Final Year Project Report

By
ALEXANDER JOHN MOTT
April 2015
Supervisor Adam Kyte
An Investigation into the use of Computational
Fluid Dynamics to Model Flow Phenomena
around a Streamlined Body, Validated by
Experimental and Analytical Means
Honours project submitted in partial fulfilment
of the requirements for the degree of
MEng (Hons) in Mechanical Engineering
School of Marine Science and Engineering
Faculty of Science and Engineering
Plymouth University

Abstract
This report entails analytical, computational and experimental techniques in analysing drag
and flow behaviour over a streamlined body. This was carried out in order to determine
how effective CFD can be in order to determine different aspects of aerodynamic design.
Turbulence has a large role within the likelihood of flow separation. Therefore identifying
the transition from laminar to turbulent location, as well as the separation region is
important in quantifying drag on a body.
Various turbulence models were used in CFD to determine which highlighted more
accuracy when correlating with theoretical and experimental study. This was done in order
to develop an understanding and to give aid in further research, which techniques are best
suited for different applications. Also highlighting where the strengths and weaknesses
appear within the different techniques.
CFD proved very effective in correlating with analytical as well as experimental results, for
both drag values and separation regions. Although, major flaws in some CFD turbulence
models were found. This is discussed in greater detail within the main body of the report.
Acknowledgements
The author would like to thank Adam Kyte for his constant support and supervision with
the project. Also to Chris Pass and Matt Sharman who offered great support with the
computational study, as well as their constant interest in how the project progressed. The
author would also like to thank Richard Pemberton for the organisation and travelling
arrangements for the trip to Southampton to use the University’s wind tunnel. Also a great
thanks to Neil Fewings, Rick Preston, and Julian Sepp for their patience with the building of
the models needed for testing.

Table of Contents
Abstract....................................................................................................................................1
Acknowledgements..................................................................................................................1
Nomenclature ..........................................................................................................................4
List of Figures ...........................................................................................................................5
List of Tables ............................................................................................................................6
1. Introduction .........................................................................................................................7
1.1 Aim of the Project ....................................................................................................7
1.2. Objectives......................................................................................................................7
2. Literature Review.................................................................................................................8
2.1. Aerodynamic Drag ........................................................................................................8
2.1.1. Boundary Layers.....................................................................................................8
2.1.2. Types of Drag .........................................................................................................9
2.1.3. Flow Separation ...................................................................................................10
2.1.4. Reduction of Drag ................................................................................................11
2.1.5. Vortex Generators................................................................................................12
2.2. Theoretical Study ........................................................................................................12
2.3. Computational Study ..................................................................................................13
2.3.1. Meshing................................................................................................................13
2.3.2. Domain Size..........................................................................................................14
2.3.3. Turbulence Models ..............................................................................................14
2.3.4. Transitional Turbulence and Turbulence Intensity..............................................15
2.3.5 Convergence Criteria.............................................................................................15
2.4. Experimental Study.....................................................................................................15
2.4.1. Wind Tunnel.........................................................................................................15
2.4.2. Flow Visualisation ................................................................................................16
2.4.3. Measuring Forces.................................................................................................17

3. Method ..............................................................................................................................18
3.1. Theoretical ..................................................................................................................18
3.1.1. Drag Analysis........................................................................................................18
3.1.2. Flow Analysis........................................................................................................19
3.2. Computational ............................................................................................................20
3.2.1. The γ-θ Model......................................................................................................21
3.2.2. The Fully Turbulent Model...................................................................................32
3.3. Experimental...............................................................................................................32
3.3.1. Plymouth Wind Tunnel ........................................................................................34
3.3.2. Southampton Wind Tunnel Testing .....................................................................34
4. Comparison of Methods ....................................................................................................39
4.1. Drag Results ................................................................................................................39
4.2. Flow Visualisation .......................................................................................................42
5. Conclusion..........................................................................................................................44
6. Recommendations.............................................................................................................45
References .............................................................................................................................46
Appendix ................................................................................................................................49
Appendix A: Plymouth University Wind Tunnel Testing....................................................49
Appendix B: Load Cell Experiment.....................................................................................53
Appendix C: Force Measuring Mechanism Validation.......................................................55
Appendix D: Mesh Generation...........................................................................................57
Appendix E: Y+ Values........................................................................................................61

Nomenclature
Symbol Variable Unit
A Area m2
CD Drag Coefficient Based on Frontal Area -
CDA Drag Coefficient Based on Wetted Area -
Cτ Local Skin Friction Coefficient -
CτA Skin Friction Coefficient Based on Area -
D Diameter m
E Calculated Modulus of Elasticity Pa
ER Referenced Modulus of Elasticity Pa
I Inertia m4
L Length m
Re Reynolds Number -
ReL Local Reynolds Number -
V Velocity m/s
b Width m
h Height m
ε Strain
ρ Density kg/m3
σ Stress Pa
Term Definition
CFD Computational Fluid Dynamics
ANSYS CFX CFD software used
ICEM Meshing software used
SST Shear Stress Transport turbulence model

List of Figures
Figure 1: The boundary layer (NASA, n.d.)
Figure 2: Laminar to turbulent transition (Frei, 2014)
Figure 3: Skin friction and pressure drag (Warner, 2010)
Figure 4: Flow separation (Rotorhead, 2011)
Figure 5: Dimple effects on golf balls (ilovebacteria, 2015)
Figure 6: Effect of vortex generators (Henrikson, 2012)
Figure 7: Streamlined body in question
Figure 8: Structured and unstructured mesh (Sharcnet, 2006), (grid-generation, 2011)
Figure 9: Tufts on an airplane wing (Tsagi, 2015)
Figure 10: Oil flow in wind tunnel (Epema et al., 2012)
Figure 11: Smoke visualisation wind tunnel (Deppe, 2015)
Figure 12: Two bodies with theoretically identical drag
Figure 13: CD against teardrop length theoretical results
Figure 14: Theoretical separation region based on Tamai’s (1999) rule of thumb
Figure 15: Quarter body domain set up within ANSYS CFX-Pre
Figure 16: γ-θ results of CD against teardrop length
Figure 17: γ-θ model pressure and viscous drags
Figure 18: Full body view vector plot of 0.45m body
Figure 19: Zoomed in view vector plot of the 0.45m body
Figure 20: Full body view vector plot of 0.35m body
Figure 21: Zoomed in view of vector plot, near starting region of separation on 0.35m
Figure 22: Zoomed in view of vector plot, trailing end of 0.35m body
Figure 23: Separation location graph obtained from γ-θ model
Figure 24: A vector plot over the 0.35m body, without trip strip (top), with trip strip
Figure 25: Graph showing drag against velocity for 0.6 and 0.35m bodies using the γ-θ
model, as well as theory
Figure 26: Vector and intermittency plot on the 0.35m body at 25 m/s.
Figure 27: Vector and intermittency plot on the 0.35m body at 35 m/s
Figure 28: A vector plot over the 0.35m body, with executable
Figure 29: A vector plot over the 0.35m body, without executable
Figure 30: Turbulence intermittency (top) and wall shear X (bottom), to identify where,
and why transition occurs

Figure 31: Graph showing drag results against velocity for fully turbulent model and
theory
Figure 32: Previous mechanism for holding models in wind tunnel
Figure 33: New mechanism for holding models in wind
Figure 34: Method of attaching force gauge to wind tunnel
Figure 35: Layout of the model set up in Southampton’s wind tunnel
Figure 37: Drag results of the 0.6m body at different pre-loads in Southampton’s wind
tunnel
Figure 38: Drag results of the 0.35m body at different pre-loads in Southampton’s wind
tunnel
Figure 39: Drag results for the 0.35m body with and without trip strip at different
velocities
Figure 40: Smoke visualisation over 0.6m body
Figure 41: Smoke visualisation over 0.35m body with (right), and without (left) trip strip
Figure 42: Graph comparing drag results from different sets of data for 0.6m body
Figure 45: Graph comparing viscous and pressure drag for 0.35m body
Figure 46: Graph showing different values of CD for different length teardrops
Figure 47: Graph showing separation region for different body lengths
Figure 48: Motor oil visualisation against surface wall shear plot for the 0.35m body
fully turbulent (left) and γ-θ (right)
List of Tables
Table 1: The effects of implementing a trip strip
Table 2: The effects of the intermittency executable

1. Introduction
CFD has become a powerful tool within aerodynamic analysis. This report concerns how
effective it can be in conjunction with designing a record breaking hand cycle. This should
aid in deciding to change the shape dependant of the effects of flow separation. In order to
do this the fundamentals are broken down to a basic, teardrop shaped, streamlined body.
This will help analyse CFD’s pros and cons for analysing different drag components, whilst
analysing the effect of flow separation.
This project is a continuation from the works of Matthew Sharman’s project from the
previous year. Sharman (2014) highlighted some flaws within the concluding results due to
the wind tunnel results. It is also believed the CFD simulations could be improved. The
same streamlined body is in question and the same analytical methods will be adopted.
Different CFD meshing software will be used, as well as looking into the different
turbulence techniques. Wind tunnel techniques will also be scrutinised for improvement.
Adding to this, the implementation of laminar to turbulent transition techniques will be
incorporated into the CFD and experimental process in order to analyse how they can
reduce flow separation in attempt to reduced drag coefficients.
1.1 Aim of the Project
 Incorporate various CFD techniques in parallel with analytical study, as well as
experimental techniques, in order to determine how effective CFD can be to
determine different aspects of aerodynamics such as transition location, separation
point as well as viscous and pressure drags. All in aim to help determine how
effective CFD can be for the development of a hand cycle and other aerodynamic
applications.
1.2. Objectives
 Research into different CFD and experimental techniques that will help analyse the
aerodynamic flow over a streamlined body
 Carry out theoretical study, CFD and experimental methods to prove the various
effects of aerodynamic drag over different sized streamlined bodies
 Correlate the three methods to identify their pros and cons, to highlight how they
can be used in carrying out a full analysis of varying hand cycle shapes

2. Literature Review
2.1. Aerodynamic Drag
Drag is formally defined as the force corresponding to the rate of decrease in momentum
in the direction of the undisturbed external flow around the body (Houghton & Carpenter,
2003). Aerodynamics is the branch of dynamics that treats the motion of air and other
gaseous fluids and of the other forces acting on bodies in motion relative to such fluids
(Gove, 1993). This project aims for the identification of drag, quantified by Equation [1]
(Tamai, 1999):
𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 = (𝐶 𝐷 𝐴)
1
2
𝜌𝑉2
The aim of reducing drag in the modern world is undisputed (Summa, 1992). From
applications such as cars to golf clubs. This comes in tandem with other methods of
improving performance in aspects such as weight reduction, material usage, aesthetic
design and more. Thus, an equilibrium must be found between the prominent areas
(Henrikson, 2012). Equation [1] exercises 2 main characteristics that are editable when
improving aerodynamic efficiency, these are Cd and A. However, these are both under
constraint due to specific design criteria for varying products (Tamia, 1999).
The following sub-sections will detail individual components of drag and their effects on
streamlined bodies.
2.1.1. Boundary Layers
Boundary layers are a thin layer of flow
over a surface where the quantity of
viscosity is highly important (Tamai,
1999). Immediately adjacent from the
surface, the molecules do not move
relative to the surface, this is called the no
slip condition (Tamai, 1999). Above this,
layers gradually move faster relative to
the surface until they reach 99% of the
free stream velocity, this area is the
boundary layer.
[1]
Figure 1: The boundary layer (NASA, n.d.)

Boundary layers are split in to two types. One is laminar flow. This is where the molecules
flow uniformly over the surface. However, after a distance, instabilities happen within the
laminar flow causing the molecules to flow more erratically, this is the turbulent boundary
layer (Hoerner, 1965). Flow most commonly starts laminar, then transitions to turbulent
over a distance whether forced or natural (Tamai, 1999).
A turbulent boundary layer will increase the amount of viscous drag induced by a body,
whereas a laminar boundary layer is more susceptible to flow separation (Tamai, 1999).
2.1.2. Types of Drag
The three main types of drag in question are viscous (skin frition) drag, pressure drag and
form drag. Viscous drag is the resultant force applied by the viscous forces applied by the
fluid (Hoerner, 1965), (Houghton & Carpenter, 2003). This is a result of the fluid molecules
passing over each other within the boundary layer (Hoerner, 1965), (Houghton &
Carpenter, 2003). Pressure drag is a result of resolved components of the forces acting
normal to the surface at all points (Houghton & Carpenter, 2003).
Figure 2: Laminar to turbulent transition (Frei, 2014)
Figure 3: Viscous and pressure drag (Warner, 2010)
(Warner,2010)

Form drag is a result of flow separation happening on a body. This forms a larger region of
low pressure at the trailing edge of the body, thus sucking the body backwards (Anderson,
1997). In terms of reducing drag, a medium has to be found between the different
components. Large surface area will increase viscous drag, with the potential to decrease
pressure and form drag, and vice versa.
2.1.3. Flow Separation
Flow separation occurs during the effect of an overcoming adverse pressure gradient
downstream of the fluid. Elements within the boundary layer that lack momentum are
forced to change direction, causing the flow to separate from the body (Tamai, 1999),
(Anderson, 2011), (Bertin & Cummins, 2009).
Laminar flow is more susceptible to flow separation (Bertin & Cummins, 2009), (Houghton
& Carpenter, 2003), (Henrikson, 2014). This is because laminar flow retains a low kinetic
energy. Whereas, a turbulent boundary layer maintains a higher level of kinetic energy
allowing it to climb the pressure hill (Bertin & Cummins, 2009), (Houghton & Carpenter,
2003) (Hoerner, 1965).
A good rule of thumb to avoid separation is to ensure that the tangent angle of the surface
relevant to the free stream flow does not exceed 17°-20° (Tamai, 1999). However,
techniques can be utilised to reduce separation of flow.
Areas of low pressure
resulting in form drag
Flow separation occurring
Figure 4: Flow separation over different objects (Rotorhead, 2011)

2.1.4. Reduction of Drag
There are two types of drag reduction techniques available. One being passive techniques,
these require no energy input into the flow. Therefore, can just be a slight design
adjustment. The other being active techniques. These require energy input into the flow,
for example, to move the fluid/body interface and to suck or blow the fluid through it
(Choi, 1996).
The point made that turbulent flow is less susceptible to flow separation has been
exploited in different applications. A famous application is the dimples on a golf ball. The
dimples cause early transition of the boundary layer. Thus, resulting in the flow to stick to
the ball for longer, resulting in less form drag (Houghton & Carpenter, 2003), (Scobie,
2014).
However, as turbulent flow contributes more to viscous drag than laminar flow (Tamai,
1999), (Bertin & Cummins, 2009), it would be a hindrance putting dimples all over a
streamlined body. Therefore, a combination of the two flows is favourable.
Figure 5: Dimple effects on golf balls (ilovebacteria, 2015)

2.1.5. Vortex Generators
Vortex generators are specifically designed to control the transition area of the boundary
layer (Lin, 2002). They work by inducing vortices along the surface, exciting the boundary
layer causing it to transition to turbulent (Tamai, 1999). They are commonly used on the
top of aircraft wings to reduce form drag (Tamai, 1999), (Houghton & Carpenter, 2003).
2.2. Theoretical Study
The streamlined body under experiment is an axisymmetric streamlined body that is
proven to be able to produce low drag coefficients (Hoerner, 1965), (Tamai, 1999).
In order to calculate the drag, a series of equations need to be used, defining different
aspects of the streamlined body. Initially calculations have to be done on the properties of
a flat plate of same dimensions of the streamlined body (Tamai, 1999). These equations are
as follows:
Ping G30 golf club without
vortex generators.
Ping G30 Golf club with
vortex generators
Laminar flow separation
Turbulent flow
sticking to body
Figure 6: Effect of vortex generators (Henrikson, 2012)
D
L
Figure 7: Example of streamlined bodies in question
D
L

𝐶𝜏,𝑙𝑎𝑚 =
0.664
√𝑅𝑒 𝐿
𝐶𝜏,𝑡𝑢𝑟𝑏 =
0.0576
𝑅𝑒𝑡^0.2
𝐶𝜏 𝐴 = ∑𝐶𝜏,𝑙𝑎𝑚 + ∑𝐶𝜏,𝑡𝑢𝑟𝑏 ∗ 𝐷
𝐶𝜏,𝑓𝑙𝑎𝑡 =
𝐶 𝜏 𝐴
𝐿∗𝐷
𝐶 𝑑 𝐴 = 𝐶𝜏,𝑓𝑙𝑎𝑡(1 + 1.5 ∗ (
𝐷
𝐿
)1.5
+ 7 ∗ (
𝐷
𝐿
)3
𝐷𝑟𝑎𝑔 = 𝐶 𝑑 𝐴 ∗ 𝐴 ∗ 0.5 ∗ 𝜌𝑉2
For the sum of the skin friction drag values, transition from laminar to turbulent is generally
recorded at the point of the largest diameter, based on the findings from Tamai (1999).
2.3. Computational Study
Working within the limits of the available computer power is a skill in itself when working
with CFD. Therefore, domain and mesh size, play an integral role in depending how
accurate and capable the simulation is.
2.3.1. Meshing
A CFD simulations accuracy is governed by the amount of mesh elements within the
domain (Tu, 2008). Therefore, to be able to produce an effective mesh, a basic mesh should
be started with, using the appropriate convergence and turbulence models (Tu, 2008),
(Kyte, 2014). Following this, the mesh should be refined in the appropriate areas until the
results from the simulation stop altering (Tu, 2008), (Kyte, 2014). This should be done in
conjunction with the computational resources available (Tu, 2008).
The two main options for mesh generation, either a structured mesh, made up of either
hexahedra or tetrahedral elements. Or an unstructured mesh, that can consist of a mixture
of tetrahedral, wedges or hexahedra elements (Langtry et al., 2006).
Structured meshes with hexahedra elements are usually more efficient as well as more
accurate form of mesh generation than tetrahedral meshes (Biswas et al., 1998).
[2], [3]
[5]
[4]
[6]
[7]

2.3.2. Domain Size
It is suggested that for a streamlined body in a CFD simulation, the domain should allow ten
times the body length away from the body for the flow field (Mirzaei, 2012). However,
domain independency was found by Sharman (2014). Therefore, appropriate domain size
was already known.
2.3.3. Turbulence Models
The turbulence model chosen for a CFD simulation will be very influential on the results
(Counsil, 2012). Therefore, the correct use of turbulence models is vital in obtaining viable
results from the simulations. A highly recommended turbulence model is the shear stress
transport model (SST), due to its strong ability to determine a more efficient solution in
adverse pressure gradients (Counsil, 2012), (Sanz, 2012). The SST model also enables the
ability to determine the transition location of the boundary layer (Counsil, 2012), (Sanz,
2012). Through experimentation of turbulence model effects, it was found by Rastgou
(2013) that the SST model coincided with experimental data much more accurately than
the k-ε model.
To accurately model the SST model, a fundamental parameter that must not be eluded is
y+ (Kyte, 2014). This is a dimensionless value for how much the first element on a surface
protrudes into the boundary layer (Kyte, 2014). To be able to efficiently use the SST model
as well as transitional turbulence, y+ should remain around or below a value of 1 (Kyte,
2014).
Figure 8: Structure mesh (left), unstructured mesh (right)
(Sharcnet, 2006), (Grid-generation, 2011)

2.3.4. Transitional Turbulence and Turbulence Intensity
Transitional turbulence is important in CFD simulations as it attempts to replicate the
effects of practical applications (Counsil, 2012), (Sanz, 2012). This is due to natural
transition from laminar to turbulent flow that occurs in real applications (Tamai, 1999).
However, it has been pointed out that CFD can struggle with transition, as well as flow
separation (Langtry et al., 2006).
Another influential factor that turbulence will rely on is the inlet turbulence intensity (Sanz,
2012). However, depending on the application will define which intensity will be best
suited. Sanz (2012) computed a simulation involving transitional turbulence over an
aerofoil, and chose a zero gradient turbulent intensity, this was to highlight where
transition happens within a perfect environment. However, as the aim is to correlate the
results with wind tunnel experimentation, a zero gradient would not be an accurate option,
as it is already known through (Barlow, 1999), (Pankhurst, 1952) that the flow quality
within a wind tunnel is most likely relatively turbulent.
2.3.5 Convergence Criteria
Convergence criteria is a setting that defines the magnitude of accuracy of the simulated
results (Kyte, 2014). It is suggested by Kyte (2014) that for course meshes and initial runs,
1e-4
is acceptable. However, to further improve reliability and accuracy of results, 1e-5
is
necessary or even 1e
-6
.
2.4. Experimental Study
2.4.1. Wind Tunnel
The key to successful experiments in small wind tunnels is to have a clear understanding of
the likely role of the Reynolds number on the objects of the experiment (Barlow, 1999).
Also, an understanding of the flow quality will be necessary as they can adversely affect
results (Owen, 2008). To retain laminar flow in wind tunnels, a contraction ratio of 24:1 or
larger is most likely needed, as well as anti-turbulence screens (Barlow, 1999), (Owen,
2008) (Groth & Johansson, 1988). As well as this, sudden expansions after test sections can
create large scale unsteady flows and distortion of results (Owen, 2008). These will all have
to be taken into consideration in the experimental study.

2.4.2. Flow Visualisation
To help understand the flow pattern around a body, various different techniques can be
used. Attaching a series of tufts along the body can help determine where flow separation
occurs. Where the tufts have changed direction under the influence of the wind tunnel
conditions, identifies where the flow is changing direction (Barlow, 1999).
Another method is to use viscous liquids to try and show surface flow. The liquid will flow
under the influence of shear stress from the air stream, as well as gravity (Pankhurst,
1952), (Barlow, 1999). Oils are the most common for this application, such as petroleum
lubricating oils (Barlow, 1999).
Tufts in flow direction, highlight
flow remaining attached
Tufts in opposite direction to
flow, highlight flow separation
Figure 9: Shows the use of tufts on an airplane wing in a wind tunnel (Tsagi, 2015)
Laminar RegionTurbulent Region
Flow Separation
Figure 10: Shows the different flow regions over streamlined shape (Epema et al., 2012)

Another effective method for flow visualisation is using a stream of smoke within the wind
tunnel (Pankhurst, 1952), (Barlow, 1999). This can be a very effective way of identifying
flow separation as shown in Figure 11 (Henrikson, 2014), (Barlow, 1999). However, for this
to be an effective technique, wind tunnels usually have to be uniquely tailored for this
method (Pankhurst, 1952), (Barlow, 1999).
2.4.3. Measuring Forces
Forces applied by airflow can be measured using 4 different techniques (Barlow, 1999). In
order of frequency used, the techniques are listed below:
1. Measuring the forces by using one or more balances
2. Measuring the stress distribution over the model by means of orifices connected to
pressure measuring devices.
3. Measuring the effect that the model has on the airstream by wake surveys and
tunnel wall pressures.
4. Measuring the motion of the model under the action of the aerodynamic forces
and computing the results through motion equations.
(Barlow, 1999).
Laminar FlowTurbulent Flow
Flow Separation
Figure 11: Showing smoke visualisation over a car in a wind tunnel (Deppe, 2015)

3. Method
3.1. Theoretical
3.1.1. Drag Analysis
The theoretical study involved analysing the boundary layer effects over the streamlined
body. A parametric spreadsheet allowed simple comparison for the different sized
teardrops. This resulted in the ability to calculate the viscous drag values for the flow over
the body, as well as to integrate the effect of pressure drag into the total drag value by
using Equation [6] (Tamai, 1999). This process was originally carried out by (Sharman,
2014), although the process was repeated and validated to ensure no discrepancies were
found.
The only problematic aspect of the total drag equation is that it does not take into account
the shape of the trailing half of the body as shown in Figure 12. This was also noted by
(Sharman, 2014). Although, no progress in to how the equation can be altered to
accommodate the shape of the body has been made as of yet.
According to Equation [6] these bodies would have the same drag coefficients, as long as
the length and maximum diameter are the same. However, it is known that due to form
drag effects this would not be the case (Tamai, 1999), (Sharman, 2014).
Figure 12: 2 bodies that would theoretically retain the same drag

Figure 13: Analytical results of drag coefficient for different length teardrops at 16m/s
From these graphs it is evident that the 0.4m body would produce the least drag in
comparison with the others. As the body is increased in length, the drag would increase,
due to viscous drag, as the body is decreased in length, the drag would increase, due to
pressure drag.
3.1.2. Flow Analysis
In attempt to estimate where the flow would separate on different sized bodies, Tamai’s
(1999) rule of thumb of any region with a 17°-20° tangent angle to the freestream velocity,
was used in parallel with the geometry of the bodies. This would give foundations of
understanding which bodies would induce separation.
0.058
0.06
0.062
0.064
0.066
0.068
0.07
0.072
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
CD
Teardrop Length (m)
CD against Teardrop Length

Figure 14: Theoretical regions based on Tamai’s (1999) rule of thumb
The lower points represent the 17° tangent region, whereas the upper points represent the
20° tangent region.
3.2. Computational
A quarter body domain was used in the computational study, utilising symmetry planes, so
that the mesh could be denser, whilst saving on computational power. Free slip walls were
used on the side of the domain in attempt to reduce solid blockage effect.
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.3 0.35 0.4 0.45 0.5 0.55 0.6
DistanceFromLeadingEdge(m)
Sized Body (m)
Theoretical Separation Region
Inlet
Outlet
Symmetry planes
Quarter body
Free slip walls
Figure 15: Quarter body domain set up within ANSYS CFX-Pre

The SST turbulence model was adopted due to the extensive recommendation through
research from (Counsil, 2012), (Sanz, 2012), (Rastgou, 2013), and its ability to work with
adverse pressure gradients. This also led to the ability of retaining a transitional turbulence
model of γ-θ. Previous work done by (Sharman, 2014), proved that CFD seemed to struggle
with the streamlined shape and allowed separated flow to reattach to the body. This
should not be the case, as for this to happen, a favourable pressure gradient must exist
(Tamai, 1999), in which does not on the bodies under testing.
3.2.1. The γ-θ Model
To prevent flow reattachment from happening, an intermittency executable was obtained
from ANSYS. This limited the intermittency coefficient, as high intermittency coefficients
promote reattachment (Langtry et al., 2006). With this implemented, various sized bodies
were simulated in order to compare various different effects that would occur. Coefficient
of drag values at 16 m/s can be seen in Figure 16.
As can be seen in Figure 16, the coefficient of drag is dramatically larger for the 0.35m
body. To get a better understanding of where the differences in drag occur, results were
split up and dissected from the output file of ANSYS obtaining pressure and viscous drags
for each body. It was expected that larger bodies would retain larger viscous drag, due to
the larger surface area. However, the shorter bodies would retain larger pressure drag as
the adverse pressure gradient will be steeper. Pressure and viscous drag values at 16 m/s
can be seen in Figure 17.
Figure 16: Showing the coefficient of drag against various length of streamlined bodies
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.35 0.4 0.45 0.5 0.55 0.6
DragForce(N)
Length of Body (m)
γ-θ Results of CD against Teardrop Length
Cd

Figure 17: Pressure and viscous drags against teardrop length
As expected, as the size of body reduces, pressure drag increases whilst viscous drags
reduce. They show a reasonable relationship of changing equal and opposite, apart from
the pressure drag of the 0.35m body, which was huge in relation to any of the others.
Further investigation was carried out to identify why this was happening.
Using ANSYS post processing, it was noticed that the 0.45m, 0.4m and 0.35m bodies all
showed evidence of flow separation. The nature of the separating flow was analysed using
vector plots to understand where the differences were occurring. Vector plots place a sized
and coloured arrow at each node, based on the velocity of the flow at each node. From
Figures 18 and 19 it can be seen that flow reattachment still occurs on the 0.45m body.
This also occurred on the 0.4m body. Whereas, flow remains completely separated on the
0.35m body. Therefore, a much larger area of low pressure within the trailing half of the
body. This explains the vast increase in pressure drag for the 0.35m body.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.35 0.4 0.45 0.5 0.55 0.6
Drag(N)
Body Length (m)
Pressure and Viscous Drags
Pressure Drag
Viscous Drag

Figure 20 Shows the vector plot of the 0.35m body. As can be seen, there is a large region
of slow moving flow (dark blue area) at the trailing half of the body. Within this area, there
is a region just above the surface where there is a lack of colour. This is due to the arrows
being very small (low velocity), where the flow is reversing. A better visualisation of this is
shown in Figures 21 and 22.
Figure 19: Zoomed in view vector plot of the 0.45m body
body
Region of separation
Figure 18: Full body view vector plot of the 0.45m body
body
Region of separation
No flow reattachment
Figure 20: A full body view vector plot of the 0.35m body

As can be seen in Figure 21 there is a large amount of separation occurring near the surface
of the body. Also, this large area of separation continues further down the body, as can be
seen in Figure 22. Whereas, on the 0.45m and 0.4m bodies, the flow had reattached by
that point.
Reversed flow shows
separated flow
Figure 21: Zoomed in view of vector plot, near starting region of separation on 0.35m body
Figure 22: Zoomed in view of vector plot, trailing end of 0.35m body

It can be noted that when simulations were carried out on the bodies that induced
separation, ANSYS CFX struggled with convergence. To help the simulation, the time step
was reduced by a factor of 10. Therefore, steadying out the simulation. However, as the
time step was reduced by a factor of 10, this meant the iteration count had to be increased
by a factor of 10, to simulate the same amount of physical time. Even though this improved
convergence of the simulation with drastic effect, it meant simulation time was increased
massively.
To give a better understanding of how soon the flow starts to separate, the location of the
separation point could be found by plotting a line along the x coordinate where the flow
within the boundary layer starts to reverse.
As expected the shorter the body, the earlier separation happens. This will be due to the
steeper gradient of the trailing half of the body.
0.15
0.17
0.19
0.21
0.23
0.25
0.27
0.29
0.3 0.35 0.4 0.45 0.5
SeperationPointFromNose(m)
Body Length (m)
Seperation Point Obtained from γ-θ Model
Seperation Point
Figure 23: Separation location from nose against teardrop
length

To determine if a trip strip could be used in order to cause early transition in an attempt to
keep the flow attached to the body, a replica of the trip strip used in the experiment, see
section 3.3.2. Southampton Wind Tunnel, was implemented into the 0.35m body.
Using Figure 24, it can be seen that the flow over the 0.35m body with the trip strip
implemented, stays attached for a longer period. This also made a difference to the drag
readings.
Table 1: The effects of implementing a trip strip
0.35m No Strip 0.35m With Strip
Total Drag (N) 0.216 0.101
Pressure Drag (N) 0.177 0.0469
Viscous Drag (N) 0.0382 0.0540
Cd 0.0827 0.0387
Separation Point from Nose (m) 0.1887 0.2885
Reattachment Point from Nose (m) - -
As Table 1 shows, the drag was dramatically reduced by implementing the trip strip onto
the 0.35m body.
With the γ-θ model implemented at 16 m/s, for all bodies where separation occurs, the
simulation time had to be dramatically increased. This was most likely due to ANSYS CFD
struggling to fully identify the transition or separation location, as the simulation will be
trying to find an average. Therefore, to understand if the transition or separation location
Separation Point
Difference
Figure 24: A vector plot over the 0.35m body, without trip strip (top), with trip strip (bottom)

was moving about throughout the simulation, a transient simulation was utilised. This
enabled the ability to plot different criteria at different time steps. Putting different plots
into an animation, it was noticed that the separation location moved very little. However,
the transition location proved to be very unsteady. Therefore, this explains the difficulty for
the steady state simulation to converge. To view the animations double click links below.
Or see “0.35m Intermittency” & “0.35m Vector Plot” videos from DVD in back of log book.
See online copy for videos
See online copy for videos

Further simulations were carried out at 25m/s and 35m/s, to determine how the drag
varied dependant on velocity. As known from Equation [1], drag should increase with
velocity2
.
As Figure 25 shows, the results from the γ-θ model show completely different patterns to
the analytical analysis. The 0.6m body retains very low values for drag, whereas the 0.35m
body increases dramatically up to 25m/s, then reduces at 35m/s.
To understand what is causing the drop in drag with velocity increased from 25m/s to
35m/s, CFX post was utilised, plotting vector, and turbulence intermittency plots for both
25m/s and 35m/s runs.
Figure 25: Graph showing drag against velocity for 0.6 and 0.35m bodies using the γ-θ
model, as well as theory
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
Drag against Velocity Using γ-θ Model
0.6m CFD
0.35m CFD
0.6m Theory
0.35m Theory

As can be seen from Figures 26 and 27, the flow separates at a similar region. However, in
Figure 26, transition from laminar to turbulent occurs gradually (blue to red) with flow at
25m/s, and remains separated. Whereas, in Figure 27, transition happens very suddenly.
Thus, causing the flow around the body to reattach, in turn causing lower pressure drag,
which resulted in a lower drag all together.
Figure 26: Vector and intermittency plot on the 0.35m body at 25 m/s.
Flow remains separated without reattaching
TurbulentTransitionLaminar
Figure 27: Vector and intermittency plot on the 0.35m body at 35 m/s
Brief separation region
TurbulentTransitionLaminar

Due to the unusual behaviour of the γ-θ model with the executable file implemented, it
was important to compare the effects it had on the simulation. The 0.35 body was
compared due to its vast difference in results in comparison with the other results. All the
same settings were implemented in the set-up. However, the intermittency executable file
was not used. Table 2 shows the difference in results with and without the executable.
Table 2: The effects of the intermittency executable
Intermittency
Executable
No Intermittency
Executable
Total Drag (N) 0.216 0.105
Pressure Drag (N) 0.177 0.0544
Viscous Drag (N) 0.0382 0.0502
Cd 0.0827 0.0401
Separation Point from Nose (m) 0.189 0.211
Reattachment Point from Nose (m) - 0.247
It is evident that the intermittency had a dramatic effect on the simulation results on the
0.35m body. As it can be seen the drag, hence the CD, was more than double the value with
the executable file. This is due to the vast increase in pressure drag. With the executable in
place the flow remained separated, as well as separating earlier along the body. This
explains the large increase in pressure drag, and reduction in viscous drag. Figures 28 and
29 show the difference in flow over the trailing end of the 0.35m body.
Figure 28: A vector plot over the 0.35m body, with executable
Flow remains separated without reattaching

Minor transition
Separation almost occurring
Major transition
Start of separation
Transition after separation
Figure 30: Turbulence intermittency (top) and wall shear X (bottom), to identify where
and why transition occurs
Flow reattachment occurred due to transition induced by separation, the same reason as
the 0.35m γ-θ at 35m/s simulation, Figure 27. So far the γ-θ model has shown resistance to
transition from laminar to turbulent, until induced by separation.
To investigate this further, turbulence intermittency, and wall shear were plotted against
each other for the 0.6m (no separation), 0.45m body (brief separation), and 0.35m body
(large separation).
From Figure 30, it is evident that transition only occurs over streamlined body when
separation is about to, or already has occurred.
Figure 29: A vector plot over the 0.35m body, without executable
file
Brief separation region

3.2.2. The Fully Turbulent Model
Due to the unusual behaviour of the γ-θ model, simulations were carried out at a variety of
velocities, with the SST fully turbulent model implemented.
As it can be seen from the Figure 31, the results from the fully turbulent model coincide
with the theoretical results to a high degree.
3.3. Experimental
Due to time constraints, only two models were manufactured for the experiment, one
where separation was not expected, and one where separation was expected.
Taking from the progress made by (Sharman, 2014), it can be noted that the wind tunnel
study could have produced unreliable results. This could have been due to the large force
balance that held the teardrop within the wind tunnel hence extra drag induced by the
balance, as well as causing turbulence along the body, see Figure 32.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
Fully Turbulent & Theory Results Against Velocity
0.6m CFD
0.35m CFD
0.6m Theory
0.35m Theory
Figure 31: Graph showing drag results against velocity for fully turbulent model and
theory
Figure 32: Previous mechanism for holding models in wind tunnel

Therefore it was decided that a new device could be made to hold the teardrop without
disturbing the drag readings as much. This was done by suspending the model with guitar
strings from above. Therefore, much less disturbance would be caused, see Figure 33.
With the models being suspended, it meant that the wind tunnels force reader could not
be utilised. To overcome this, the initial idea was to design a load cell, incorporated with a
strain gauge, to calculate force from the body pulling on the load cell. It was found that this
would not produce high enough accuracy for the minute drag readings expected, see
Appendix B. Therefore, it was decided that a digital Newton meter would be ordered to
ensure accuracy of measuring drag. However, this instigated a new problem to be tackled.
The force gauge would have to be fixed to the wind tunnel with a certain mechanism.
Firstly it was thought that this would have to sit just before the constriction. However, due
to the ability to feed a guitar string through the bodies, and out of the back, this allowed
the force gauge to be attached to the back of the wind tunnel, by adding a pre-load from
the body, then the force deducted from the air flow would equal the drag of the body. See
Figure 34.
Figure 33: New mechanism for holding models in wind
tunnel

3.3.1. Plymouth Wind Tunnel
Several experiments were carried out in Plymouth University’s wind tunnel although due to
uncertainty of wind speed and excessive vibration of the wind tunnel, the results obtained
were not repeatable enough to be used as reliable data. Adding to this, Plymouth
University’s wind tunnel has a sudden expansion after the testing section. As previously
explained in section 2.4.1 Wind Tunnel, this could cause distortion to results, due to large
scale unsteady flows (Owen, 2008). For further detail about the experiment carried out in
Plymouth University’s wind tunnel, see Appendix A.
3.3.2. Southampton Wind Tunnel Testing
A cage was built to accommodate the same suspended method that could be applied in
Southampton’s wind tunnel, see Figures 35, and 36. Utilising the attachment points of the
force gauge on to the cage, numerous runs with different pre-loads could be carried out
again to try and gain repeatability from results.
Figure 34: Method of attaching force gauge to wind tunnel

Teardrop body
Cage to support teardrop body
Force gauge

From Figure 37 it can be seen that the 3 sets of data for the 0.6m body testing, were very
repeatable.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
0.6m Body at Different Pre-Loads
6.82
6.7
14.7
Figure 37: Drag results of the 0.6m body at different pre-loads in Southampton’s wind tunnel
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
7.68
10.82
10.7
Figure 38: Drag results of the 0.35m body at different pre-loads in Southampton’s wind tunnel

From Figure 38 it can be seen that the 7.68N pre-load test for the 0.35m body, retained
lower drag values apart from at 35m/s. This could have been due to the 0.35m body being
less stable in the tunnel due to its smaller mass, and the lower pre-load not damping the
vibration as much.
In addition to the experiment, was the investigation into tripping the flow from laminar to
turbulent at a desired point, to see how drag was effected. This consisted of a piece of
double sided tape, 8mm in depth, 94mm from the leading edge, covered in C80
carborundum powder. The surface roughness was found from (Struers, 2015) so it could be
replicated in ANSYS CFX.
From Figure 39 it can be seen that using the carborundum powder to trip the flow caused
an increase in drag. This will most likely be due to the added friction from the strip, as well
as the strip would have caused early transition to turbulent flow. Thus, resulting in larger
viscous drag from turbulent flow.
As well as the values obtained from the experiment, flow visualisation techniques were
used. The aim was to find out where the flow would separate on the body, as well as
finding the transition location. There was little to no separation expected on the 0.6m
body. Whereas, separation was expected to happen early on the 0.35m body. Also, a
delayed separation was expected on the 0.35m body with a trip strip implemented.
Figure 39: Drag results for the 0.35m body with and without trip strip at different velocities
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
0.35m Body - Natural Transition vs Forced Transition
10.82
Carb Powder

Figures 40 and 41 show the streamlined bodies under smoke visualisation. Due to the
transient behaviour of the flow, it was difficult to pick out an exact separation location.
Therefore, screen shots, taken at different times of the video, for the 0.35m body, with and
without the trip strip, are shown in Figure 41. Or see “Smoke Visualisation” video from DVD
in back of log book.
Tufts were also used in order to try and determine the separation region. Although, they
proved ineffective in the experiment.
Figure 40: Smoke visualisation over 0.6m body
Figure 41: Smoke visualisation over 0.35m body with (right), and without (left) trip strip.

4. Comparison of Methods
4.1. Drag Results
First of all the drag values of the 0.6m and 0.35m were compared for all methods at
different velocities. Figure 42 shows the results from each method.
From Figure 42 it was evident that the γ-θ model retained much lower drag values than the
other methods.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
0.6m Drag Results Against Velocity
Theory
CFD Turbulent
Experiment
CFD γ-θ

From Figure 43 it is evident that the γ-θ model retained a very unusual relationship as
velocity increased. To identify where the differences occurred, pressure and viscous drags
were plotted at different velocities.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5 10 15 20 25 30 35
Drag(N)
Velocity (m/s)
0.35m Drag Results Against Velocity
Theory
CFD Turbulent
Experiment
CFD γ-θ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
15 20 25 30 35
Drag(N)
Velocity (m/s)
0.6m Pressure and Viscous Drag Results
Theory Pressure Drag
Theory Viscous Drag
γ-θ Pressure Drag
γ-θ Viscous Drag
Turbulent Pressure Drag
Turbulent Viscous Drag

Figure 45: Graph comparing viscous and pressure drag for 0.35m body
From Figures 42-45 it is evident that the fully turbulent SST model matches up much better
with the theory and the experimental data than the γ-θ model.
Figure 46: Graph showing different values of CD for different length teardrops using the
turbulent CFD model
0
0.1
0.2
0.3
0.4
0.5
0.6
15 20 25 30 35
Drag(N)
Velocity (m/s)
0.35m Pressure and Viscous Drag Results
γ-θ Pressure Drag
γ-θ Viscous Drag
Theory Pressure Drag
Theory Viscous Drag
Turbulent Pressure Drag
Turbulent Viscous Drag
0.058
0.059
0.06
0.061
0.062
0.063
0.064
0.065
0.066
0.067
0.068
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
Cd
Teardrop Length (m)
Cd against Teardrop Length
Theory
CFD
Experiment

As Figure 46 shows the theory and the CFD correlate well in relation to CD values against
teardrop length. Adding to this, the experiment proved effective in highlighting that the
0.35m body retained a lower Cd value in comparison with the 0.6m body.
4.2. Flow Visualisation
To determine how much Tamai’s (1999) rule of thumb matches up with the CFD, a graph
was plotted for separation regions based on the 17°-20° tangent to freestream flow (blue
points), as well as the separation locations based on the CFD results (Turbulent – red
points, γ-θ – green points).
Figure 47: Graph showing separation region for different body lengths
From Figure 47 it is evident that the γ-θ model predicted earlier separation, whilst the
turbulent model predicted later separation. Adding to this Tamai’s (1999) rule of thumb
predicted separation for all bodies. Although, the rule of thumb is a basic estimation, and is
also most likely used in conjunction with sudden changes of tangent angle, rather than
steady decline, in which the teardrop shape retains.
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
DistanceFromLeadingEdge(m)
Sized Body (m)
Seperation Region

Due to the uncertainty of the smoke generator for identifying flow separation, motor oil
pictures from (Sharman, 2014) were used to identify the separation point with
experimental methods.
From Figures 48 it is evident that the turbulent SST model matches up with the experiment
perfectly. Whereas, the γ-θ model causes much earlier separation. The theoretical
separation region also occurs before the experimental and turbulent SST model. Although,
this is based on Tamai’s (1999) rule of thumb. Therefore, inaccuracies are expected with
this method.
Figure 48: Motor oil visualisation against surface wall shear plot for the 0.35m body fully
turbulent (left) and γ-θ (right)
γ-θ Turbulent
CFD separation point
Experiment separation point Identical
separation point
Theoretical
separation point

5. Conclusion
This project utilised a wide array of CFD setups in order to compare them with theory and
experimental data, to try and determine the best method for approaching streamlined
body design. Whilst some methods proved unrealistic and inaccurate, some aspects of CFD
proved excellent in aerodynamic analysis.
It is suggested that if using CFD to try and understand the flow, and obtain drag results,
that the γ-θ model should not be adopted. This is due to its unusual behaviour that has
been proven over a basic model. Not only separation regions that do not match up, also it’s
unwillingness to allow laminar flow to turn turbulent until it is induced by separation.
However, the SST model adopted as fully turbulent, proved excellent in obtaining drag
results similar to experiment and theory, as well as accurate separation locations.
Unfortunately so far flow visualisation techniques have not been found to prove effective
in defining a transition location of the flow over a body, which could prove pivotal in
developing a full understanding of how the flow reacts over streamlined bodies.
The experiment carried out analysed small bodies, in comparison with what would most
likely be used in typical engineering applications. Thus, developing small drag values, this in
turn, would create larger percentage errors than using a larger body. Therefore, to improve
the experiment with further accuracy, larger scaled bodies could be analysed in attempt to
reduce the percentage error. Adding to this, a more realistic shape, for applications such as
developing a record breaking hand cycle, could be analysed to understand if the same
findings would be developed.
The overall findings of this project were as follows:
 The SST γ-θ model proved ineffective for simulations accuracy, whilst the SST
turbulent model proved very effective
 The wind tunnel drag results showed repeatability and great confidence in their
accuracy has been shown
 Not enough confidence in the transition location along the body has been obtained

6. Recommendations
Further analysis using flow visualisation techniques to understand the exact transition
location could be adopted. ANSYS could then be manipulated to set the known transition
location, to determine if this would prove more reliable.
Further experiments on different sized bodies would help reduce any percentage error that
might have developed within the experiment. Thus adding further validation to the
experiment and comparison with CFD methods.
Taking on a study of a more complex shape would also help greatly in ensuring CFD’s
accuracy of drag results and ability to determine correct flow visualisations such as
separation region. Thus, also developing further insight into how flow behaves over
streamlined bodies.

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Appendix
Appendix A: Plymouth University Wind Tunnel Testing
The experiment was carried out several times within Plymouth University’s wind tunnel to
try and obtain as reliable results as possible. Different predetermined loads were used to
see if they had an effect on the accuracy of results. Also, the force gauge software was
utilised as it had the ability to take a certain amount of readings per second. For the
experiment carried out it was decided that 50 readings per second would be suffice to deal
with the vibration of the model and the wind tunnel.
For each of the runs, the velocity of the air flow had to be measured as the wind tunnel can
only be operated by motor speed. Measuring the velocity was done by using a Pitot-static
tube to take the dynamic pressure. Then this was converted using the formula:
𝑉 = √
2 ∗ 𝛥𝑃
𝜌
As this was done for each experiment, not all of the velocities were identical.
The experiment carried out on the longer body showed little correlation between different
test set ups. There is some similarity shown between the 19N and 9N set up. However, the
8N set up has shown lower drag values.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 10 12 14 16
DragForce(N)
Velocity (m/s)
8N
9N
19N

As the graph shows, drag gradually increases with velocity. However, it does have areas
where it reduces with velocity. There is an evident leap in drag between 4m/s and 6m/s,
even with the 10N pre-load showing higher drag results, the jump in drag still existed. This
could be down to several factors within the experiment such as:
 The wind tunnel at low speeds vibrated a lot. Thus, could have cause distortion to
results
 At the specific speed, the natural frequency and the vortex shedding frequency
could have been matched, causing exaggerated vibration to the model
 A laminar to turbulent transition occurring causing further drag to the model
One issue with the force readings in comparison with their relative velocities is that they do
not correlate well with the theoretical results for altering velocity. Theoretically the drag
should increase with velocity2
. However, it is evident that this does not occur, due to the
unsteady behaviour of the graphs.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 10 12 14 16
DragForce(N)
Velocity (m/s)
8N
10N
15N

To ensure the force gauge was set up so that it was reading correct values of force, a
calibration experiment was taken out. This involved setting up a pulley system behind the
force gauge, and adding known weights to the pulley, acting the same way drag would act
on the model. Readings were taken from the force gauge in 10g (0.0981N) increments and
proved that the method was sufficient for reading force acting in the same direction. For
further detail see Appendix B.
There were a few fundamental flaws in the experiment carried out in Plymouth University’s
wind tunnel. These were such as:
 The velocity was measured using a Pitot-Static tube, which fluctuated largely,
especially at high wind speeds, therefore velocity could not be full confirmed
 The wind tunnel vibrated a lot causing the model, and force gauge to move about
 Due to the vibration, the readings on the force gauge fluctuated monumentally
 The maximum velocity of the wind tunnel was only 16m/s. Therefore, relationships
were hard to recognise at such low velocities.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 2 4 6 8 10 12 14 16
Drag(N)
Velocity (m/s)
Experiment vs Theory
0.6m Experiment 0.35m Experiment 0.6m Theory 0.35 Theory

Below are graphs from the force gauge readings. As it can be seen, a lot of fluctuation
occurs whilst the results were being obtained.
Although the experiment in Plymouths wind tunnel has some flaws in it, it has shown the
method in which the drag force is being measured has proven somewhat effective for both
bodies. Therefore, to try and reduce the experimental error Southampton’s wind tunnel
was used. The benefits brought by Southampton’s wind tunnel was that:
 The output of the wind tunnel was altered by wind speed rather than motor speed.
Therefore, the exact wind speed was known
 Much less vibration occurred as the wind tunnel was much larger and solidly fixed
to the floor
 The flow through the testing section would be much less turbulent
 The maximum velocity was 40m/s

Appendix B: Load Cell Experiment
The initial plan was to manufacture a load cell that would be accommodated with a strain
gauge to measure to drag force.
Once this was designed, a replica of the testing section was made to ensure the measuring
method would be suffice. This was done by using a flat metal plate, attaching a strain
gauge, and adding weights on in increments of 10g, in 3 different locations to measure the
strain. The results of strain were put into an excel spreadsheet. Once this was done, the
following formulae were applied to the set of results:
𝐼 =
𝑏ℎ3
12
, 𝑇 = 𝐹 ∗ 𝐷 𝜎 =
𝑇
𝐼
∗
ℎ
2
𝐸 =
𝜎
𝜀
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 =
𝐸−𝐸 𝑅
𝐸 𝑅
∗ 100
ER is the modulus of elasticity obtained from (Groover, 2011). This was used so there was a
basis in which the accuracy of the results could be found.
Mass of Weights (kg)
Distance to Centre of Strain Gauge (m)
0.05 0.06 0.07
% Out
0.01 33.3 28.0 24.4
0.02 18.5 16.3 14.8
0.03 6.63 6.63 1.78
0.04 -7.28 -8.60 -9.53
0.05 2.53 3.19 3.67
0.06 -0.03 3.75 4.15
0.07 0.87 1.78 2.45
0.08 4.02 -1.57 1.21
0.09 2.09 1.02 1.78
0.10 2.53 -0.03 0.87
Average % Out 7.04 5.90 5.51
Range % Out 33.3 29.5 23.5
Testing Section
Taken as an anomaly due to re-calibration of strain gauge reader.

Due to varying accuracies obtained from the experiment, it was found that this method
would not have the desired accuracy for measuring drag over the streamlined body.
0.06m
0.07m
0.05m

Appendix C: Force Measuring Mechanism Validation
To ensure the method of measuring drag was sufficient, a calibration study was carried out.
The experiment was set up ready for a wind tunnel analysis to be carried out. Then a pulley
system was fitted onto the back of the wind tunnel. This allowed known weights to be
added to the pulley, which would then take off the force from the force gauge, acting in the
same way drag would.

As the graph shows, the method of measuring force would be suffice for the experiment as
the measured mass was almost identical to the added mass.

Appendix D: Mesh Generation
This Appendix is a walkthrough of how the mesh for the CFD simulations was created.
Firstly the quarter body domain was imported into ICEM as a parasolid, and the surfaces of
the domain were named so that their specific features could be assigned when setting up
the simulation.
Points were drawn at specific locations along the teardrop shape, in order to allow the
mesh to be associated with the geometry of the body.
Inlet
Walls
Teardrop Symmetry plane
Symmetry
plane
Outlet
Points added

Then individual sections of the domain were split into blocks so that unique mesh patterns
could be implemented in certain areas. Each block edge was then associated with its
individual curves, and block vertices with the added geometry points, in order to assign the
mesh sizing’s in the correct places.
Once all associations had been made correctly, the mesh could be sized accordingly, ready
to be imported into ANSYS CFX.

0.35m
Appendix E: Y+ Values
0.45m
0.5m
0.4m

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