Aerofoil Lab
MCEN90008 Fluid Dynamics
Semester 2, 2022
Instructions
• The lab report is due on Friday at 11:59PM, four weeks after the week in which you
attend the lab. For example: if you attend the lab in Week 3, your due date will be
week 7.
• The lab report should be done in groups of 2 students. Both students in the group
will get the same marks. Please choose your group partner carefully.
• If you choose to do the report alone, no concession will be given. Your assignment will
be marked the same as an assignment done by two students.
• Only hand in one assignment per group. The name and student IDs of both members
should be mentioned on the cover page.
• Your submission will be through Gradescope and will comprise of:
– One PDF document with computer generated graphs and figures, containing all
the questions and discussions required for this report. Indicate on the cover page
the session(s) in which you attended the lab.
– Copies of all computer programs used to generate the figures and results appended
as original files. DO NOT append them to the PDF of the report.
– Marks will be deducted for illegible figures, incorrect or absent axis labels (with
appropriate units) and missing captions.
1 Introduction
The forces exerted on a body moving through a fluid maybe be resolved into two compo-
nents:
• Lift (L) - the force perpendicular to the free stream or direction of travel.
• Drag (D) - the force parallel to the free stream or direction of travel.
1
The drag, D, is the sum of the form drag (due to pressure forces) and skin friction
drag (due to viscous stresses).
An aerofoil is a body designed to produce much more lift than drag when moving
through a fluid. The production of a lifting force for these types of bodies is best under-
stood in terms of potential flow. In order to avoid infinite velocity at the sharp trailing edge,
a circulation (bound vortex) is superimposed on the flow around the aerofoil. This tends to
increase fluid speed over one side, decreasing the pressure there (by Bernoulli’s principle)
and vice versa for the other side. The resulting pressure differences between either side cause
the lifting force.
Potential flow theory, however, predicts zero drag, which is not observed experimentally.
The presence of even tiny viscosity causes potential flow theory to be invalid in thin regions
close to the surface known as boundary layers. In these regions, fluid velocity varies from
zero at the wall (no-slip) to the potential flow velocity outside the boundary layer. Large
velocity gradients at the wall result in high skin friction drag, Cf ,
du
Cf ∝ µ (1)
dn n=0
for a given Reynolds number (Re). Note that u is the local mean fluid velocity, µ is the
dynamic fluid viscosity and n is the coordinate normal to the surface of the body.
In adverse pressure gradients (i.e. pressure increasing with downstream distance) or
where there are sharp edges, these boundary layers may separate from the surface causing
a large increase in the size of the wake. Separation and wake formation at the rear of the
aerofoil prevent the pressure there from increasing and the same is predicted by the potential
flow theory. The resulting pressure difference between the upstream and downstream halves
of the aerofoil results in form drag.
Figure 1: Geometric features of an aerofoil.
Hence, efficient, low speed aerofoils have a geometry similar to that shown in Figure 1.
A rounded nose prevents separation that might occur from sharp edges, whilst a smooth
‘streamlined’ shape prevents unnecessary separation. Some of the terminology and geometric
features include:
• Leading edge - the upstream edge of the aerofoil.
2
• Trailing edge - the downstream edge of aerofoil.
• Chord line - the straight line from the leading edge to the trailing edge and has length
c.
• Camber line - the locus of points halfway between upper and lower surfaces measured
normal to the chord line.
• Thickness - the maximum distance between the upper and lower surfaces measured
normal to the chord line.
• Angle of attack - the angle (α) between the free stream velocity and the chord line.
Using dimensional analysis, it can be shown that the non-dimensional lift coefficient CL
and drag coefficient CD , which are defined by,
L
CL = 1
(2)
2
ρU 2 A
D
CD = 1
(3)
2
ρU 2 A
are functions of the aerofoil geometry, the angle of attack α and the Reynolds number
Re = ρU c/µ for an incompressible flow. Here, ρ is the fluid density, µ is the absolute vis-
cosity, U the free-stream velocity and A is a representative area. If L and D are redefined
to be the forces per unit span of wing then it is common to choose A = 1 · c.
Similarly, a pressure coefficient Cp may also be defined as,
p − p∞
Cp = 1
(4)
2
ρU 2
where p∞ is the static pressure far upstream.
Usually, CL increases approximately linearly with respect to α for small α, whilst the
variation of CD is often described by the empirically derived relationship,
CD = A + BCL2 (5)
where A and B are constants to be determined from the data. However, beyond an
angle of attack of approximately 15 degrees, the lift reaches a peak value and then starts to
decrease, whilst the drag suddenly increases. This behaviour is associated with boundary
layer separation close to the leading edge and is known as the stall. This phenomenon
is undesirable since it substantially reduces performance (e.g. loss of altitude in aircraft,
decrease in efficiency and increase in vibration of fans) although it may be used to maintain
loads within structural limitations (e.g. aircraft, wind turbines).
2 Aims
• To measure the pressure distribution around an aerofoil.
• To estimate the lift and form drag of an aerofoil at various angle of attack.
• To identify the stall angle and maximum lift coefficient.
• To identify the optimum angle of attack.
3
3 Theory
To calculate the forces acting on an aerofoil, we consider the pressure p acting on an element
of aerofoil surface, as shown in Figure 2. The force per unit span dF acting on this element
is dF = p · 1 · ds. Resolving this in the x and y directions, we see from Figure 3 that,
dy
dFx = dF sin θ = pds = pdy (6)
ds
dx
dFy = −dF cos θ = −pds = −pdx (7)
ds
Figure 2: Forces and coordinate system definition.
Figure 3: Pressure forces acting on an infinitesimally small element of the aerofoil surface.
The forces are then obtained by integrating over the surface S of the aerofoil so that,
Z ymax
Fx = (pf ront − pback ) dy (8)
ymin
Z c
Fy = (plower − pupper ) dx (9)
0
The force coefficients in the x and y directions are then given by,
I
Fx y
Cx = 1 2 = Cp d (10)
2
ρU c · 1 c
S
4
I
Fy x
Cy = 1 2 = −Cp d (11)
2
ρU c · 1 c
S
where the constant terms containing p∞ disappear when integrated over S (using equation
4). Using Figure 2, the lift and drag coefficients may be written as,
CL = Cy cos α − Cx sin α (12)
CD = Cy sin α + Cx cos α (13)
Hence, to find CL and CD the Cp distribution over the surface of the aerofoil is required.
This may be determined by drilling small holes (pressure tappings) over the aerofoil surface
and measuring the pressure at each hole using a manometer. The total pressure pT is the
sum of the dynamic pressure 21 ρU 2 and the static pressure p∞ so that,
1 2
ρU = pT − p∞ this difference in pressure is measured via a Pitot-static tube (14)
2
which when inserted into the definition of Cp (4) becomes,
p − p∞
Cp = (15)
pT − p∞
Since the head reading of the manometer is proportional to the pressure measured, (15) can
be rewritten as,
h − h∞
Cp = (16)
hT − h∞
where h is the local pressure head of a particular tapping, h∞ is the static pressure head
and hT is the total pressure head.
Using the pressure tapping coordinates in the Appendix, it is thus possible to construct
plots of Cp versus x/c and Cp versus y/c . Integration may then be performed using a simple
trapezoidal numerical integration scheme.
4 Report
You will prepare a lab report for this experiment comprising of an aims, methods, results,
discussions and conclusions sections.
4.1 Introduction (10 marks)
• Provide an introduction describing the aims of this experiment. (2 marks).
Describe the method and procedures used in the experiment by elaborating on the following:
• Name all the equipment used. What is the role of each equipment? (3 marks)
• The procedure used to measure the Cp distribution and the variation in CL and CD
with α for one value of the Reynolds number. How was α = 0 determined?
(5 marks)
5
4.2 Results (40 marks)
• Tabulated data along with CL and CD for each α. (5 marks)
• Calculations of U and Re. (5 marks)
• Plots of Cp vs. x/c and Cp vs. y/c for each α. (18 marks)
• Plots of CL and CD vs. α. (12 marks)
4.3 Discussion (45 marks)
As a basis for the discussion, consider the following:
• Identify and discuss any significant sources of error (four at least). (4 marks)
• Describe how the signal-to-noise ratio of the manometer array is improved by its design
and the choice of the working fluid. (2 marks)
• If u is defined to be the speed on the surface of the aerofoil in potential flow theory,
show that,
u 2
Cp = 1 − (17)
U
(4 marks)
• The theoretical distribution of obtained from potential flow theory is given in the
Appendix for α = 0. Plot the theoretical Cp distribution on the experimental plot
for Cp versus x/c at α = 0. How well do these compare? Does potential flow theory
provide a reasonable estimate of the pressure distribution for this case? Why/Why
not? (7 marks)
• Determine the slope in CL vs. α for α less than the stall angle. How does this compare
with the predictions from the thin aerofoil theory? (5 marks)
• Determine the maximum lift coefficient and its angle of attack for this aerofoil. Would
potential flow theory give useful results in this regime? Why/Why not? (5 marks)
• From the plot of CD vs. CL2 , determine if the proposed empirical relationship (CD =
A + BCL2 ) is suitable for α less than the stall angle. If so, determine the constants A
and B. (5 marks)
• The lift-drag ratio, L/D = CL /CD is used as a measure of aerofoil efficiency. Determine
the maximum lift-drag ratio for this aerofoil and the optimum angle of attack.
(5 marks)
• Explain the importance of the Reynolds number (Re), particularly when applying test
results to the design of a device (e.g. aircraft) which is geometrically similar, but much
larger in size. For an aircraft incorporating the present aerofoil with a chord c = 1
m, calculate the speed from the present results at sea level in standard atmospheric
conditions for matched Re. Comment on the velocity and Re. For the same chord
c = 1 m and conditions, determine Re for the aircraft flying at a speed of U = 100
m/s. How could experimental results be obtained for a geometrically similar model at
the calculated Re? (8 marks)
6
4.4 Conclusion (5 marks)
• Summarize the important results. (3.5 marks)
• Elaborate on the main assumptions made throughout the experiment, and how they
could impact the results. (1.5 mark)
5 Bibliography
(1) Clancy, L.J. (1991) Aerodynamics, Longman Scientific and Technical, England.
(2) Abbott, I.H. and Von Doenhoff, A.E. (1959) Theory of wing sections, Dover publications,
New York.
(3) Pope, A. and Harper, J.J. (1966) Low-speed wind tunnel testing, John Wiley & Sons,
New York.
(4) Hunsaker, J.C. and Rightmire, B.G. (1947) Engineering applications of fluid dynamics,
McGraw-Hill, New York.
7
6 Appendix
