Abstract
Lift, drag and pressure measurements of a NACA 0018 (what is NACA?) under varied angle
of attack (what angles? 0-90 in 10 degree steps?) was compared numerically using fluent
and experimentally in a wind tunnel. A NACA 0018 model of (no need to restate model)
chord length of 0.4 m was tested at a Reynolds number of 360,000 in the University of
Limerick (the location of the wind tunnel is irrelavent).
A two dimensional CFD analysis was conducted on the airfoil. The airfoil was meshed in a
freestream farfield; allowing for a varying angle of attack, by changing the components of
the velocity magnitude (I don’t like how it’s worded, I know I changed it but having two
sentences seemed pointless). The airfoil was also meshed at a fixed 16 degrees with the top
and bottom wind tunnel walls (what was the purpose? Mention in first paragraph?).
During attached flow, the experimental lift curve matched the CFD; however, in separated
flow, the CFD stalled at a much earlier (lower?) angle of attack than the experimental. A
marginally larger (steeper?) slope has been published from previous work by Sheldahl et al.
(possibly say in the paper CCC) with the stall angle corresponding to CFD results. The
pressure distributions over the airfoil showed excellent correlation between CFD and
experimental, especially at lower angles of attack where the flow was more attached (This
paragraph is in need of reorder, you have mentioned you are doing CFD and experiments
previously and you would compare them so reiterating it constantly is annoying and a waste
of space. You also mention published work and then go on to compare CFD and
experimental again, do one then the other).
The wind tunnel walls account for the difference between the experimental lift, CFD and
published data stall mechanism (stall mechanism?) (Note: seeing most likely implies you
have no concrete results). The walled mesh, at an angle of attack of 16 degrees, was run in
Fluent (first time mentioning fluent!) and produced a CL (you had used CL not CL, also
curve? Value? I would be inclinded to use coefficient of lift here instead of CL as it isn’t
mentioned anywhere previously; is CL and lift different?) close to that of the experimental
at the same angle (if you must tell your reader that you are comparing experimental and
numerical then you haven’t explained it well enough previously. Experimental results would
i
probably be fine). This supported the hypothesis that the walls of the wind tunnel were
interfering with the lift on the airfoil in the experimental testing (this sentence should either
be in the first paragraph if it was your hypothesis).
The experimental airfoil model was believed to be producing long bubble stall from the stall
mechanism shown in the lift curve and the large difference in stall angle between the CFD
and published data (believed to?). In order to remove the long bubble stall to produce
results similar to CFD and published data, a boundary layer trip was placed on the
experimental model. The tripped airfoil stalled at the same angle as the CFD and published
data and a similar lift slope (woah! you just wasted the last couple of paragraphs on me. You
found CFD and experimental data matched up to published work. The previous paragraphs
have become waffle and I would disregard them. it wouldn’t be if you were investigating the
effects of long bubble stall on a NACA 0018 airfoil, however you are comparing
experimental and numerical models of a NACA 0018 airfoil (aerofoil?) and you didn’t find
every airfoil did this, only because yours didn’t use boundary layer trips.
Acknowledgements
Legend
Needs to be re-worded
Incorrect
Has been re-read, but needs to be read by someone else
Suggested rewording by Kevin
Comment by Kevin
ii
Contents
Abstract ................................................................................................................................................................... i
Acknowledgements ................................................................................................................................................ ii
Table of Figures ...................................................................................................................................................... v
Nomenclature ....................................................................................................................................................... vii
Chapter 1: Introduction .......................................................................................................................................... 2
1.1 Organisation of Thesis.................................................................................................................................. 3
1.2 Objectives .................................................................................................................................................... 4
Chapter 2: Literature Review .................................................................................................................................. 6
2.1 Airfoil Nomenclature.................................................................................................................................... 6
2.2 Aerodynamic Coefficients ............................................................................................................................ 9
2.1.1 Coefficients of Lift and Drag...................................................................................................................... 9
2.1.2 Pressure Distribution............................................................................................................................ 9
2.3 Reynolds Number and Mach number ........................................................................................................ 11
2.4 Three-Dimensional Effects ......................................................................................................................... 11
2.5 Incompressible and Compressible Flows ................................................................................................... 13
2.5.1 Compressible Flow ............................................................................................................................. 13
2.5.2 Incompressible Flow .......................................................................................................................... 13
2.6 Viscous Effects, Flow Separation and the Boundary Layer ........................................................................ 14
2.6.1 The Boundary Layer and Viscous Flow ............................................................................................... 14
2.6.2 Shear Stress ........................................................................................................................................ 15
2.6.3 Adverse Pressure Gradients and Flow Separation ............................................................................. 16
2.6.4 Laminar and Turbulent Flows ............................................................................................................. 17
2.6.5 Boundary Layer Control ..................................................................................................................... 20
2.7 Types of Airfoil Stall ................................................................................................................................... 21
2.7.1 Thin Airfoil Stall .................................................................................................................................. 21
2.7.2 Leading Edge Stall .............................................................................................................................. 22
2.7.3 Trailing Edge Stall ............................................................................................................................... 22
2.8 Influence of Reynolds Number on Stall ..................................................................................................... 22
2.9 Flow Visualisation ...................................................................................................................................... 25
iii
Chapter 3: Theory ................................................................................................................................................. 27
3.1 Calculation of Coefficient of Pressure ........................................................................................................ 27
3.2 Integration of Pressures ............................................................................................................................. 28
3.3 Thin Airfoil Theory ..................................................................................................................................... 30
Chapter 4: Experimental Design and Procedure................................................................................................... 32
4.1 Apparatus ................................................................................................................................................... 32
4.1.1 Wind Tunnel ....................................................................................................................................... 32
4.1.2 Test Model ......................................................................................................................................... 33
4.1.3 Three-Component Under-Floor Balance ............................................................................................ 35
4.1.4 Pressure Scanner ................................................................................................................................ 36
4.1.5 Micro Manometer .............................................................................................................................. 36
4.2 Experimental Setup .................................................................................................................................... 37
4.2.1 Model Setup ....................................................................................................................................... 37
4.2.2 Lift, Drag and Pressure Measurements Procedure ................................................................................. 37
Chapter 5: CFD Analysis ........................................................................................................................................ 39
5.1 Pre-Processing ........................................................................................................................................... 39
5.1.1 Freestream Model .............................................................................................................................. 39
5.1.2 Walled Model ..................................................................................................................................... 41
5.2 FLUENT Setup ............................................................................................................................................. 42
Chapter 6: Discussion and Results ........................................................................................................................ 45
6.1 Discrepancies ........................................................................................................................................ 56
Chapter 7: Conclusions ......................................................................................................................................... 57
7.1 Recommendations for Future Work .......................................................................................................... 59
References ............................................................................................................................................................ 60
Appendix ................................................................................................................................................................. A
Appendix A ......................................................................................................................................................... A
Appendix B ......................................................................................................................................................... B
Appendix C ......................................................................................................................................................... C
iv
Should Appendix on page A? I don’t like the Chapter 7/8 thing….
Table of Figures
Figure
Number
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 2.16
Figure 2.17
Figure 2.18
Figure 2.19
Figure 2.20
Figure 2.21
Figure 2.22
Figure 3.1
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Description
Airfoil in Relation to a Wing
Airfoil Nomenclature
Forces on an Airfoil
Alternate Force Components
Clancy page 59
Clancy page 60
Clancy page 75
Lift Induced Drag
Mach number vs. Density Variation
Sketch of Boundary Layer on a Flat Plate in Parallel Flow pg25
Anderson page 62
Adverse Pressure Gradient over a Curved Surface
Insert picture from Anderson p226
Apparatus used by O. Reynolds
Dye in a Pipe with Increasing Turbulence
Laminar and Turbulent Velocity vs. Distance from Wall check
tab
Clancy Page 52
Results of Independent Reynolds number and Mach number
Variations of the CL,Max of a NACA 64-210
Structure of a Laminar Separation Bubble
Fluorescent Mini-Tufts on an Aircraft Wing
China Clay Flow Visualisation
UV on Oil Showing Transition Point
Insert Picture from Anderson page 21
Diagram of Wind Tunnel
Location of Pressure Taps on Experimental Model
Effect of Wingtip Vortices on the Airfoil despite the Presence of
Endplates
Old Endplates (front) and New Endplates (behind)
Refined Airfoil
Three-Component Under-Floor Balance
Model in the Large Low Speed Wind Tunnel
Freestream Mesh
Freestream Mesh Close Up
Mesh with the Wind Tunnel Walls
Reference Values Used, Walled Mesh Left and Freestream
v
Page
Number
5
6
6
7
9
9
10
11
12
13
14
15
15
16
17
17
18
21
22
23
24
25
3
3
3
3
3
3
3
3
3
3
3
3
Figure 5.5
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17
Figure 6.18
Figure 6.19
Figure 6.20
Right
Under-Relaxation Factors, Walled Mesh Left, and Freestream
Right
4 Degrees
6 Degrees
8 Degrees
10 Degrees
12 Degrees
14 Degrees
15 Degrees
Coefficient of Lift vs. Angle of Attack
Contour Plot of Velocities Magnitudes in Wind Tunnel
Coefficient of Pressure vs. x/c at 16 Degrees
Coefficient of Drag vs. Angle of Attack
4 Degrees (Tripped)
6 Degrees (Tripped)
8 Degrees (Tripped)
10 Degrees (Tripped)
12 Degrees (Tripped)
14 Degrees (Tripped)
15 Degrees (Tripped)
Coefficient of Lift vs. Angle of Attack (Tripped)
Coefficient of Drag vs. Angle of Attack (Tripped)
Also making assumption this isn’t complete
vi
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
Nomenclature
Symbol
a
c
g
h
x
CD
CL
Cp
D
L
M
P
Re
S
V∞ V∞
α
ε
μ
ρ
τ
Description
Speed of Sound
Chord Length
Acceleration due to Gravity
Height of Water
Airfoil Reference Length
Coefficient of Drag
Coefficient of Lift
Coefficient of Pressure
Drag Force
Lift Force
Mach Number
Measured Pressure
Reynolds Number
Planform Area
Free stream Velocity
Angle of Attack
Induced Downwash Angle
Dynamic Viscosity
Density
Shear Stress
(Make alphabetical)
vii
Units
m/s
m/s
m/s2
m
m
N
N
Pa
m2
m/s
Degrees
Degrees
kg/m.s
kg/m3
N/m2
Chapter 1: Introduction
This final year project focuses on analysing the aerodynamic characteristics of low
Mach number airfoil stall on a NACA-0018 airfoil (you didn’t use a – earlier for the NACA
0018, also what does NACA stand for? You should be specific with what aerodynamic
characteristics). Airfoil shape, wing planform, wing twist, taper ratio and many others
aspects, affect the stall characteristics of a three-dimensional wing (if you are going to
mention specific aspects at least say they are the most important). Studying an airfoil’s
characteristics is a key step in analysing the overall performance of three-dimensional wing
stall (I’m not sure here, why are you mentioning this? Are you using it this characteristics in
choosing an airfoil?).
Understanding and predicting flow separation is an important tool in wing design. In order
to understand and predict flow separation, the key aspects of an airfoil’s performance must
be known (what key aspects? You haven’t mentioned any yet…).
An important aspect of airfoil performance is the maximum lift coefficient that an airfoil
may reach before stall occurs. The stalling speed of an aircraft is determined by the
maximum lift coefficient. The lift coefficient varies linearly with angle of attack at low to
moderate angles of attack. When a sufficient angle of attack is reached, the flow on the
upper surface of the airfoil begins to separate due to viscous effects and the flow within the
separated region begins to reverse direction. The viscous effects near the airfoil surface are
the cause of flow separation (could remove this). Flow reverses in direction and separates
from the surface of an airfoil because the shear stress between the airfoil surface and the
fluid moving through an area of increasing pressure (this sentence didn’t make sense, needs
commas sooo badly).
As the flow on the upper surface separates more with increasing angle of attack, a particular
angle of attack is reached where the lift on the airfoil stops increasing (angle of attack
restated too much). This angle is known as the critical angle, and is the angle at which the
airfoil stalls.
During stall the boundary layer is an area of interest (why?). In determining the maximum
lift coefficient, the transition from laminar to turbulent boundary layer is of great
2
importance(why?). Insight into wing stall may be achieved by observing the influence of
boundary layer separation in two dimensional flow fields (?).
The previous theses by (Tarrant, 2010) (incorrect reference) on low Mach number airfoil
stall from the University of Limerick aimed to investigate the stall characteristics of a NACA
0018 airfoil. A NACA 0018 airfoil model with a chord of 0.4 m was created during the
project. Lift, drag and pressure measurements were taken experimentally and numerically.
The results from the thesis were inconclusive as the CFD (what is CFD?), experimental and
published data provided results that did not correlate with each other (Don’t say the fyp is
wrong…).
This thesis continues from where the previous thesis started, by recreating the experimental
testing on the same NACA 0018 model and using CFD in order to gather new data for the
same Reynolds. The airfoil was tested experimentally in the University of Limerick large
wind tunnel, and analysed using the computational fluid dynamics (CFD) (here it is!)
software package ANSYS Fluent (location irrelavent). These results were then compared to
published results from (Sheldahl, et al., 1981) (what about published results from the
thesis?). This thesis aims to provide a greater insight into the stall characteristics and airfoil
performance of the NACA 0018 airfoil (I wouldn’t use greater insight, implies you didn’t
achieve anything but suggested areas to work on). The data produced from this work may
be used as reference to any further work on the NACA 0018 airfoil (isn’t that the purpose of
recommending future work?).
(This section didn’t feel like an introduction to me, it felt like you couldn’t pin down an
introduction and just took stabs at a load of places)
1.1 Organisation of Thesis
This report is divided into seven main sections. Chapter 1 simply provides a brief
introduction, background and outline of the project, stating the main aims and how these
are to be achieved. Chapter 2 provides a base to the reader on the fundamental concepts of
aerodynamics such as viscous flow and boundary layer effects. Chapter 3 provides a
background into the theoretical equations used and shows any derivations needed to
provide some of the equations needed. Chapter 4 describes the experimental apparatus and
procedures used in any testing done for this project. Chapter 5 describes how the model
3
was meshed in the software program ICEM and how the mesh was analysed in the CFD
software package ANSYS Fluent. Chapter 6 describes the results from experimental testing
and CFD analysis in detail, and discusses any observations and discrepancies found. Chapter
7 states the main conclusions from the thesis (along with further work? Didn’t read this
section, I figured you would know more about each section then me).
1.2 Objectives
This thesis is a continuation from the previous academic year. The experimental data
gathered from the previous year was incorrect (I wouldn’t say incorrect). This means that
some of the objectives will be based around re-doing all the experiments. The primary aim
of this final year project is to investigate the aerodynamic characteristics of a NACA-0018
airfoil at various angles of attack by comparing detailed wind tunnel airfoil measurements
with numerical results obtained from the CFD software package FLUENT. The specific
objectives of this thesis are: (objectives are: finish reviewing this and go to bed)
1. To refine the previous NACA-0018 airfoil model.
The previous FYP resulted in incorrect wind tunnel data due to the airfoil model. The
endplates on the model were too small. Vortex drag could be seen to go over the
endplates, which resulted in incorrect test data. New endplates will be designed and
manufactured to resolve this problem. The model will also be sanded down to
improve smoothness and painted matt black to improve flow visualisation.
2. To re-do the previous wind tunnel testing with the refined NACA-0018 test model
and gather new test data.
All previous wind tunnel test data on the airfoil was incorrect due to the inaccuracies
caused by the un-refined model. All previous testing will be re-done to get correct
results that correlate with CFD results and published data. At a Reynolds number of
360,000; CL vs. α, CD vs. α and CP vs. x/c at various angles of attack will be tested and
graphed.
4
3. To perform a numerical analysis on the airfoil, using the software package FLUENT.
A comparison to the numerical solution and the experimental results can then be
analysed.
The previous numerical analysis was incorrect, so a new numerical analysis will be
carried out. The model will be re-meshed using ICEM. Using the appropriate
boundary conditions and model, the airfoil in the wind tunnel will be simulated in
ANSYS FLUENT to compare the solution against the new wind tunnel test data.
4. To study the effects of boundary layer control on the NACA-0018 airfoil model.
Wind tunnel testing will be carried out using layer control techniques such as surface
roughening or using a thin wire.
5
Chapter 2: Literature Review
2.1 Airfoil Nomenclature
Figure 2.1 shows the wing of an airplane (shows more than that, plus the next
sentence kinda makes this one redundant). The cross-sectional shape obtained by the
intersection of the wing with the perpendicular plane shown in Figure 2.1 is called an airfoil
(Anderson, 2008). Therefore an airfoil can be thought of as a 2-dimensional shape with a
constant infinite wing span, i.e. no variations in aerodynamic characteristics through the
spanwise length. Airfoils are often used for theoretical work however it is important to note
that when using an airfoil in real world applications, three-dimensional effects must be
taken into consideration, as the airfoil will now have a finite span. This is discussed further
in section 2.4.
Figure 2.1: Airfoil in Relation to a Wing (Anderson, 2008)
A typical airfoil is shown in Figure 2.2. The chord is a straight line connecting the leading
edge to the trailing edge. This is not to be confused with the mean camber line, which also
connects the leading edge and trailing edge. The mean camber line is the locus of points
halfway between the upper and lower surfaces, as measured perpendicular to the mean
camber line itself (it uses itself to measure itself?). Camber is measured perpendicular to the
chord, and is the maximum distance between the mean camber line and the chord. When
an airfoil is symmetrical, like the NACA 0018 used in this project, there is no camber, thus
6
the mean camber line is the same as the chord. The thickness is the maximum distance
between the upper and lower surface measure perpendicular to the chord. The lift and
moment characteristics of an airfoil are essentially controlled by the camber and the shape
of the camber line (Anderson, 2008).
Figure 2.2: Airfoil Nomenclature (Anderson, 2008)
Figure 2.3 shows an airfoil inclined to a stream of air with a velocity V ∞. The free-stream
velocity V∞ is the velocity of the air far upstream of the airfoil. The relative wind is the
direction of V∞, and is generally shown to run horizontally. The angle of attack α is the angle
between the relative wind V∞ and the chord line. The resultant force R is the total
aerodynamic force seen by the airfoil. The aerodynamic force R can be resolved into two
components, parallel and perpendicular to the relative wind. The drag D is defined as the
aerodynamic force component parallel to the relative wind. The lift L is defined as the
aerodynamic force component perpendicular to the relative wind (Anderson, 2001) (also
shown in figure 2.4, might want to mention it before you use it).
7
Figure 2.3: Forces on an Airfoil (Anderson, 2008)
Figure 2.4: Alternate Force Components (Anderson, 2008)
An alternate way to view the forces on an airfoil is shown in Figure 2.4. The total
aerodynamic force on the airfoil R is broken up into two components, the normal force N
and axial force A. The force component N is perpendicular to the chord, thus making it a
normal force. The force component A is parallel to the chord, thus making it an axial force.
Describing the force in terms of the components N and A is not generally used, but it is
useful to be familiar with both systems of notation (why?). The forces N and A can be
converted to L and D through the equations (Anderson, 2001):
𝐿 = 𝑁𝑐𝑜𝑠𝛼 − 𝐴𝑠𝑖𝑛𝛼
Eq. 2.1
𝐷 = 𝑁𝑠𝑖𝑛𝛼 + 𝐴𝑐𝑜𝑠𝛼
Eq. 2.2
8
2.2 Aerodynamic Coefficients
2.1.1 Coefficients of Lift and Drag
It is more desirable to describe the forces on an airfoil in terms of non-dimensional
coefficients as the size of the airfoil will not matter as long as it encounters the same
Reynolds number. The three-dimensional lift L and the drag D are commonly converted to
the non-dimensional coefficients CL and CD through the formulas:
𝐶𝐿 =
𝐿
1 2
2 𝜌𝑉 𝑆
Eq. 2.3
𝐶𝐷 =
𝐷
1 2
2 𝜌𝑉 𝑆
Eq. 2.4
The symbol S in the above formulae is the reference area for the given geometric body,
generally the planform area. As an airfoil is a two-dimensional shape, the reference area S is
replaced by the chord C. Thus to covert two-dimensional lift L and drag D on an airfoil to the
non-dimensional coefficients cl and cd the below formulas must be used:
𝑐𝑙 =
𝐿
1 2
2 𝜌𝑉 𝑐
Eq. 2.5
𝑐𝑑 =
𝐷
1 2
2 𝜌𝑉 𝑐
Eq. 2.6
2.1.2 Pressure Distribution
In accordance with Bernoulli’s Theorem, changes in static pressure occur when a
stream of air flow past the airfoil causing local changes in velocity around an airfoil. The
distribution of pressure determines the lift, pitching moment and form drag of the airfoil.
Pressure can be expressed in terms of coefficient of pressure:
9
𝑃 − 𝑃∞
𝑉 2
𝐶𝑝 =
= 1−( )
1⁄ 𝜌 𝑉 2
𝑉∞
∞
∞
2
Pressure coefficient has a maximum value of 1 at the stagnation point. A positive pressure
coefficient implies a pressure greater than a freestream value. A negative coefficient implies
a pressure less than the freestream value, and can be referred to as suction (Clancy, 1975).
Pressure distributions around the airfoil can be depicted graphically. One way to depict the
distribution of pressure over an airfoil is through a sketch of an airfoil and lines normal to
the surface of the airfoil, proportional to the pressure coefficient at that point (Figure 2.5).
Lines pointing away from the airfoil represent suction and those inwards represent a
positive pressure.
Figure 2.5: Clancy page 59 (Clancy, 1975)
A more useful way to depict pressure distribution is to graph pressure coefficient against
x/c, where x is the distance along the chord, and c is the chord length (Figure 2.6) (use
𝑥
equation to show 𝑐 ). By convention the negative values of Cp are plotted above the
horizontal axis as they generally represent the upper surface of the airfoil. Pressure
coefficients are graphically depicted this way in the reports and discussion of this thesis.
10
Figure 2.6: Clancy page 60 (Clancy, 1975)
2.3 Reynolds Number and Mach number
The Reynolds number and the Mach number are both dimensionless quantities
important in the both theoretical and experimental aerodynamics. The Reynolds number is
defined as
𝜌𝑉𝑐
𝜇
, and the Mach number is defined as
𝑉
𝑎
(see you use equations here but not
previously!). According to Anderson (2001) the Reynolds number is the ratio of inertia forces
to viscous forces in a flow. Mach number is simply the ratio of the free stream velocity to
the velocity of sound at the particular atmospheric conditions.
Reynolds number and Mach number are critical in wind tunnel testing. A scale model can be
used to represent real world conditions (how?). Aerodynamic coefficients will be the same
on a scale model as free flight as long as the Mach number and Reynolds in the test are the
same as that of free flight (as free flight?).
2.4 Three-Dimensional Effects
Airfoils as discussed already are a two dimensional shape (in chapter 2.1). When
applying an airfoil to a wing, three dimensional effects must be taken into consideration.
Airfoils are thought to have an infinite span; when applied to a finite span, lift induced drag
occurs. Lift induced drag is caused by the difference in pressure between the upper and
lower surface of a wing. The airflow tries to escape from the high pressure lower surface, to
11
the low pressure upper surface. This causes vortices around the edges of the wing as shown
in Figure 2.7 (Clancy, 1975) (Massey, 1998) (double reference?!).
Figure 2.7: Clancy page 75 (Clancy, 1975)
The vortices deflect the airflow from the trailing edge downwards. This downwards airflow
is caused downwash (called?). Downwash causes the relative wind to act at an angle with
reference to the chord line. This effective relative wind causes the lift vector to act at an
angle ε (downwash angle). The lift vector now has two components, a lift component and a
drag component, shown in Figure 2.8 (Clancy, 1975) (Massey, 1998).
Figure 2.8: Lift Induced Drag (Massey, 1998)
It is therefore important to prevent lift induced drag from occurring in experimental testing
of airfoils, as theoretical two-dimensional models in CFD have an infinite wing span, and
thus no lift induced drag. Lift induced drag is prevented from occurring with the use of
endplates. Endplates are large plates, with either an elliptical, rectangular or airfoil shaped
12
profiles, and are attached to the ends of the model. The plates prevent the high pressure air
from escaping to the top surface, and stop the creation of vortices, thus preventing lift
induced drag. Airfoil shaped MDF endplates were attached to the model to prevent threedimensional effects during experimental testing.
2.5 Incompressible and Compressible Flows
In nature all matter is compressible to some extent. However flow can be modelled
as incompressible under certain conditions. The definitions of both compressible and
incompressible are as follows:
2.5.1 Compressible Flow
Compressible flow means that the density of the fluid element changes. However
when matter is compressed, the mass of the element stays constant, therefore it is the
volume that changes. Referring to the continuity equation 𝜌1 𝐴1 𝑉1 = 𝜌2 𝐴2 𝑉2 it can be seen
that if flow is compressible, then 𝜌1 ≠ 𝜌2 (Anderson, 2008).
2.5.2 Incompressible Flow
When the difference between 𝜌1 and 𝜌2 is extremely small, then flow can be
modelled as incompressible. Therefore if flow is to be considered incompressible then 𝜌1 =
𝜌2 and the resulting continuity equation is left as 𝐴1 𝑉1 = 𝐴2 𝑉2 (Anderson, 2008).
An important aspect of incompressible flow is the threshold at which flow can no longer be
thought as incompressible, and must be then thought of as compressible. If the equation
below is considered
1
𝜌0
𝛾 − 1 2 𝛾−1
= (1 +
𝑀 )
𝜌
2
For values of M ranging from 0 to 1,
0.3,
𝜌0
𝜌
𝜌0
𝜌
is seen to decrease as M gets larger. However at M =
has undergone only a 5% change in value. After Mach 0.3, the value of
𝜌0
𝜌
is seen to
decrease dramatically from its original value. Hence the applicable threshold for
incompressible flow is considered to be Mach 0.3. This can be shown graphically in Figure
2.9 (Anderson, 2001).
13
Figure 2.9 Mach number vs. Density Variation (Anderson, 2008)
For the purpose of this investigation, the Mach number will not reach a value greater than
0.3, so flow in this investigation is modelled as incompressible.
2.6 Viscous Effects, Flow Separation and the Boundary Layer
2.6.1 The Boundary Layer and Viscous Flow
A flow field may be divided up into two unequal regions. The bulk of the flow region
is known as the freestream, where viscosity can be neglected and flow can be treated as
inviscid flow without much error. The second region is the very thin boundary layer that
occurs close to wall in the flow. In this region effects of viscosity must be taken into account.
Frictional forces retard the motion of the flow near to the wall as a no slip condition exists
on the wall. The velocity of the fluid increases from zero at the wall to its full value. The
height from the wall at which the velocity of the flow reaches the freestream value is the
height of the boundary layer (Schlichting, 1987).
14
Figure 2.10: Sketch of Boundary Layer on a Flat Plate in Parallel Flow pg25 (Schlichting, 1987).
The lift curve slope of an airfoil is generally linear until it starts approaching its stall angle.
Thus inviscid flow theory can be use used to gauge a result for a specific CL at a specific α if
only a few CL values and their corresponding angles of attack are known, and as long as the
angles of attack are not in the region of flow separation. As the angle of attack approaches
flow separation the lift curve slope changes and is no longer linear, thus inviscid flow theory
can no longer be used. Viscous flow theory must be used in order to predict CL and α during
flow separation. Viscous flow is a flow type where the effects of viscosity, thermal
conduction and mass diffusion are of importance. In aerodynamics there are two
phenomena governed by viscous effects; these are flow separation, and the transition from
laminar to turbulent flow (Abbot, et al., 1959).
2.6.2 Shear Stress
Shear stress is a force that acts tangential to the surface of an airfoil, and is
influenced by the viscosity of the fluid. Shear stress is caused due to the frictional effect of
the flow rubbing against the surface of the airfoil as it moves around it. Shear stress acts
against the relative motion of the airfoil. The shear stress τw is defined as the force per unit
area acting tangentially on the surface due to friction as shown in Figure 2.10 (Anderson,
2008).
15
Figure 2.11: Anderson page 62 (Anderson, 2008)
2.6.3 Adverse Pressure Gradients and Flow Separation
Adverse pressure gradients are an important aspect of flow separation. This can be
shown in Figure 2.11 (mentioned after picture?). From points A to C the flow velocity has
accelerated to reach its max at point C. At point C the minimum pressure is found. This
results in a favourable negative pressure gradient. Beyond point C the pressure increases.
The fluid closest to the surface of the airfoil has less momentum than the fluid directly
above it. The increase in pressure reduces the momentum further. An adverse pressure
gradient that opposes flow can now be seen. The momentum eventually becomes zero at
point D. As the pressure increases further downstream, the flow reverses direction as
shown at point E. The point at which momentum becomes zero is deemed the separation
point.
Figure 2.12: Adverse Pressure Gradient over a Curved Surface (Anderson, 2008)
16
In short, separation is caused by the reduction of velocity in the boundary layer, combined
with a positive pressure gradient. This is known as an adverse pressure gradient, since it
opposes flow. Separation only occurs when this adverse pressure gradient exists (Massey,
1998).
When separation occurs, drag is also increased. Consider an airfoil as shown in Figure 2.12,
which shows the pressure distribution that occurs in both separation and attached flow.
Figure 2.13: Insert picture from Anderson p226 (Anderson, 2008)
On the leading edge of the top surface a higher pressure exists when the flow is separated.
The higher pressure pushes down on the leading edge reducing lift. On the leading edge
when flow is separated, the direction in which the pressure is acting is closely aligned to
vertical, and hence almost the full effect of the increase pressure is felt by the lift. On the
trailing edge on the top surface the separated pressure is now smaller on the attached
pressure. As the airfoil is quite angled, this means that in separated flow there is less
pressure force pushing acting leftwards opposing the drag force, which is trying to pull the
airfoil to the right. Therefore the consequences of the flow separating are: A major increase
in drag, caused by pressure drag due to separation; and a dramatic loss of lift which leads to
stalling (Anderson, 2008).
2.6.4 Laminar and Turbulent Flows
Fluid flow can generally be broken up into two types, laminar flow and turbulent
flow. This was discovered by O. Reynolds who used the apparatus shown in Figure 2.14 to
17
discharge a thin streamline of dye. Reynolds saw that at low velocities the dye would not
mix with the water in the tube (Figure 4.15.a), and can be described as laminar flow. If the
velocity of the fluid was increased by opening the valve more, the streamline would begin to
waver (Figure 4.15.b) (Massey, 1998).
Figure 2.14: Apparatus used by O. Reynolds (Massey, 1998)
By further increasing the velocity of flow the movement and fluctuations of the streamline
became more erratic. The dye now only travelled a small length of the tube as an unbroken
thread, before mixing entirely with the water (Figure 4.15.c). This type of flow can be
described as turbulent flow (Massey, 1998) (mention transititonal? Is Reynolds apparatus
important, it’s not a history lesson).
Figure 2.15: Dye in a Pipe with Increasing Turbulence (Massey, 1998)
Laminar flow generally occurs at lower velocities. Particles in laminar fluid flow move in
straight lines. Turbulent fluid flow tends to occur at higher velocity gradients. Particles
within the flow are not straight but disorderly and intertwining, and cause mixing within the
fluid. The difference in velocity gradients between layers can be seen in Figure 2.16.
18
Figure 2.16: Laminar and Turbulent Velocity vs. Distance from Wall check tab (Anderson, 2008)
The turbulent profile has fuller profile than the laminar profile. Figure 2.16 shows that from
the outer edge to a point near the surface, the velocity of the turbulent flow remains
reasonably close to the freestream velocity, then it rapidly decreases to zero at the surface
from the outer edge to the surface. The laminar velocity profile gradually decreases to zero
at an almost linear fashion. The reciprocal of the slope of the curves in Figure 2.16 evaluated
𝑑𝑉
𝑑𝑉
at y=0 is the velocity gradient at the wall (𝑑𝑦 )
𝑦=0
. From this it can be deduced that (𝑑𝑦 )
𝑦=0
is less for laminar flow than turbulent flow. Hence using the equation below leads to the
conclusion that laminar shear stress is less than turbulent shear stress (Anderson, 2008).
𝑑𝑉
𝜏𝑤 = 𝜇 ( )
𝑑𝑦 𝑦=0
Pressure drag occurs when flow over a surface occurs in a direction that is not parallel to the
main stream of fluid. This causes a pressure difference over the surface resulting in an
additional drag force. Skin friction drag occurs when a fluid travels over a surface causing
the fluid to exert a drag force on the surface which is a result of viscous action. Skin friction
drag is the resultant force in the downstream direction of frictional force caused by flow
over a surface.
The type of viscous flow that is preferred is dependent on the shape of the body. Thin
slender bodies are affected by skin friction drag more than pressure drag, so laminar flow is
more desirable as it will provide low skin friction drag. Bodies that are blunt, such as
19
spheres, are affected much more by pressure drag rather than skin friction drag, so
turbulent flow is more desirable in this case.
It is not always desirable to keep a boundary layer laminar. Laminar flow separates more
readily than turbulent flow, so in certain cases it is more desirable to apple turbulent flow to
a body (apple?). Consider the circular cylinder with laminar flow in Figure 2.17.a (a? This
sentence sounds pointless). When a low Reynolds number laminar flow is applied to the
cylinder, a large amount of pressure drag due to separation is visible. Creating early
transition to turbulent flow, by means of a boundary layer trip, the flow remains attached
for much more of the body’s surface (Figure 2.17.b), leading to less pressure drag due to
separation (Clancy, 1975) (what’s a and b?).
Figure 2.17: Clancy Page 52 (Clancy, 1975)
2.6.5 Boundary Layer Control
A fixed airfoil shape has a given CL, Max for a certain Reynolds number (no comma?
How about 𝐶𝐿𝑚𝑎𝑥 ). To increase CL, Max for a given shape and Reynolds number, the boundary
layer must be controlled to delay separation. Skin friction drag is also of great importance.
Skin friction drag can be greatly reduced by delaying the transition from laminar to
turbulent flow, as well as the onset of separation. Control of the boundary layer is achieved
by delaying separation by accelerating the boundary layer. Accelerating the boundary layer
causes a sudden increase in turbulence. This sudden increase in turbulence is commonly
referred to as ‘tripping’ the boundary layer. Methods of ‘tripping’ the boundary layer consist
20
of surface roughness, or with a wire along the surface of the airfoil. Both methods are
applicable to the NACA 0018 airfoil model used in this project.
Another method of accelerating the boundary layer is to either rejuvenate slow moving air
in the boundary layer, or to remove it all together. Slow moving air in the boundary layer
can be rejuvenated by injecting air at high velocity from slots that face backwards. If the
boundary layer is laminar injecting high velocity air can trip the boundary layer into
turbulence causing increased skin friction. This can be avoided using suction. Suction on the
surface of an airfoil removes slow moving air in the boundary layer. Suction greatly delays
the transition from laminar to turbulent and thus reduces skin friction drag. While suction is
excellent at reducing skin friction drag and increasing an airfoil’s CL,
Max
it is extremely
complex to apply to in practical applications. Suction would be too complex to apply to the
NACA-0018 model. The airfoil is too small and the inside of the model is used to house the
pressure tubes (Massey, 1998).
2.7 Types of Airfoil Stall
At low speed there are three types of stall predominantly found over a range of
airfoils. These are commonly described as: (maybe mention them first…)
2.7.1 Thin Airfoil Stall
Thin airfoil stall generally occurs on airfoils with a thickness ratio below 0.09 at a low
Reynolds number. High adverse pressure near the leading edge caused by the airfoils sharp
nose radius leads to separation. The laminar boundary layer over the airfoil separates at low
angles of attack, and reattaches further down the airfoil as turbulent boundary layer. This
reattachment causes a bubble of dead air, called a long separation bubble. As the angle of
attack increases, the reattachment point of the turbulent boundary layer moves further
down the trailing edge causing a longer separation bubble. As more of the upper surface is
covered by the separation bubble, a progressive increase in nose-down pitching moment is
seen. If the angle of attack continues to increase the boundary layer will not reattach and
the airfoil will stall. (Anderson, 2001) (Leishman, 2000). (Where are the long bubble stalls?
Also I’m kinda going to bed now so meh….)
21
2.7.2 Leading Edge Stall
Airfoils with a thickness ratio from 0.1 to 0.16 experience leading edge stall. This
airfoil sees a high max lift before a sudden stall. In the leading edge region, laminar
separation bubbles of size 2-3% chord length causing transition to occur over them are
found. A mild adverse pressure gradient is found on the leading edge; this in conjunction
with the separation of the laminar boundary layer due to the relative thinness of the airfoil
causes these bubbles to form. The laminar separation bubble is normally situated just aft of
the leading edge. Leading edge stall has a sharp peaked lift curve slope and after the stall
CL,max decrease rapidly (Anderson, 2001) (Leishman, 2000).
2.7.3 Trailing Edge Stall
Trailing edge stall affects airfoils with thickness ratios of 0.17 and above. The model
used in this study has a ratio of 0.18, so this is the stall type most pertinent to this
investigation. As the angle of attack of the airfoil increases, flow gradually separates from
the trailing edge up towards the leading edge. A gentle lift curve slope is normally seen. At
high Reynolds numbers however, stall can be quite abrupt. The separation point can move
forward very quickly, and can be confused with leading edge stall unless pressure
distributions and flow visualisation is used to support this (Anderson, 2001) (Leishman,
2000).
2.8 Influence of Reynolds Number on Stall
At low Mach numbers, variations is Reynolds number will affect both the type of stall
and the maximum lift coefficient. Increasing the Reynolds number increases the inertial
effects in the flow, which will dominate over the viscous effects and, all other factors being
equal, will thin the boundary layer and delay the onset of flow separation to higher angles of
attack and lift coefficient.
22
Figure 2.18: Results of Independent Reynolds number and Mach number Variations of the CL,Max of a NACA 64-210
(Leishman, 2000)
The effects of varying Reynolds number on the maximum lift and stall characteristics can be
significant up to Mach numbers of about 0.4 m. For example, results showing independent
Mach number and Reynolds number variation of the maximum lift of a NACA 64-210 airfoil
section are given in Figure 2.18. These data show that the Reynolds number has a strong
influence on the maximum lift capability at a given Mach number, with larger Reynolds
number leading to higher values of CL,max for a given Mach number. At higher freestream
Mach numbers the effects of Reynolds number are secondary compared to the effects of
compressibility as confirmed by the fact that the curves for each Reynolds number show a
converging trend (Leishman, 2000).
At low Reynolds numbers, airfoil boundary layers will typically remain laminar for a large
percentage of the airfoil chord, whereas at high Reynolds numbers the boundary layer will
undergo transition to turbulence near the airfoil leading edge and the boundary layer will be
mostly turbulent. The transition process, and hence location, is more sensitive at low
Reynolds numbers and must be predicted accurately in order to determine aerodynamic
performance. Since boundary layers remain laminar for a greater streamwise extent,
laminar separation is more common at low Reynolds numbers, and the resultant separated
shear-layer may also remain laminar for a significant extent before transition to turbulence
occurs. Upon transition the increased wall-normal momentum transfer typically means that
the boundary layer reattaches, followed by a developing turbulent boundary layer. The
23
resultant structure formed by laminar separation, transition to turbulence and
reattachment is termed a laminar separation bubble (LSB) and is a classic hallmark of low
Reynolds number flows (Figure 2.19).
Figure 2.19: Structure of a Laminar Separation Bubble (Jones, 2008)
In the classical model a laminar separation bubble forms when, under the influence of an
adverse pressure gradient, the boundary layer separates, forming a free shear layer which is
highly unstable. The separated shear layer undergoes rapid transition to turbulence, and
subsequent reattachment. Just downstream of the separation point, within the bubble, the
fluid velocity is close to zero and thus this region is denoted the `dead air' region. Just
upstream of the reattachment point a vortical structure is present, associated with the
circulation of air within the bubble, called the `reverse-flow vortex'. This steady model of a
separation bubble, where the only time dependent behaviour is the transition to turbulence
and subsequent turbulent behaviour downstream, became the widely accepted model.
Bubbles of this type can be classified as either `short' bubbles or `long' bubbles. Short
bubbles were defined as possessing bubble length approximately 10^2 times the
displacement thickness at the separation point, whereas long separation bubbles were
defined as being of order 10^4 times the displacement thickness at the separation point.
Perhaps more importantly, short separation bubbles are defined as having little effect on
the external potential flow, whereas long bubbles have a marked impact, e.g. completely
altering the circulation around an airfoil (Jones, 2008).
24
2.9 Flow Visualisation
There are many methods of flow visualisation suitable to this project. Tuft flow
visualisation is one of the oldest methods of flow visualisation used in both testing and in
flight. Tuft flow visualisation works by showing the direction of the flow over the surface of
an airfoil as most fluids (air in this case) are invisible. Tufts are usually made of small lengths
of string or yarn attached to the surface of an airfoil (Figure 2.16). Tufts are generally made
of monofilament nylon, polyester or cotton. Tufts are often coated in fluorescent dyes to
improve visibility for photography. Adhesives to attach the tufts to the model include tape
and glue.
The advantages of tuft flow are that at any model position the flow can be visualised. Yarn
tufts are easy to install. A tuft grid provides a view of the flow pattern over a large area.
Mini-tufts have a negligible effect on force data. Sewing thread makes a good tuft due to its
clear visibility in UV or normal light, it has smaller flow effects compared with yarn, and its
ease of application compared to mini-tufts. The disadvantages of tuft flow are that it does
not provide a detailed flow pattern since they are constantly moving with the air flow. Minitufts require more time to install but can be left on the model (Washington, 2010).
Figure 2.20: Fluorescent Mini-Tufts on an Aircraft Wing (Washington, 2010)
China clay is a mixture of kerosene, clay powder, and fluorescent pigment is applied to the
model surface with the wind off. When the wind is turned on it causes the kerosene to
evaporate, leaving streaks of clay powder in the form of the flow pattern. The advantages of
china clay are that it is easiest method to setup and apply. China clay provides lasting flow
pattern on the model for photos when the wind is off (Figure 2.17). Clearly shows flow
pattern; shows flow separation well. The disadvantages of china clay are that the model
position during flow visualization cannot vary. The model must be a dark colour, preferably
25
matt black, for contrasting the powder against the model surface. Pressure taps must be
protected to prevent clogging (Washington, 2010).
Figure 2.21: China Clay Flow Visualisation (Washington, 2010)
A mixture of oil or oil substitute and dye can be applied to the model surface. When the
wind is turned on, the oil and dye particles slowly move in the direction of the local flow. For
improved visibility of the oil flow, an ultraviolet dye can be used such that when illuminated
with an ultraviolet light the dye fluoresces to clearly show the flow pattern (Figure 2.18).
Advantages are that it provides somewhat lasting air flow pattern on the model for photos
when the wind is off. Gravity will slowly change the oil pattern. Oil clearly shows flow
pattern, especially the transition between turbulent and laminar flow as well as separation.
UV oil is the most photogenic of the flow visualization methods. The disadvantages of oil are
after time, all of the oil will run off the model. Model must be a dark colour, preferably matt
black, for contrasting the oil mixture against the model surface. Pressure taps must be
protected to prevent clogging (Washington, 2010).
Figure 2.22: UV on Oil Showing Transition Point (Washington, 2010)
26
Chapter 3: Theory
This chapter provides a theoretical background to the derivations used to calculate
the coefficient of pressures and integration of pressures from the experimental results.
3.1 Calculation of Coefficient of Pressure
The Mach number of the freestream velocity used experimentally and theoretically
for this project is less than 0.3, and therefore the fluid can be considered incompressible,
thus Bernoulli’s equation (Massey, 1998) can be used derive the coefficient of pressure.
𝑃𝐴
𝑉𝐴2
𝑃𝐵
𝑉𝐵2
+
+ 𝑍𝐴 =
+
+ 𝑍𝐵
𝜌𝑔 2𝑔
𝜌𝑔 2𝑔
Eq. 3.1
The tunnel is level so we can let 𝑍𝐴 = 𝑍𝐵 . Density is assumed to be constant so the
equation can be reduced to:
𝑃𝐴 + 1⁄2 𝜌𝑉𝐴2 = 𝑃𝐵 + 1⁄2 𝜌𝑉𝐵2
Eq. 3.2
Assuming 𝑉𝐵 ≪ 𝑉𝐴 → 1⁄2 𝜌𝑉𝐴2 ≅ 0
𝑃𝐴 − 𝑃𝐵 = 1⁄2 𝜌𝑎 𝑉∞2
Eq. 3.3
Where 𝑉∞ = 𝑉𝐵 = freestream velocity. Equation 3.3 can now be written as:
∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 = 1⁄2 𝜌𝑎 𝑉∞2
Eq. 3.4
From (Massey, 1998) the pressure due to the head of water in the manometer is given by:
∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 = 𝜌𝑤 𝑔∆ℎ
Eq. 3.5
The manometer gives out ∆ℎ so ∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 can be found by inserting values for ∆ℎ.
The coefficient of pressure is defined by (Massey, 1998) as:
𝐶𝑝 =
𝑃 − 𝑃∞
1⁄ 𝜌 𝑉 2
2 ∞ ∞
Eq. 3.6
27
From equation 3.3, 𝑃𝐴 is the static pressure at the wall of the test section and 𝑃𝐵 is the static
pressure on the surface of the airfoil. Taking 𝑃𝐴 = 𝑃∞ and 𝑃𝐵 = 𝑃 Eq. 3.6 can therefore be
written as:
𝐶𝑝 =
𝑃𝐵 − 𝑃𝐴
1⁄ 𝜌 𝑉 2
2 ∞ ∞
Knowing that ∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 = 𝑃𝐴 − 𝑃𝐵 then the following equation can be achieved by
substitution:
𝐶𝑝 =
−∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶
1⁄ 𝜌 𝑉 2
2 ∞ ∞
Eq. 3.7
The coefficient of pressure at each pressure tap can be achieved by reading of the
manometer, converting ∆ℎ to ∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 with equation 3.5 and then inserting values for
∆𝑃𝑆𝑇𝐴𝑇𝐼𝐶 into Eq. 3.7.
3.2 Integration of Pressures
The integration of pressures allows for values of lift to be taken from pressure plots.
This is a useful tool in investigating the lift distribution over an airfoil, and comparing it to
the lift from the force balance. Referring back to Eq. 2.1 and 2.2 in Section 2.2, the lift and
drag can be calculated by calculating the values for N and A.
𝐿 = 𝑁𝑐𝑜𝑠𝛼 − 𝐴𝑠𝑖𝑛𝛼
Eq. 2.1
𝐷 = 𝑁𝑠𝑖𝑛𝛼 + 𝐴𝑐𝑜𝑠𝛼
Eq. 2.2
In order to calculate N and A, the airfoil must be divided into two surfaces, the upper
surface and the lower surface.
28
Figure 3.1: Insert Picture from Anderson page 21 (Anderson, 2001)
The pressure and the shear stress on the upper surface are denoted by pu and tu. The
distance from the leading edge to an arbitrary point A is denoted by su. The pressure and
the shear stress on the lower surface are denoted by pl and tl. The distance from the leading
edge to an arbitrary point B is denoted by sl. The angle theta is the angle between vertical
and the normal to the surface. From (Anderson, 2001) the elemental normal and axial forces
acting the upper and lower surfaces are given by:
On the elemental surface dS on the upper surface are:
𝑑𝑁𝑢 ′ = −𝑝𝑢 𝑑𝑠𝑢 cos 𝜃 − 𝜏𝑢 𝑑𝑠𝑢 sin 𝜃
Eq. 3.8
𝑑𝑁𝑢 ′ = −𝑝𝑢 𝑑𝑠𝑢 cos 𝜃 − 𝜏𝑢 𝑑𝑠𝑢 sin 𝜃
Eq. 3.9
On the elemental surface dl lower surface they are:
𝑑𝑁𝑙 ′ = −𝑝𝑙 𝑑𝑠𝑙 cos 𝜃 − 𝜏𝑙 𝑑𝑠𝑙 sin 𝜃
Eq. 3.10
𝑑𝑁𝑙 ′ = −𝑝𝑙 𝑑𝑠𝑙 cos 𝜃 − 𝜏𝑙 𝑑𝑠𝑙 sin 𝜃
Eq. 3.11
If Eq. 3.8 to 3.11 are grouped together the result is:
29
𝑇𝐸
𝑇𝐸
′
𝑁 = − ∫ (𝑝𝑢 cos 𝜃 + 𝜏𝑢 sin 𝜃) 𝑑𝑠𝑢 + ∫ (𝑝𝑙 cos 𝜃 − 𝜏𝑙 sin 𝜃) 𝑑𝑠𝑙
𝐿𝐸
𝐿𝐸
Eq. 3.12
𝑇𝐸
𝑇𝐸
𝐴′ = ∫ (−𝑝𝑢 sin 𝜃 + 𝜏𝑢 cos 𝜃) 𝑑𝑠𝑢 + ∫ (𝑝𝑙 sin 𝜃 − 𝜏𝑙 cos 𝜃) 𝑑𝑠𝑙
𝐿𝐸
𝐿𝐸
Eq. 3.13
Shear stress cannot be measured experimentally, so the shear stress is let equal to zero. The
equations now become:
𝑇𝐸
𝑇𝐸
𝑁 ′ = − ∫ (𝑝𝑢 cos 𝜃) 𝑑𝑠𝑢 + ∫ (𝑝𝑙 cos 𝜃) 𝑑𝑠𝑙
𝐿𝐸
𝐿𝐸
Eq. 3.14
𝑇𝐸
𝑇𝐸
′
𝐴 = ∫ (−𝑝𝑢 sin 𝜃) 𝑑𝑠𝑢 + ∫ (𝑝𝑙 sin 𝜃) 𝑑𝑠𝑙
𝐿𝐸
𝐿𝐸
Eq. 3.15
Taking the pressure from each tap a knowing its distance from the leading edge, Eq. 3.14
and Eq. 3.15 can be used to calculate values for 𝑁 ′ and 𝐴′ . Substituting 𝑁 ′ and 𝐴′ into Eq.
2.1 produces a lift force for a certain angle of attack. When this is done over various angles
of attack, and the lift force is converted to coefficient of lift using Eq. 2.3, then a lift slope
can be produced and used to compare against other lift slopes.
3.3 Thin Airfoil Theory
Consider a symmetrical airfoil with an infinite wing span, and so thin that its camber
line lies on its chord line. Assuming the flow is incompressible and inviscid the lift on the
airfoil can be theoretically predicted with the equation (Clancy, 1975):
𝐶𝐿 = 2𝜋𝛼
Eq. 3.16
Thin airfoil theory predicts only a linear slope, so it is only useful for lower angles of attack.
For angles greater than 10 degrees thin airfoil theory is not used as most airfoils have a lift
30
curve that start curve before stall. It is important to note that the lift slope predicted using
this method will be more than the NACA 0018 can ever produce as the NACA 0018 is thick
airfoil and the theory is for an infinitely thin airfoil.
31
Chapter 4: Experimental Design and Procedure
The airfoil model was tested from zero degrees angle of attack until the airfoil
stalled. Pressure along the surface of the airfoil, lift force and drag force were measured.
This chapter describes the experimental procedures and apparatus used to test this.
4.1 Apparatus
4.1.1 Wind Tunnel
The University of Limerick non-return low-speed large wind tunnel was used for all
experimental testing. A schematic of the wind tunnel is shown in Figure 4.1. The wind tunnel
has an octagonal shaped test section that has a maximum horizontal and vertical dimension
of 930 mm. The wind tunnel can provide velocities up to 25 m/s through the test section. A
honeycomb section is positioned upstream of the test section. The honeycomb section
reduces turbulence generated by the fan and also straightens out the flow. The flow is then
accelerated through an inlet contraction before passing through the test section. The
diffuser downstream of the test section reduces the speed of the air flow as it exits the wind
tunnel.
Figure 4.1: Diagram of Wind Tunnel (reference?)
32
The wind tunnel has a catch net placed downstream of the test section. The catch net
prevents any damage to the propeller blades and reduces the damage to any parts that may
separate from the model.
4.1.2 Test Model
A NACA 0018 airfoil was used as the experimental test model. The model was
designed and manufactured during the previous final year project. The maximum thickness
of the airfoil is located at 30% of the chord and is a thickness of 18% of the chord. The
model had a chord of 400 mm and a span of 410 mm. The model was made up of 16
fibreboard modular sections each 25.4 mm in width. Pressure orifices of 3 mm diameter are
located on the upper and lower surfaces of the model. Silicon tubing of 3 mm diameter with
an inner diameter of 1 mm is placed in the orifices. The tubing and the orifices are used to
give pressure reading when connected to the pressure scanner. The model is hollowed out
leaving a wall thickness of 10 mm to allow for the tubing. The locations of the pressure taps
are shown in Figure 4.2.
Figure 4.2: Location of Pressure Taps on Experimental Model
The airfoil is supported within the wind tunnel by three brackets which attach to the three
struts of the under-floor balance. The brackets are fixed to the bottom surface of the airfoil
with 5 mm wood screws. Endplates are fixed to the model during testing to reduce threedimensional effects.
The model as it stood after the previous project had some deficiencies which needed to be
rectified:
33

The endplates on the model were too small. Vortices can be seen to go over the
endplates and push down the tufts of yarn along the edge of the model during
turbulent flow when all the pieces of yarn should have been pushed up. This can be
seen in Figure 4. 3.
Figure 4.3: Effect of Wingtip Vortices on the Airfoil despite the Presence of Endplates (Tarrant, 2010)

New endplates were designed, manufactured and assembled onto the airfoil. The
Endplates were properly attached to the model using 7 off 5 mm diameter wood
screws.
Figure 4.4: Old Endplates (front) and New Endplates (behind)

The airfoil was not sufficiently aerodynamically smooth. The varnish to cover the
model used left small imperfections on the surface, possibly disrupting flow over the
surface. The varnish was completely sanded off to a smooth surface. The model was
34
the sprayed matt black. Matt black is a common colour to use in tuft flow
visualisation as white or fluorescent yarn is easier to see against it.
Figure 4.5: Refined Airfoil
4.1.3 Three-Component Under-Floor Balance
The three-component under-floor balance is used to measure lift, drag and pitching
moment during wind tunnel testing. Lift, pitch and drag measurements are read using an
Operator’s Graphical Interface (OGI) on a computer beneath the wind tunnel.
The under-floor balance consists of an earth section and a live section. The earth section (1)
is grey in colour and attached to a support frame. The live section (2) is blue in colour and
free to move with respect to the earth section. Two lift torque tubes carrying a beam lift
system (3) are pivoted on the balance earth frame, supported from the forces frame via four
cross-spring elements is an incidence tube. Struts are attached to the model platform on the
top of the forces frame. The struts are designed to support a model by the wing tips.
Positioned downstream is a third strut that supports a model’s tail. Yellow vertical links (4)
attach to the outer ends of the coupled beams and transfer force through a lever arm ratio.
An incident adjuster (5) allows the angle of attack of the model to be changed by rotating
the incidence tube which moves the tail arm vertically.
Lift is measure via the model support equipment and vertical links to the outer ends of the
coupled beams. Force is transferred through the lever arm ratio of the lift-input lever to a
vertical link connected to the lift loadcell mounted on the balance earth frame. A
35
corresponding parallel force on the forces frame receives the drag force the model imparts.
Streamwise movement is resisted by the horizontal drag link via a precision bell crank to the
drag load cell fixed to the earth. The output of this loadcell is thus linearly proportional to
the applied drag (Aerotech ATE Ltd, 2005).
Figure 4.6: Three-Component Under-Floor Balance
4.1.4 Pressure Scanner
A Furness Controls FCS421 Pressure Scanner was used to measure multi source
pressure with just one pressure reading instrument; in this case it was a micromanometer.
The tubes from the model were connected to the numbered 3 mm ports at the rear of the
scanner. The positive port was connected to the micro manometer and the negative port
was left open to the atmosphere. Channels were manually selected through the channel
select buttons (Furness Controls Ltd).
4.1.5 Micro Manometer
A Furness Controls FC012 200 mm micromanometer was used to measure pressures
during wind tunnel testing. The micromanometer measured the difference in static pressure
between the wind tunnel wall and the pressure at each pressure tap on the airfoil model.
The micromanometer was connected to the pressure scanner so that multiple pressures
could be read at one go.
36
4.2 Experimental Setup
4.2.1 Model Setup
The model, with endplates attached, was placed into the wind tunnel. The three
brackets on the lower surface of the airfoil were attached to the three struts of the underfloor balance using 2.2 mm screws. The pressure tubing was pulled out through a hole
located in the centre of the endplates prior to being placed in the wind tunnel. The tubing
was then fed through a small hole at the back of the wind tunnel and connected to the
pressure scanner. Each pressure tap on the model was connected to a unique channel on
the pressure scanner. The tubing was taped down to prevent excess movement during
testing. Any holes in the wind tunnel not used were taped over. The model set up in the
wind tunnel is shown in Figure 4.7.
Figure 4.7: Model in the Large Low Speed Wind Tunnel
4.2.2 Lift, Drag and Pressure Measurements Procedure
1. Using Operators Graphical Interface (OGI), a new file for data acquisition is set up.
2. The model is placed into the wind tunnel, attached to the force balance and the
balance components zeroed.
3. The tunnel was switched on to 13.2 m/s. With the model used this corresponds to a
Reynolds number of 360,000. The free-stream velocity was measured with the
micromanometer. The high tube from the settling chamber went into the negative
port and the tube from the test section went into the positive port.
4. The model was set to an aerodynamic zero degrees angle of attack by adjusting the
model incidence until the force balance measured zero lift when the model was in
37
the wind tunnel with a velocity of 13.2 m/s. Once this was done the balance
components were zeroed again.
5. The static port in the test section was connected to the high pressure static port
(plus port) in the micromanometer. The low pressure static port (minus port) in the
manometer was connected to the positive port in the pressure scanner. The negative
port in the pressure scanner was left open.
6. Each channel corresponded to a different pressure tap on the model. The channels
on the pressure scanner were manually scanned through and a pressure reading for
each channel was recorded.
7. The ‘Start Log’ button was clicked to record lift and drag readings on OGI. OGI
allowed a log duration of 10 seconds for each reading to achieve consistent readings.
8. Steps 6 and 7 were repeated until stall occurred.
38
Chapter 5: CFD Analysis
This chapter describes the procedures involved in creating a mesh and running the
mesh in a CFD software package. The first section explains how the mesh was created in the
program ANSYS ICEM and how boundary conditions were then applied to the mesh. The
second section explains how the mesh was run in the program ANSYS Fluent and the post
processing involved.
5.1 Pre-Processing
5.1.1 Freestream Model
The mesh was created using the software program ANSYS ICEM. The airfoil
coordinates were imported into ICEM as a .dat file. This provided ICEM with a series of
points for the airfoil. The points were then joined together in two curves. This created the
airfoil shape. The mesh was then built around the curves of the airfoil.
A boundary for the mesh, or farfield was then applied. The coordinates to the farfield are
shown in Table 5.1 below. The coordinates to the farfield were joined up using the curve
function to make a c-shape boundary. The curves were called FF. The farfield was placed far
enough away that good results could be attained and the farfield would not disrupt or
interfere in the flow around the airfoil, but not excessively far way either. Too large a
farfield requires more cells which increase the computing time, and does not necessarily
give better results. A surface was then created to join up the curves that make up the
farfield. The curve was named fluid.
Table 5.1: Farfield Coordinates for Freestream Mesh
Point
a
b
c
d
e
X (m)
-2
0
0
2
2
Y (m)
0
2
-2
2
-2
Z (m)
0
0
0
0
0
Once the farfield was defined, the farfield was blocked into different sections. A basic mesh
was then applied. The vertices in the blocking were moved to avoid bunching in the cells.
Using the split block tool, two areas of mesh were created, one area just around the airfoil,
39
and another area outside it as far as the farfield. The inner mesh was then defined. 125
nodes were applied to the edge of the inner mesh with a ratio of 1.05 and spacing 0.0002.
This allowed the cell size of the inner mesh to get smaller as it approached the wall of the
airfoil. This is ideal for measuring boundary layer flow. The outer mesh had 100 nodes
applied to it edge with a ratio of 1.2 and a spacing 0.02. These settings set the cells close to
the farfield larger, and allowed the cells to gradually get smaller as the inner mesh was
approached.
The pre-mesh was then converted to an unstructured mesh, creating the mesh. Smoothing
could then be applied as it the mesh was unstructured. The mesh was smoothed five times.
Each time smoothing was applied the smoothing ran with 10 iterations. Default settings in
ICEM were used for smoothing. Once the smoothing was finished the transition between
the outer mesh and inner mesh was smoothed out and made the mesh into one.
Figure 5.1: Freestream Mesh
Once the mesh was complete (Figure 5.1 and Figure 5.2), boundary conditions were applied.
The Farfield was chosen as a velocity inlet, the curves of the airfoil were set to wall and the
surface fluid was set to fluid. The basic boundary conditions were then set.
40
Figure 5.2: Freestream Mesh Close Up
5.1.2 Walled Model
The mesh was created using the software program ANSYS ICEM. The airfoil
coordinates were imported into ICEM as a .dat file. The points were then joined together in
four curves. The airfoil was then rotated to an angle of 16 degrees.
The walls around the airfoil were then added. The walls were placed at a height that
simulates the conditions in the large wind tunnel. The coordinates to the walls are shown in
Table 5.2 below. The upper and lower wind tunnel walls were joined up with the curves inlet
and outlet.
Table 5.2: Farfield Coordinates for Walled Mesh
Point
a
b
c
d
X (m)
-3
3
-3
3
Y (m)
0.44
0.44
-0.48
-0.48
Z (m)
0
0
0
0
Once the boundary around the airfoil was defined, it was blocked. A basic mesh was then
applied. The vertices in the blocking were moved to avoid bunching in the cells. Using the
split block tool and merge block tool, six areas of mesh were created. The mesh was then
adjusted using until a fine mesh was achieved on the airfoil surface and on the surface of
the wind tunnel wall (Figure 5.3).
41
Figure 5.3: Mesh with the Wind Tunnel Walls
The pre-mesh was then converted to an unstructured mesh, creating the mesh. Once the
mesh was complete, boundary conditions were applied. The inlet was chosen as a velocity
inlet, the curves of the airfoil were set to wall, the outlet was set to outflow, the walls of the
wind tunnel set to wall, and the surface fluid was set to fluid. The basic boundary conditions
were then set.
5.2 FLUENT Setup
The model was imported into ANSYS Fluent version 12 once it was meshed in ICEM.
A 2D steady pressure solver was used to model the flow around the airfoil in Fluent. The
pressure based solver is used for incompressible flow. Spalart-Allmaras was chosen as the
viscous model. Spalart-Allmaras is a turbulent model. When a laminar model was used, the
residuals in the solution would not converge, indicating that large amounts of flow
separation were occurring, hence Spalart-Allmaras had to be used.
The Spalart-Allmaras model is a relatively simple one-equation model that solves a modelled
transport equation for the kinematic eddy (turbulent) viscosity. This embodies a relatively
new class of one-equation models in which it is not necessary to calculate a length scale
related to the local shear layer thickness. The Spalart-Allmaras model was designed
specifically for aerospace applications involving wall-bounded flows and has been shown to
give good results for boundary layers subjected to adverse pressure gradients (Sydney,
2008).
42
Figure 5.4: Reference Values Used, Walled Mesh Left and Freestream Right
Boundary conditions were then set. Figure 5.4 shows the reference values used for the
numerical analysis. The velocity inlet (Farfield in section 5.1.1 and Inlet in section 5.1.2) was
given a velocity magnitude defined by components. Changing the components of velocity
the angle of attack was easily changed. The walled mesh did not have a varying angle of
attack as the model was already set at 16 degrees with respect to the walls. The under
relaxation factors were left at the default setting shown in Figure 5.5.
Figure 5.5: Under-Relaxation Factors, Walled Mesh Left, and Freestream Right
43
A second order upwind discretisation scheme was used to solve the flow problem. The
second order solution was used as it provides more accurate results when compared with
linear or first order solutions. The solution was initialised before running the calculation.
Enough iterations were set (10000) to allow the solution to run in one go. Once the
calculation was complete, readings for lift force, drag force and pressure distribution were
taken from the reports option.
44
Chapter 6: Discussion and Results
The major findings from this project are shown and discussed in this section of the
report. Figure 6.1 to Figure 6.7 show the coefficient of pressure distribution over the chord
for both experimental and CFD at various angles of attack at a Reynolds number of 360,000.
The y axes on the graphs for the coefficient of pressure distribution are reversed. This is
commonly done for pressure distribution curves, as the more negative curve corresponds to
the upper surface of the airfoil, and the more positive surface corresponds to the lower
surface of the airfoil.
-1.5
-1
-0.5
CFD
Cp
0
0.2
0.4
0.6
0.8
1
Experimental
0
0.5
1
1.5
x/c
Figure 6.1: 4 Degrees
-2
-1.5
-1
CFD
Cp
-0.5
0
0.2
0.4
0.6
0
0.5
1
1.5
x/c
Figure 6.2: 6 Degrees
45
0.8
1
Experimental
-2.5
-2
-1.5
Cp
-1
CFD
-0.5
0
0.2
0.4
0.6
0.8
1
Experimental
0
0.5
1
1.5
x/c
Figure 6.3: 8 Degrees
-3.5
-3
-2.5
-2
Cp
-1.5
CFD
-1
-0.5 0
0
0.2
0.4
0.6
0.8
1
Experimental
0.5
1
1.5
x/c
Figure 6.4: 10 Degrees
-4
-3
Cp
-2
CFD
-1
0
0.2
0.4
0.6
0
1
2
x/c
Figure 6.5: 12 Degrees
46
0.8
1
Experimental
-5
-4
-3
CFD
Cp
-2
-1
Experimental
0
0.2
0.4
0.6
0.8
1
0
1
2
x/c
Figure 6.6: 14 Degrees
Figures 6.1 to 6.6 show CFD and experimental coefficient of pressure distributions over the
NACA 0018 airfoil at various angles of attack. The leading edge of the CFD pressures show a
much higher peak value compared to the experimental. There is a Cp difference of
approximately 1 from 6 degrees to 14 degrees and approximately 0.25 at 4 degrees. Once
the peak pressure is reached, the pressures in the CFD and the experimental begin to
decrease in magnitude. After the initial peak pressure (0.2 x/c) the CFD and experimental
show excellent correlation on the top and bottom surfaces.
-5
-4
-3
CFD
Cp
-2
Experimental
-1
0
0.2
0.4
0.6
0.8
1
0
1
2
x/c
Figure 6.7: 15 Degrees
Figure 6.7 shows the pressure distribution at an angle of attack of 15 degrees. The CFD
shows stall on the upper surface. This can be deduced by the flattened out pressure
distribution curve after 0.4 x/c. Some lift can be seen on the leading edge from the high C p
47
value where the flow is still attached; however most of the airfoil has separated, hence stall
has occurred. The experimental pressure distribution still shows attached flow. From the
low magnitude of values over the aft section of the airfoil, it is clear that the experimental
flow is slowly separating, however it should be noted that it has not fully separated yet
unlike the CFD.
From the coefficient of pressure distributions it is clear that the CFD has predicted stall over
the entire surface of the airfoil at 15 degrees. This does not correlate with the experimental,
as the pressure distribution still shows attached flow. Figure 6.8 shows CL vs. α for
experimental, published and CFD data. The published data and the CFD both show trailing
edge stall which would be expected from this type of airfoil. The published data from
(Sheldahl, et al., 1981) shows a similar critical angle and max CL to the CFD. The
experimental however, has the same lift curve slope as the CFD, but continues to increase,
until it stalls at 20 degrees.
1.6
1.4
1.2
CL
1
Experimental
Integration of Pressure
0.8
Walled CFD
CFD
0.6
Published Data
0.4
Thin Airfoil Theory
0.2
0
0
5
10
15
20
25
α (Degrees)
Figure 6.8: Coefficient of Lift vs. Angle of Attack
The experimental lift curve shows a sharp and sudden loss of lift at 20 degrees. The sharp
drop in lift, combined with the high stall angels, leads to the hypothesis that a long laminar
separation bubble formed on the upper surface during lower angles of attack. The sudden
48
drop in lift occurs when the bubble bursts and airfoil becomes fully separated. The bubble
effectively increases the thickness of the airfoil, which is the most likely cause of the
increased stall angle, as thicker airfoils generally have a higher stall angle. This type of stall
displays elements of thin airfoil stall and trailing edge stall. In the CFD model, the airfoil was
run under the turbulent model Spalart Allmaras. The Spalart-Allmaras model cannot predict
laminar separation bubbles, which accounts for the large difference in the stall angle.
The black line indicates the lift curve from thin airfoil theory. The NACA 0018 is a thick
airfoil, so the actual lift curve slope should be less than 2πα, which is for an infinitely thin
airfoil. The experimental data, CFD and integration of pressures all lie at a slope less than
that of the thin airfoil theory, as it should due to the thickness of the airfoil. The published
data however, follows the thin airfoil theory, which could indicate that the published data
may be incorrect.
The orange squares indicate the lift points from the integration of pressures. The slope of
the lift curve produced is slightly less than that of the CFD. This can be attributed to the fact
that shear stress cannot be measured in the wind tunnel. Therefore the effect of viscous
forces on the lift curve had to be neglected. The viscous forces would add an increase of
approximately 4% to the current lift curve, bringing it closer to the slope of the CFD and
experimental lift. The integration of pressure lift points roughly follows the same path as the
experimental points. If more angles of attack for pressure measurements were to be taken
then a similar stall angle would be seen.
The purple point indicates the coefficient of lift at 16 degrees from a CFD model with the
walls of the wind tunnel included. The point is only 0.15 higher than with the experimental
lift curve. The increased CL can be accounted for by the fact that the CFD takes the airfoil
spanning the entire wind tunnel; whereas in reality it only spanned half the width of the
wind tunnel giving a less CL than what is shown. The CFD and published data had both
already stalled at an angle of 16 degrees. This shows that the wind tunnel walls have an
enormous effect on the stall mechanism of the airfoil. Separation is delayed by the walls of
the wind tunnel, causing an increased CL as seen in the experimental and the Walled CFD.
This point from the Walled CFD supports the hypothesis that the wind tunnel walls are
greatly affecting the experimental airfoil model’s separation mechanism.
49
Figure 6.9: Contour Plot of Velocities Magnitudes in Wind Tunnel
Figure 6.9 shows a contour plot of velocity magnitude in the walled CFD mesh. The areas of
deep green show a velocity magnitude of approximately 14.5 m/s, which is faster than the
initial freestream velocity of 13.2 m/s. The deep green areas occur along the walls of the
wind tunnel. This shows that there is an increase of speed along the walls of the wind
tunnel. The dark blue shows regions of very slow moving air. The dark blue region over the
top surface of the airfoil indicates an area separation; however there is still some attached
flow on the airfoil, thus there is still lift being produced. This is confirmed by Figure 6.10
which shows the coefficient of pressure distribution over the airfoil at 16 degrees for the
experimental and walled CFD. The two pressure distributions show similar results. The lack
of peak pressure in the experimental can be accounted by the fact that CFD assumes the
airfoil spans across the entire wind tunnel, when it only spans across half of it, so this
doubles the effect of the wind tunnel walls.
-6
-5
-4
Cp
-3
Experimental
-2
-1
Walled CFD
0
0.2
0.4
0.6
0.8
0
1
2
x/c
Figure 6.10: Coefficient of Pressure vs. x/c at 16 Degrees
50
1
0.35
0.3
0.25
0.2
CD
Experimental
0.15
CFD
0.1
Published Data
0.05
0
0
5
10
15
20
25
α (Degrees)
Figure 6.11: Coefficient of Drag vs. Angle of Attack
Figure 6.11 shows the coefficient of drag vs. the angle of attack. The CFD and the
experimental values show similar curves, slowly increasing initially, and then increasing
much faster after about 10 degrees. The published data shows almost no increase in the
coefficient drag until an angle of attack of 13 degrees, where a sharp increase in CD is seen.
The CFD mesh was run under the turbulence model Spalart-Allmaras. CFD cannot predict
laminar separation bubbles or and long bubble stall. In order to recreate the CFD, and
published data results, boundary layer control was used. The experimental airfoil was
tripped with a metal bar of 3mm diameter running across the leading edge at 5% of the
chord. Tripping the airfoil caused a fully turbulent surface, where a laminar separation
bubble could not form, giving results that better match the CFD and published data. The
effects on the pressure distribution, lift and drag, can be seen in Figures 6.10 to Figures
6.18.
51
-2
-1.5
CFD
-1
Experimental
-0.5
Cp
0
0.2
0.4
0.6
0.8
1
0
Experimental
Trip
0.5
1
1.5
x/c
Figure 6.12: 4 Degrees (Tripped)
-2
-1.5
-1
CFD
-0.5
Cp
0
0.2
0.4
0.6
0.8
1
0
Experimental
Experimental
Trip
0.5
1
1.5
x/c
Figure 6.13: 6 Degrees (Tripped)
-2.5
-2
-1.5
CFD
Cp
-1
-0.5
0
0.2
0.4
0.6
0
0.5
1
1.5
x/c
Figure 6.14: 8 Degrees (Tripped)
52
0.8
1
Experiment
al
Experiment
al Trip
-3.5
-3
-2.5
-2
CFD
Cp
-1.5
Experimental
-1
-0.5 0
0
0.2
0.4
0.6
0.8
1
Experimental
Trip
0.5
1
1.5
x/c
Figure 6.15: 10 Degrees (Tripped)
-4
-3
Cp
-2
CFD
Experimental
-1
0
0.2
0.4
0.6
0.8
0
1
Experimental
Trip
1
2
x/c
Figure 6.16: 12 Degrees (Tripped)
The tripped pressure distributions show good agreement at lower angles of attack. From 4
degrees to 12 degrees the Figures 6.10 to 6.14 shows similar pressure distributions to CFD.
The initial peak pressure that occurs before the trip in the CFD is destroyed by the trip in the
tripped distributions. After the trip the pressure rises dramatically up to the curve of the
CFD. The pressure distribution follows the CFD from then on.
53
-5
-4
-3
CFD
Cp
-2
-1
0
0.2
0.4
0.6
0.8
1
0
Experimenta
l
Experimenta
l Trip
1
2
x/c
Figure 6.17: 14 Degrees (Tripped)
-5
-4
-3
CFD
Cp
-2
-1
0
0.2
0.4
0.6
0
0.8
1
Experiment
al
Experiment
al Trip
1
2
x/c
Figure 6.18: 15 Degrees (Tripped)
After 12 degrees the tripped airfoil stalls completely. The completely flat upper surface in
Figures 6.15 and 6.16 show complete stall. The CFD still shows a peak pressure at the
leading edge, however, the peak pressure which would exist on the non-tripped airfoil could
be disrupted by the trip, destroying any lift that would occur on the leading edge.
54
1.4
1.2
1
Experimental Trip
0.6
Experimental
CL
0.8
CFD
0.4
Published Data
0.2
0
0
5
10
15
20
25
α (Degrees)
Figure 6.19: Coefficient of Lift vs. Angle of Attack (Tripped)
Figure 6.17 shows the CL vs. α graph with the boundary layer on the experimental model
tripped. The tripped model stalls at 14 degrees and displays the same lift slope as the CFD
and the original experimental. The tripped model follow shows excellent agreement with
the CFD model which is also fully turbulent. The tripped airfoil displays a trailing edge stall
mechanism. The earlier hypothesis that a laminar bubble occurs in the original experimental
lift curve, causing the increased stall angle, is supported by the results of the tripped airfoil.
The effect of the wind tunnel walls still exist, however as the boundary layer is turbulent the
effects are less noticeable compared to a laminar boundary layer.
0.35
0.3
0.25
Experimental Trip
CD
0.2
Experimental
0.15
CFD
0.1
Published Data
0.05
0
0
5
10
15
α (Degrees)
20
25
Figure 6.20: Coefficient of Drag vs. Angle of Attack (Tripped)
55
The experimental trip drag shows a higher drag curve compared to the experimental,
published and CFD data, as would be as expected. The increased drag can be attributed to
the metal bar used to trip the boundary layer, and the increase in skin friction drag from the
now fully turbulent airfoil.
6.1 Discrepancies

Aerodynamic zero degrees angle of attack did not match geometric zero degrees
angle of attack. This may have been due to the model its self or unevenness in the
wind tunnel.

It is very difficult to accurately move the angle of attack by single degrees as the dial
is very small and hard to see.

There are many large holes in the large wind tunnel. Most of the holes in the wind
tunnel were taped over; however some of the large holes which allow the underfloor balance to connect to the airfoil model could not be taped over.

The large wind tunnel’s speed controller cannot keep a steady speed which causes
the speed, and hence the pressure to fluctuate.

The struts add both lift and drag to the force balance; however these were easily
accounted for.
56
Chapter 7: Conclusions
These are WAAAAAYYYYYY to long, requiring me to think about what you conclude; here is
my suggested rewording after yours

The NACA 0018 model was found to contain many deficiencies that hindered its
performance. The main problem with the model was that the endplates were too
small, which allowed vortices to occur over the outer edges of the airfoil. The model
was refined by attaching new larger endplates.

Large endplates are required ro reduce vortices on the outer edge of the airfoil (In
your one I must actual have to work out what you concluded..)

Experimental wind tunnel testing with the NACA 0018 model produced lift slope that
matched CFD. The experimental model stalled at 19 degrees; however the CFD
stalled at 14 degrees. The published data showed a slope that was marginally higher
than the CFD and experimental, but stalled at 13 degrees, correlating with the stall
angle of the CFD. This indicated a difference in the stall mechanism between the
experimental data and the CFD, most likely from the presence of the wind tunnel
walls due to the size of the model.

The wind tunnel walls produce long bubble stall unless a boundary layer trip is used

The airfoil was meshed in the computer program ICEM with the wind tunnel walls
included. The model was placed at a fixed angle of attack of 16 degrees, where the
original CFD model and published data had already stalled. The walled mesh was run
in Fluent and gave a CL of 1.36 at 16 degrees, similar to the 1.2 that the experimental
gave. This supported the hypothesis that the walls of the wind tunnel were
interfering with the lift on the airfoil in the experimental testing.

(I don’t even know what you did in that point… is an error of 0.16 insignificant? How
insignificant is it? Is this something you concluded? It sounds more like the last point
in more detail)

The experimental airfoil model was believed to be undergoing long bubble stall from
the stall mechanism shown in the lift curve, and the large difference in stall angle
between the CFD and published data. The experimental model’s results were
distorted by the wind tunnel walls which are believed to be the root cause of the
long bubble stall.
57

(this is the same as two points ago..)

The pressure distributions over the airfoil showed excellent correlation between CFD
and experimental, especially at lower to moderate angles of attack. The peak
pressure on the CFD model was higher at all angles of attack. As the angle of attack
reached 15 degrees, the CFD shows separation from approximately 0.4 x/c onwards;
however the experimental pressure distribution shows a pressure distribution that is
still attached for most of the airfoil.

The pressure distributions over the airfoil showed excellent correlation between CFD
and experimental data, especially at lower to moderate angles of attack.

Experimental data showed a pressure distribution attached to most of the airfoil.

At 15 degrees, the CFD shows separation from approximately 0.4 x/c onwards

The integration of pressures gave a shallower lift slope than the CFD and
experimental data. The lift slope was less as viscous forces were neglected because
they cannot be measured experimentally. The viscous forces account for
approximately 4% of the total lift force for this particular set up (this sounds like
apart of the literature review).

In order to remove the long bubble stall to produce results similar to CFD and
published data, a boundary layer trip was placed on the experimental model. A
metal bar of 3mm diameter was placed on the leading edge of the airfoil at 5% of the
chord. The tripped airfoil stalled at the same angle as the CFD and published data.

The tripped airfoil stalled at the same angle as the CFD and published data.

At low angles of attack the tripped pressure distributions show initial low pressure
before the boundary layer is tripped. After the trip the pressure increases
dramatically. The pressure reaches a peak pressure and decreases gradually. The
peak pressure of the tripped airfoil falls on the same curve as the CFD and follows
the CFD from that point on (this sounds like a discussion of results).

At higher angles of attack (13 degrees onwards) the tripped pressure distributions
showed complete stall (best conclusion by FAR!).
58
7.1 Recommendations for Future Work

Build a smaller wind tunnel airfoil model and run it at the same Reynolds number to
see if the wind tunnel walls have less of an effect on a smaller model.

A new speed controller should be installed into the large wind tunnel (surely testing
with this new speed controller and not actually just installing it is your
recommendation…).

Investigation in to the effects of boundary layer control on an airfoil’s maximum CL
using boundary layer control techniques (don’t think you need to give an example…).

Flow visualisation with tufts, china clay and castor oil should be done to further
investigate the stall mechanism of the airfoil model further and the impact of the
wind tunnel walls (sounds like it could be reworded).

Actually write a good FYP (BURN!).
59
References
Abbot, Ira H. and Von Doenhoff, E. Albert. 1959. Theory of Wing Sections. Toronto :
General Publishing Company Ltd, 1959.
Aerotech ATE Ltd. 2005. 3 Component Underfloor Balance Operations Manual for University
of Limerick. East Sussex : Aerotech ATE Ltd, 2005.
Anderson, John D. 2001. Fundementals of Aerodynamics. 3rd . New York : McGraw Hill,
2001.
—. 2008. Introduction to Flight. International . New York : McGraw Hill, 2008.
Clancy, L. J. 1975. Aerodynamics. Essex : Longman Scientific & Technical, 1975.
Furness Controls Ltd. FCS421 Pressure Scanner User Guide. Sussex : s.n.
Leishman, J. Gordon. 2000. Principals of Helicopter Aerodynamics. New York : Cambridge
University Press, 2000.
Massey, Bernard. 1998. Mechanics of Fluids. Cheltenham : Stanley Thornes Ltd, 1998.
Schlichting, Herman. 1987. Boundary-Layer Theory. New York : McGraw-Hill Inc, 1987.
Sheldahl, E. Robert and Klimas, C. Paul. 1981. Aerodynamic Characteristics of Seven
Symmetrical Airfoil Sections Through 180-Degree Angle of Attack for Use in Aerodynamic
Analysis of Vertical Axis Wind Turbines. Albuquerque : Sandia National Laboratories, 1981.
Sydney, The Univeristy of. 2008. The Spalart-Allmaras Model. The University of Sydney.
[Online]
2008.
[Cited:
16
February
2011.]
http://sydney.edu.au/engineering/aeromech/AMME4210/documents/manuals/fluent_help
/html/ug/node414.htm.
Tarrant, Kevin. 2010. Low Mach Number Airfoil Stall. Limerick : University of Limerick, 2010.
Washington, University of. 2010. Flow Visualisation. University of Washington Aeronautical
Laboratory.
[Online]
2010.
[Cited:
http://www.uwal.org/uwalinfo/techguide/flowvis.htm.
60
2011
February
20.]
Appendix
Appendix A
Turn it in
http://temasekpoly.wordpress.com/2008/01/28/
wind tunnel picture
http://eprints.soton.ac.uk/66082/1.hasCoversheetVersion/JONES_Lloyd.pdf
A
Appendix B
The endplates drawing
B
Appendix C
C