to connect certain pieces together. Aluminium can be welded to itself but cannot
be joined as easily to steel which may cause issues due to the use of steel nuts to fasten the
struts to the load cells. Pieces 3 and 5 have nuts set into the ends so that they can be connected
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to the load cells. Obtaining aluminium nuts is difficult and welding something so small is
considerably difficult. Eventually, the nuts were fixed with strong adhesive which has been
successful.
All connections for the force balance system are made with M5 fasteners. M5 fasteners were
used as this is what is required by the load cells purchased. By designing the force balance with
M5 fasteners only, assembly is made easier by preventing mix ups and replacement parts are
easier to source.
Figure 13 – Photo of completed force balance installed in the wind tunnel
As with the initial design, three mounts will be used with this device (Figure 14). The first is a
flat plate mount for aerofoils or models that need to be held from below. This model is secured
in place by two M6 bolts. A second plate is included to be placed on the top in order to distribute
the clamping force of the bolts. Similar to the force balance, this mount has been constructed
from aluminium. The second mount, also primarily for aerofoils, has four telescopic arms that
grip the aerofoil from the sides. The arms are steel rod and they slide within aluminium tubing.
Steel was used in this instance as it is more malleable and less brittle than aluminium (Ashby
& Jones, 2005). Each arm is secured at the desired position by an M5 bolt. This mount was
designed in order to accommodate models with a round bottom surface that would not be able
to be mounted on the flat plate. The third mount is the rear plate mount that allows models to
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be mounted from the rear. Models are mounted with four fasteners. For further information
regarding the dimensions of the force balance and model mounts see section 1 in Appendix A
(Force Balance Practical Exercise Manual).
Figure 14 – Aerofoil mount diagrams
The second design was tested initially with a Clark Y aerofoil. The load cells were calibrated
statically by a 10N load applied in both the horizontal and vertical directions. At this stage of
calibration, the apparatus was not perfectly square and so it was noted that a drag force did
influence the lift load cell slightly and vice versa. The design was tweaked so that the apparatus
was square which resulted in the successful separation of the lift and drag forces. The results
from the initial test (see Section 4.2.5) with the Clark Y aerofoil were acceptable and similar to
calculated values.
4.3. Clark-Y Aerofoil on Flat Plate Mount Analysis
Testing with the Clark-Y aerofoil on the flat plate mount was conducted. During testing no illeffects were noticed and the model was subjected to the maximum fluid velocity of 40ms-1. The
following data regarding the lift and drag results for the Clark-Y aerofoil can be seen below in
Table 4.
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Table 4 – Clark-Y aerofoil wind tunnel testing
Fluid Velocity (m s-1)
Lift (N)
Drag (N)
10
0.7
0.1
20
2.9
0.9
30
8.3
2.0
40
16.8
3.8
4.3.1. Pressure Distribution Method
After measuring the forces using the force balance, pressure measurements along the profile of
the aerofoil were taken using a manometer. These manometer readings were then converted to
pressure differences and the segment lengths calculated. Once this was completed, they were
inputted into equation 2 from Section 2.4.2.1 and the lift was calculated. The resultant lift force
can be seen in Table 5.
Table 5 - Lift force calculated via pressure distribution.
Fluid Velocity (m s-1)
Lift (N)
10
1.12
20
4.28
30
8.65
40
12.82
4.3.2. CFD Simulation Results
In addition to wind tunnel testing, CFD simulations were conducted on the model. COMSOL
simulation software (Figure 15) was used for this procedure and the following results in Table
6 achieved. The figure shows how the velocity changes along the aerofoils profile. As can be
seen, the areas on top of the aerofoil have a higher velocity flow than those underneath
indicating that there is a lower pressure on the top surface.
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Figure 15 – Image of COMSOL being used on the Clark-Y Aerofoil at 20m/s
Table 6 – COMSOL computational fluid analysis results
Fluid Velocity (ms-1)
Lift (N)
Drag (N)
10
0.74
0.12
20
2.97
0.48
30
6.72
1.08
40
12.00
1.91
4.3.3. Data Comparison
At first view, the data in Table 6 is comparable to the data obtained for wind tunnel testing
(Table 4). Particularly at the slower two velocities. However, the higher velocities differ with
both the drag and lift being higher in the wind tunnel than in the simulations. Figure 16 shows
a graph that compares lift values for the various methods used to calculate and measure the
forces.
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Figure 16 – Comparison of lift forces
Figure 16 indicates that lift forces calculated with Zimmerman’s coefficient and the
computational fluid simulations are quite similar to the results achieved in the wind tunnel. The
Silverstein coefficient, which was significantly higher than Zimmerman’s, produces
significantly more lift. Due to this reasoning and the evidence shown in results from simulations
and testing it can safely be assumed that the results achieved with Silverstein’s coefficients are
not representative of this model.
Some discrepancy does exist between the test results, simulations and Zimmerman coefficient
results. Zimmerman coefficient does not take into account the surface roughness of the material
and while the simulation software has inputs for the surface roughness these are not likely to
be exact. This would have some effect on the discrepancies. Another source of discrepancy
could be in the shape of the aerofoil. While close to the desired shape, irregularities will exist
in the test model and this could affect the lift results. Interference from the mount could also be
affecting the lift of the model. Results for the lower velocities however are very similar,
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particularly between the test results and simulations, and so the results obtained for lift are
acceptable.
The results for the drag force of the wind tunnel tests compared to the simulation and coefficient
methods showed that the wind tunnel test drag forces are significantly higher than the
simulation results which are again higher than the coefficient results. This was expected as
additional drag force was expected to be created by the mount. The drag force would be caused
predominantly from the mount parts in contact with the model aerofoil. These areas will cause
added turbulence which will increase drag. For an aerofoil model with the flat plate mount the
additional drag at mid-range fluid velocities (20-30m/s) has been calculated to be 85% more
which increases as the fluid velocity increases.
4.4. Flat Plate Model on Rear Plate Mount Analysis
To ensure that the drag cell was working correctly and independently to the lift cell a flat plate
of know dimensions was tested. This model was also tested in section 4.2.3 with the preliminary
design and coefficient data can be seen in Table 2. The model was mounted using four bolts to
the rear plate mount and was tested through a range of fluid velocities from 9.5ms-1 to
33.25ms-1. Drag force data can be seen below in Table 7.
Table 7 – Flat plate drag force measurements
Fluid Velocity (ms-1)
Drag Force (N)
9.50
1.40
19.00
6.51
23.75
10.70
28.50
15.46
33.25
20.80
The flat plate was relatively heavy compared to other models tested and the effect this had on
vibrations was evident. The vibrations in the horizontal component were not excessive due to
the constant force in that direction. The vibration in the vertical component was substantial and
this meant that an accurate lift reading could not be obtained. Despite this, it was evident that
the lift force was relatively constant as the vibrations stayed centred around the -3.5N mark
(-3.5N were the initial conditions due to the weight of the plate). The reason that the vibrations
were an issue with this system is because of the large ratio between the contact area of the
mount and the area of the model as well as the centre of gravity of the model not being directly
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over the top of the support. A lot of force acts upon the outer extremities of the plate and so
when vibration occurs there is considerable momentum involved.
When the data from testing is compared to the calculated and computational fluid analysis
values (Table 8), the difference is considerable. The measured drag force has been linearly
interpolated due to the data being taken at frequencies that did not match the desired fluid
velocities. This will introduce some error as the relationship is polynomial but this error is
insignificant compared to the discrepancy between the calculated and measured results. The
measured results are 30% less than the Fail et al (1959) coefficient calculated drag forces and
nearly 250% less than the Munson et al (2009) coefficient calculated drag force. Meanwhile,
the COMSOL drag force is nearly 300% greater (for 20 and 30m/s) than measured. Due to the
small aspect ratio of the plate, it is suggested that substantial vortices are forming behind the
flat plate which increases the base pressure, reducing the drag. The sharpness of the edges of
the plates, and the considerable roughness of the sides, may also have affected the amount of
vortices as both of these characteristics would introduce turbulent flow more quickly. The
difference in results could be caused by some friction in the force balance causing a loss of
force during transmission to the load cells.
Table 8 – Flat plate drag force comparison
Fluid Velocity Coefficient
Drag COMSOL Drag Force Measured
Drag
(m/s)
Force (N)
(N)
(interpolated) (N)
10
2.65-4.45
5.37
1.67
20
10.58-17.81
21.61
7.39
30
23.80-40.07
49.06
17.15
40
42.30-71.26
88.37
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5. PEER TESTING AND EVALUATION
5.1. Effect of dimples on objects in air flow
In conjunction with this thesis, a fellow thesis student has been completing his own studies in
regards to fluid flow over smooth and dimpled geometries. Due to the geometries being
relatively simple the results were to be used as a guide as to how the force balance was
performing. The objects included a cylinder and an orgive shape. Two models were created for
each geometry with the only difference being the surface finish; one model was smooth and the
other dimpled. These models would then be tested in the wind tunnel to determine if there would
be a reduction in drag by dimpling the surface. Computational fluid dynamics simulations were
conducted to provide values for comparison.
5.1.1. Cylinder
The cylinder to be tested was hollow inside though had its ends capped and had a diameter of
50mm and a length of 100mm. The model was mounted directly onto the support (Figure 17)
so that the additional drag of a model mount would not affect the results. The cylinder was held
in place by two M5 threaded rods and 4 nuts.
Figure 17 - Smooth cylinder mounted in the wind tunnel
Testing was undertaken at 10m/s intervals starting at 5m/s. The cylinder performed well with
limited vibrations. The supporting rods were kept in the same orientation for both dimpled and
smooth models to ensure that they did not have an unexpected effect on the results. The results
for the smooth cylinder from testing and computational fluid simulations can be seen in Table
8.
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Table 9 - Smooth cylinder results
Fluid Velocity (m s-1)
Wind Tunnel Drag (N)
Simulated Drag (N)
10
0.183
0.193
15
0.467
0.492
20
0.846
0.891
25
1.381
1.454
30
1.976
2.080
35
2.572
2.707
40
3.152
3.318
The results from this testing indicate that less drag is occurring in the wind tunnel than in the
simulations. From 15m/s through to 35m/s it is noted that the percentage error between the wind
tunnel results and the simulated results is between 7% and 12%. At fluid velocities below 10m/s
it is observed that the force being measured for small to medium sized models is often not
attained effectively and there is often a large error. It should be noted that for most models
simulated there was very little difference in drag for sub-10m/s velocities.
It was unexpected that the wind tunnel drag would be less than the simulated drag. This could
be caused due to friction losses in the apparatus or some error in the shape of the model.
The dimpled model experienced similar forces to that of the smooth model. From the simulation
results, a drastic decrease in drag of approximately 57% was expected from the dimpled model.
Though the dimpled model did produce less drag, it was not percentage based as expected. The
reduction in drag over all speeds was approximately constant and centred around 0.16N.
Resultantly, the dimpled simulation results would be quite different percentage-wise to the test
result. Issues with surface finish could have affected the performance of the dimples and
increased drag. Also, due to the complex surface structure of the dimples, the computational
fluid dynamics software had difficulty running the dimpled model at high mesh frequencies.
This could mean that the simulation drag data is lower than it should be.
5.1.2. Orgive
The orgive to be tested comprises of two sections. A 50mm diameter cylinder that is 80mm tall
which connects to a 50mm diameter based cone with a 4.5mm diameter tip and is 90mm tall.
This model was mounted from the rear using a flat plate with two bolt holes (Figure 18). It was
expected that the mount would increase drag slightly though not significantly. This was due to
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the mount being thin and completely behind the back of the orgive. The main effect the mount
would have would be on the wake of the orgive.
Figure 18 - Orgive model mounted in wind tunnel
The results from the orgive (Table 9) indicate that the drag force for the wind tunnel results and
the simulation results are quite similar. The percentage error between the test and simulation
results within the 15 to 30m/s is approximately 11%. This error indicates that the model mount
may have slightly increased the drag on the model. Alternatively, the surface finish was not
exceptionally smooth and this may have had an effect on the results.
Table 10 - Smooth orgive results
Fluid Velocity (m s-1)
Wind Tunnel Drag Force (N)
Simulation Drag Force (N)
10
0.025
0.038
15
0.076
0.086
20
0.160
0.153
25
0.236
0.239
30
0.382
0.344
35
0.554
0.468
40
0.741
0.611
The simulations predicted that the dimpled model would have slightly lower drag values (1015% reduction at mid-range velocities) than its smooth counterpart. As the resultant forces are
quite low, this reduction of force was minimal. During testing, it was noted that the dimpled
orgive shape achieved very similar results to the smooth model and that it could not be
conclusively said whether the drag was increased or decreased by the dimples.
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5.2. ENG480 Projects
The students of ENG480 were tasked with designing models throughout the semester to
demonstrate fluid flow properties. These properties included lift and drag for the first two
projects and, for the last, the power generated by a turbine. The various uses of the force balance
show that the functionality and versatility is exemplary.
5.2.1. Aerofoils
Aerofoils are a good method of demonstrating the concepts of lift and drag and so a number of
students built aerofoils to demonstrate these fluid properties.
The first project involved the construction of an aerofoil that would be suited to supersonic flow
and testing it in subsonic conditions. The students expected to achieve less lift than drag for
their supersonic aerofoil (Figure 19), though the difference between lift and drag would
decrease as fluid velocity increased (Daley et al, 1947). This theory, when tested at the natural
angle of 6o, was proved correct as can be seen in Table 8 (fluid velocity (m/s) is equal to
approximately 0.76 times the fan frequency (Hz)).
Figure 19 – Supersonic aerofoil fitted with pressure taps (Kelly et al, 2014)
Table 11 – Data from testing of supersonic aerofoil (Kelly et al, 2014)
Fan Frequency (Hz)
Lift (N)
Drag (N)
Percentage difference
between lift and drag (%)
35
1.21482
3.80756
68.09
40
2.78265
5.04995
44.95
45
4.83952
6.52868
26.15
50
7.46969
8.35844
10.84
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5.2.2. Magnus Effect Demonstration
One group of students decided to demonstrate lift and drag by creating a rotating cylinder. The
purpose of this apparatus was to demonstrate the Magnus Effect. This phenomenon is where a
force is produced due to the rotation of an object submerged in fluid flow. This is not unlike the
sideways movement seen when a soccer ball is kicked with side spin on it or how a tennis ball
dips when top spin is applied in tennis. The effect is caused by frictional forces increasing the
fluid velocity on one side of the rotating object where the surface is travelling in the same
direction as the fluid while decreasing it on the other side where the surface is travelling against
the fluid flow (Figure 20). The increase in velocity on the one side decreases pressure, while
the decrease in velocity on the other increases pressure. As a result the rotating object will
experience a force towards the side where the surface is travelling in the same direction as the
fluid flow (Reid, 1997).
Figure 20 – Magnus effect (Aviation-for-kids, 2012)
The students designed an apparatus that would use paddles to grip the air and make the cylinder
spin at a certain speed (Figure 21). They calculated the rotational frequency to achieve 2N of
lift to be 760rpm though they could not determine how to determine the rotational frequency
during experimentation and so could not compare their results to theoretical data. The apparatus
was tested and at a fluid velocity of 20m/s they achieved 0.5N of lift and that, over a range of
speeds, the force was proportional with the square of the velocity as expected. The apparatus
successfully proved the Magnus effect at work.
Development of a Wind Tunnel Force Balance Practical
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Figure 21 – Magnus effect apparatus to demonstrate lift force
5.2.3. Wind Turbine
The final project that ENG480 students undertook was the design construction of a model wind
turbine. The students were to design the turbine for specific conditions power outputs then,
using scaling laws, downsize their models to fit in the wind tunnel. The apparatus would then
be tested to determine how much torque it produced. One group of students successfully built
a model (Figure 22) and tested the apparatus. They obtained torque values by attaching a string
from the outer surface of the shaft to the apparatus. By knowing the shaft diameter, and finding
the force in the vertical direction, they could calculate the torque. The results (Table 9) indicate
that the theoretical torque is considerably less than the measured torque for the model. The
measured torque is likely to be higher as, when scaling, smaller models generally have higher
efficiencies. In addition, the theoretical torque of the turbine was calculated from the power
which implies that the turbine is rotating. The torque measured was with the model stationary
and so does not take into account blade tip considerations which would reduce the torque.
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Figure 22 – Wind turbine secured in tunnel
Table 12 – Wind turbine results
Fluid velocity (m/s) Force measured (N) Torque produced
Torque calculated
(Nm)
(Nm)
15
2.3
0.0345
0.0015
20
4.0
0.0600
0.0037
25
6.3
0.0945
0.0072
30
9.0
0.1350
0.0140
35
12.6
0.1890
0.0248
As can be seen in Table 9, the measured forces are considerably different to the calculated
forces due to the reasons mentioned. The results do show polynomial behaviour which is to be
expected as the force should be proportional to the square of the fluid velocity. Overall, the
measured torque gives an indication of what forces are applied to a turbine in fluid flow.
5.3. Peer Testing Summary
Peer testing throughout this thesis has been useful as it has incorporated a wide range of model
types. The variety in models points to the versatility of the apparatus. The variety also leads to
a number of deductions regarding the force balances accuracy. The best operating range for the
force balance is between 15 and 30m/s. The percentage errors for all models when compared to
simulated data have been less in this range. At speeds lower than 10m/s the force balance loses
accuracy with speeds lower than 5m/s difficult to detect. It was also noted that at speeds higher
than 35m/s that the accuracy started to decrease again. This could be caused by increased
vibration at higher speeds making it difficult to gauge an accurate reading.
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The variety of models also indicated areas where improvements are required. The strut is not
completely rigid and so with heavier models tends to move laterally (in the direction
perpendicular to the flow). This observation has been highlighted, with others, as one area
where the force balance and wind tunnel can be improved.
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6. PRACTICAL OUTLINE DESIGN
The objectives of this practical are to encourage students to design, build and test their own
model to be used in the wind tunnel. Students will be grouped and asked to design and build a
model that is capable of meeting certain targets. They will be required to use their theoretical
knowledge to determine forces that will be encountered when the model is submerged in fluid
flow. These theoretical calculations will be conducted before the testing of the models. If a
group is unable to build their own, they will be able to use one of the test models.
Once the theoretical calculations have been obtained students can then test their models with
the force balance. Students will test their models over a range of velocities and determine lift
and drag coefficients from the data obtained. The students will then be asked discussion
questions about the practical and the apparatus to encourage further research and original
thought.
The information regarding the practical exercise will be delivered to the students via a Practical
Exercise Manual. The manual format has been based on existing apparatus manuals (Ebidon,
2013) used throughout the university in an effort to maintain a universal system. The manual
(Appendix A) contains information and instructions regarding the following items:п‚·
Detailed apparatus description
п‚·
Model mounting and construction guide
п‚·
Software operating instructions
п‚·
Software calibration instructions
п‚·
Wind tunnel operation guide
п‚·
Apparatus assembly procedures
п‚·
Velocity testing and coefficient derivations practical exercise method
п‚·
Basic theory
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7. CONCLUSION
Wind tunnels, even in this day where computer simulations are commonplace, are still an
important part of research and product testing. The force balance is an important apparatus for
wind tunnels as it provides the quantitative data that is required for further calculations. As
such, this thesis was focussed around the construction of a force balance and a subsequent
practical exercises manual.
The first part of this thesis involved the construction of an apparatus to measure force. An initial
design was manufactured in an attempt to directly measure the forces on the support via load
cells. It was noted that the forces were not successfully decoupled and so the design was
revisited and an improved design completed that successfully decoupled the forces by using a
series of linkages.
In addition to the physical apparatus, a software program had to be developed to convert the
data to a force. Once the software was completed and statically calibrated, test models were
used to determine whether the forces were being decoupled with initial testing yielded good
results.
Throughout this thesis, forces were calculated for each model using literature coefficients and
computational fluid analysis software. These theoretical forces would be used as a guide as to
how accurate the results from the force balance were. Results compared well with the Clark Y
aerofoil test model which obtained lift forces within 5% of the theoretical values at intermediate
speeds of 20 and 30m/s. The aerofoil also achieved significantly more drag which was expected
due to the interference of the model mount. Excellent results were also obtained when peer
testing was conducted. For the cylinder and orgive models, errors of less than 12% were
obtained. These results indicate that the force balance is achieving relatively accurate results
considering that they will experience some interference from the mounting system.
The production of a practical exercise manual was a major deliverable in the context of this
thesis. The manual was made available to ENG480 students prior to them commencing their
projects and was successful in communicating the operation and constraints of the wind tunnel
and force balance. Their use highlighted the versatility of the apparatus and the use over the
semester showed that it was easily removed and durable. The manual will also be used by
laboratory technicians who will be required to calibrate and maintain the apparatus.
The force balance produced achieved all of the primary objectives in that it is versatile,
removable and provides an accurate representation of forces on a model submerged in fluid
flow in the wind tunnel.
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8. RECOMMENDATIONS
Recommendations for future works into developing the force balance and wind tunnel include:п‚·
Create a software program that enables easier calibration, better display and potential
plotting against time. This will allow for the average to be taken and reduce the impact
of vibrations on readings.
п‚·
Alter the balance to allow for the angle of attack to be altered
п‚·
Install rollers that support the force balance laterally to reduce vibration and increase
stability
п‚·
Alter the balance so that two struts can be used to support models which will allow for
additional stability.
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9. APPENDIX
Appendix A: Practical Exercise Manual
Force Balance Practical Exercises Manual
Contents
1.
General Description of the System ............................................................................................... 48
1.1.
Apparatus Description........................................................................................................... 48
1.2.
Force Balance Specifications ................................................................................................. 50
1.3.
Model Mount Specifications and Installation Guide ............................................................. 51
1.4.
Software ................................................................................................................................ 52
1.4.1.
Software Instructions ........................................................................................................ 52
1.4.2.
Software Calibration.......................................................................................................... 53
1.5.
2.
Wind Tunnel Operation ......................................................................................................... 54
Theory ........................................................................................................................................... 55
2.1.
Force Balance Theory ............................................................................................................ 55
2.2.
Coefficient Theory ................................................................................................................. 56
2.3.
Pressure Distributions and Simulation Software .................................................................. 56
3.
Practical Exercises ......................................................................................................................... 57
3.1.
Model Construction................................................................................................................... 57
3.1.1.
3.2.
Model Construction Guide and Tips.................................................................................. 57
Velocity Testing and Coefficient Derivations ............................................................................ 57
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1. General Description of the System
1.1. Apparatus Description
The force balance unit (Figure 1) uses a series of struts to transfer the lift and drag forces encountered
by a model in the wind tunnel to two external load cells to measure lift and drag. The strut system
consists of the main strut (1) which links to the support strut (2) and the drag force strut (3) which
connects directly to the drag load cell (4). The support strut connects to the lift strut (5) which transfers
force to the lift load cell (6). The struts are 3mm thick by 25mm wide aluminium members and are
connected with M5 bolts. At the end of the support strut is a counterbalance (7) to negate the weight of
the model. Readings from the two load cells are transferred via four wires to the bridge (8) which
transmits these to the computer via the micro-USB cable (9).
In addition to the strut and load cell assembly, there are three interchangeable model mounts (Figure 2)
that can be placed on the top of the main strut. The first of these is the flat plate aerofoil mount (10) for
flat bottomed aerofoils or models that are to be mounted from below. The second mount is the telescopic
aerofoil mount (11) which has 4 telescopic arms that clamp the model in place from its sides. The final
mount is the flat rear mount (12) that allows a model to be mounted from the rear with screws or pins.
Figure 1: Force balance unit
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Figure 2: Model attachment parts
1.2. Assembly
The apparatus should be assembled in the following sequence. See figure 1 for diagram.
1) Attach strut 2 to the base at the pinned point ensuring the orientation is correct.
2) Screw the lift load cell (6) into position ensuring the directional arrow is pointing up.
3) Attach the lift strut (5) to strut 2 and then insert bolt through the bottom of the base,
through the lift load cell and into the end of the strut.
4) Attach the drag load cell (4) onto the base support, ensuring that the arrow is pointing in
the same direction as the fluid. Use a spring washer to ensure the load cell stays in
position when tightened.
5) Secure the apparatus in position under the wind tunnel test chamber.
6) Attach the main support (1) to the end of strut 2, ensuring that the model support end is
inside the test chamber.
7) Attach the drag strut (3) to the main support (1) and then secure the end to the drag load
cell (4).
8) Connect the load cells to the bridge as per the wiring diagram in the next section.
9) Connect bridge to the laptop using the micro-USB cable provided.
Adjust the screws that connect the lift and drag load cells to the struts to ensure that the
apparatus is square. For disassembly, the order should be reversed.
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1.3. Force Balance Specifications
Struts – the strut members in this balance are all made of 3mm by 25mm aluminium to reduce the
weight of the apparatus.
Bolted connections – all bolted connections are M5 galvanized steel Philips head bolts, typically 20mm
in length.
Load Cells – the load cells are 3133_0 Micro Load Cells (0-5kg) from Phidgets Inc. They have two M5
threaded holes at either end (40mm apart) for supporting and applying loads. Each load cell has four
wires; red, black, white and green which connect to the bridge.
Bridge – the bridge is a 1046 4-input Phidget bridge from Phidgets Inc. The bridge has 4 channels with
each channel accepting 4 wires. Marked on the bridge for each channel are the channel number, 5V, +,
- and G. Figure 3 indicates how the load cells are connected to the bridge, note the channel number
indicated (channel 0 is connected) at the centre of the channel. The bridge is then connected to a
computer via a micro-USB cable.
Figure 3: Phidget bridge showing correct wiring for micro load cells (red to 5V, green to +, white to – and black to G);
Image taken from http://www.phidgets.com/products.php?category=34&product_id=3133_0
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1.4. Model Mount Specifications and Installation Guide
Flat Plate Aerofoil Mount
The flat plate aerofoil mount is an 80mm long by 40mm wide aluminium base with two M6 holes drilled
60mm apart. The model should be prepared by drilling to 6mm diameter holes at the centre of the
aerofoil 60mm apart so that they match the holes in the baseplate. The model should then be placed on
the baseplate and bolted into place. A second plate is present to be placed on top in order to distribute
the forces better. Ensure the model is clamped tightly as not tightening sufficiently will cause the models
angle of attack to change mid-testing as the bolts have room to shift.
Telescopic Aerofoil Mount
The telescopic aerofoil mount is used for aerofoils or objects with curved bottom surfaces that will not
fit on the Flat Plate Aerofoil Mount. The mount has four telescopic arms that hold the model in place by
inserting the 6mm pins into holes predrilled into the model. The arms can extend to accommodate for
models ranging from 100mm to 430mm in width. There is 40mm between the base and the centre of the
pins and the pins are spaced 30mm apart. The telescopic arms are mounted on a flat plate with 4 M5
bolts and the arms are locked into place with a M5 screw. Ensure that the screws are tightened
sufficiently to ensure that the model does not rotate under the forces.
Rear Plate Mount
This mount is for models that have a flat rear surface. This mount is a base plate with 4 holes 30mm
apart horizontally and 25mm apart vertically. M5 bolts or screws are to be screwed into the back of
models to hold them in place. For models that will see repeated use, it is advised that a threaded collar
or a number of nuts be inserted into the model for easy attachment that will not damage the model.
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1.5. Software
Software for the force balance apparatus has been developed with National Instruments LabVIEW 2011.
The software takes the mV/V data obtained from the load cell and automatically converts the value to a
force in Newtons (N). The image below (Figure 4) shows the interface for the balance. An executable
program was created for this program however this limits the balance to its initial calibration parameters
as recalibration requires access to the block diagram (Figure 5) which can only be achieved using
LabVIEW.
1.5.1. Software Instructions
1. Open ForceBalanceProgram.vi on the computer.
2. Before running program ensure mini-USB cable is plugged into bridge and computer
3. On the bridge, check the channels for the DRAG and LIFT load cells and ensure that these are
selected in the Channel drop menu below
4. Ensure the Enable button for each cell is ticked, Gain should be left equal to 1
5. Press the RUN button (Play arrow in top left corner)
6. If Lift and Drag forces are not zero (or near zero) refer to calibration guide or record initial
values before proceeding with tests.
Instructions are also written on the interface for ease of use once the program is opened. If it is difficult
to read the data, the data rate can be adjusted for easier reading. The program may not work again if
stopped after being run. If this occurs, save and close the program before reopening.
Figure 4: LabVIEW Interface with instructions
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Figure 5: LabVIEW block diagram, note the place to add calibration formulas
1.5.2. Software Calibration
To recalibrate the force balance follow the steps below:
1. Remove any models or attachments on the main strut
2. Open Force Balance Program.vi in Labview and run the program
3. Record the Bridge Value’s when there is no force applied.
4. Apply a force of 10N to the strut using the Digital Force Meter and the hook attachment in the
horizontal direction (in the direction of flow) and record the Bridge Value for the drag load cell.
5. Reapply the force of 10N in the upwards direction and record the Bridge Value for the lift load
cell.
6. Being a linear system, the calibration formula is equal to y=mx+c where m=10/(Bridge Value
2 – Bridge Value 1) and c can be found by inputting the data for x and y for one of the readings.
7. Once formulae have been found they can be inputted into the Labview program by opening the
block diagram (Ctrl+E) and replacing the appropriate formulas.
8. Save the Labview program as once stopped the program may need to be reopened.
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1.6. Wind Tunnel Operation
Follow the below instructions when operating the wind tunnel:1. Ensure the wind tunnel is closed correctly, the door at the diffuser end is open and nothing is
left loose inside the tunnel.
2. Turn wind tunnel on at the power point; turn on main switch on switchboard; insert key, depress
and turn. The green light on the switchboard should now be on.
3. Insert starting velocity using <RESET button to scroll and arrow buttons to change. Once done,
hit enter and then run. Wind tunnel will start. Ensure someone is ready at all times to hit the
emergency stop button if something comes loose in the tunnel or any other issues arise.
4. The wind tunnel does not need to be stopped to change the speed. This can be done by changing
the frequency with the <RESET button and the arrows and once the selected frequency has been
inputted press the enter button.
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2. Theory
Lift and drag are two important concepts in engineering. Lift is created by a difference in pressure
between the top and the bottom of an object. For lift to occur there must be a lower pressure on top of
the object and a higher pressure underneath which pushes the object upwards. This is generally achieved
in aerofoils by forcing the air flowing over the top of the foil to travel faster therefore reducing the
pressure. This is why most aerofoils will have a larger curve on top so that the surface is longer.
Drag is also partly created by a pressure difference. Lower pressures will exist behind an object as
pressure at the front increases as the fluid encounters the object and is slowed down. Once behind the
object it accelerates again to produce a lower pressure. An easier explanation is that the inertia of the
fluid impacting the object will create a force that pushes the object in the direction of the free flowing
fluid. In addition to the drag due to the pressure difference, there will also be a force due to the friction
created as the fluid flows over the object.
A number of different methods exist to find the drag and lift forces. Firstly, research has been conducted
on many different objects and shapes. This research leads to the development of lift and drag coefficients
which can be used to find lift and drag forces for different dimensions and fluid velocities. Secondly,
for lift especially, the pressure difference can be found between the top and the bottom (or front and
back for drag) of the aerofoil. Thirdly, with the rise of computers, simulation software exists that will
use algorithms to calculate forces on an object in fluid flow and finally, there is the use of a balance or
force measuring device to directly measure the forces.
2.1. Force Balance Theory
The force balance works by physically putting a model in the fluid flow and measuring the forces upon
it. The purpose of the strut system seen in this force balance takes the resultant force and separates it
into the two constituent lift and drag forces. These forces are then read by the load cells and converted
to a force value by the software.
The load cells work by measuring the deformation of a specimen of known dimensions using a strain
gauge. The strain gauge measures the resistance of the strain gauge and, as the wires of the gauge are
stretched due to the deformation of the specimen, the resistance will change. This changes the amount
of voltage returning through the circuit. From this point, the strain gauge transmits the return voltage to
the bridge and thru to the computer where it can be converted and manipulated.
The balance will have an adverse effect on the drag performance of the model. A small part of this will
be due to the strut being directly exposed to the fluid, however as the strut is 3mm thick and only 25mm
long (in the direction of fluid flow) this drag will be minimal. The drag caused by interference of the
strut on the model however will be significant. When two objects join, fluid flowing around each object
is forced through smaller areas meaning it accelerates which uses additional energy and creates added
Development of a Wind Tunnel Force Balance Practical
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turbulence. This is particularly evident when the join is sudden and so designs are often altered to
accommodate this or reduce its effects.
2.2. Coefficient Theory
Perhaps one of the simplest methods of calculating the lift and drag forces for various models is by using
lift and drag coefficients. These coefficient are tabulated in various forms of literature. The coefficients,
however, are dependent on the Reynolds number and so a coefficient for a model at low speeds may be
different to the model’s coefficient at higher speeds. As well as being reliant on the Reynolds number,
the angle of attack is also very important to the coefficient, particularly in aerofoils. As the angle
changes, so does the profile of the object and therefore the amount of force produced. As a result,
coefficients are generally tabulated against the angle of attack or alternatively against each other (ie
Drag coefficient vs Lift coefficient).
Once the coefficients for a model is found at a certain Reynolds number and angle of attack, it can be
used in the coefficient formula. The formula for drag can be seen below where ПЃ is the density of the
fluid, V is the fluid velocity and As is the cross sectional area (area perpendicular to flow for drag and
parallel for lift):-
The force (F) and coefficient (C) can be changed with the respective lift values without altering the
formula (the area will also change due to the direction of the force changing). These values, presuming
the model is dimensionally accurate, should give close representations to the true force acting on the
model.
2.3. Pressure Distributions and Simulation Software
Other methods of calculating forces include finding the pressure distributions across a model. Once
found, the overall pressure can be calculated and then multiplied by the respective area to find the force.
This method can be done experimentally with a manometer or pressure measuring apparatus.
Simulation software can also be used to calculate the forces on a model. Using algorithms, the software
creates a mesh over an object and then calculates the pressure distribution. This distribution is then
converted to a resultant force. These simulations are generally good representations of actual forces and
will be a lot more precise than an experimental pressure distribution method.
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3. Practical Exercises
3.1.
Model Construction
The aim of this practical exercise is to develop a model that demonstrates the properties of lift and drag.
This model can then be produced and tested as per section 3.2 of this manual.
3.1.1. Model Construction Guide and Tips
In order to construct a model that can be analysed the following tips should help produce a model that
will perform as expected.
п‚·
Use a shape that lift and drag forces can be calculated for.
п‚·
Set a goal for the model to achieve. One method of doing this is to create a real life scenario and
then use scaling laws to create a model that will represent the scenario.
п‚·
Keep model weight down. Models should be as lightweight as possible to take stress of the
apparatus.
п‚·
Keep the maximum model width/height to 360mm. Good wind tunnel practice is to ensure that
models are not interfered with by the sides of the tunnel. The accepted maximum width for a
model is 80% of the test chambers width.
п‚·
Aerofoil models should be relatively large to reduce the effect that the apparatus will have on
the force readings.
п‚·
Allow for pressure taps to be inserted so that pressure distributions can be taken in other
practical exercises
п‚·
If using the flat plate mount and an angle of attack is desired, create a wedge to clamp between
the bottom plate and the model.
3.2.
Velocity Testing and Coefficient Derivations
The purpose of this exercise is to test a model at a range of different velocities and use the data obtained
calculate the coefficients of lift and drag for the model at its natural angle of attack.
1. Create model (this should be completed well in advance to the practical), preferably based on a
shape that has literature values for lift and drag coefficients available.
2. Mount model on the most applicable mount (see section 1.3) and bolt mount to the main strut.
3. Open the LabVIEW program and commence with the instructions seen in section 1.4.1 or on the
program interface.
4. Once setup, start the wind tunnel (see section 1.5 for basic wind tunnel operation procedures) at a
low fluid velocity (10m/s or 12.5Hz is a good starting speed).
5. Increase the speed to the first desired fluid velocity. Allow the flow to stabilise by waiting 30
seconds and record the lift and drag force displayed.
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6. Once measurements are completed, turn off wind tunnel, open the test chamber and remove the
model.
7. Using the lift and drag data obtained, calculate the lift and drag coefficients. Compare the calculated
and literature coefficient values for your model and plot against each other. Discuss the results and
any discrepancies or trends in the data.
8. (Optional) Create a 3D model of your object using a 3D CAD program and use Computational Fluid
Dynamics software to find lift and drag forces for comparison with the lift and drag obtained in the
testing.
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Appendix B: Design Calculations
Plexiglass properties
Yield Strength = Пѓy=72MPa; Elastic Modulus = E=3.3GPa (Evonik Industries, n.d.)
Average shear stress
Safety factor = 4; F=300N
рќђ№
300
𝜏𝑦 = 𝐴 = 0.01∗𝑥 =
72 000 000
4
Therefore minimum thickness to avoid failure by shear is x = 1.67mm
Maximum bending stress
𝜎𝑦 =
𝑀𝑦
, 𝜎𝑦 = 18 000 000𝑃𝑎
рќђј
рќ‘Џв„Ћ3 0.01 в€— рќ‘Ґ 3
рќђј=
=
;
12
12
𝑀𝑦 = 𝐹𝐿 = 300 ∗ 0.3 = 90𝑁𝑚
𝜎𝑦 =
𝑀𝑦 12 ∗ 𝑥 ∗ 90
=
;
рќђј
2 в€— 0.01рќ‘Ґ 3
рќ‘Ґ = 0.0548рќ‘љ
Minimum thickness to avoid failure from bending stress is 54.8mm
Deflection at x=55mm
I = 1.4*10-7m4
рќ›ї=
рќђ№рќђї3
300 в€— 0.33
=
= 0.0058рќ‘љ
3рќђёрќђј 3 в€— 3.3 в€— 109 в€— 1.4 в€— 10в€’7
5.8mm deflection considered to be too much so x was increased to 70mm. This yielded a
deflection of 2.9mm which was considered suitable.
Development of a Wind Tunnel Force Balance Practical
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Appendix C: Force Balance Drawing
10.REFERENCES
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Anderson, JD 2001, Fundamentals of Aerodynamics, McGraw-Hill Science, New York, NY
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<http://www.aviation-for-kids.com/the-magnus-force.html>
Barlow, JB, Rae, WH & Pope, A 1999, Low-Speed Wind Tunnel Testing, 3rd edn, John Wiley
& Sons, Inc, Massachusetts, USA
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University, Sweden, accessed 10/10/2013,
<http://www.umu.se/digitalAssets/120/120985_instructions-forfluiddynamics_comsol_v4.3a.pdf>
Daley, BN, Humprey, MD & Lindsey, WF 1947, The Flow and Force Characteristics of
Supersonic Airfoils at High Subsonic Speeds, National Advisory Committee for Aeronautics,
Washington, USA, accessed 25/05/2014,
<http://naca.central.cranfield.ac.uk/reports/1947/naca-tn-1211.pdf>
Ebidon 2013, UCPCN-UB Base Unit Manual, Ebidon International, Madrid, Spain
Evonik Industries 2013, Technical Information: Plexiglass, Evonik Industries, Darmstadt,
Germany, accessed 20/10/2013,
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