程序代写案例-ECM3151
时间:2021-02-28
Fluids Practical - Lift Force on an Aerofoil ECM3151
Lift Force on an Aerofoil
Due date – 8/3/2021
1 Objectives
This experiment is performed using the TQ Air Flow bench, which is a vertically oriented
wind tunnel with a series of interchangeable working sections (this practical uses the
AF18 Aerofoil with Tappings experiment). The objective is to examine the pressure
distribution on the surface of the aerofoil at various angles of attack and relate this to
the lift produced by the aerofoil. You should read through this sheet and familiarise
yourself with the concepts, particularly the use of a Pitot tube (DGSJ section 6.6). The
experiment has been performed by our lab technician Julian Yates, and a recording is
available from ELE which shows the readings being taken, from which you can transcribe
the numerical results to complete your practical. Additionally, you should compare your
results with values calculated using the javaFoil panel method code; this is availble on
the Virtual Desktop or online at https://www.mh-aerotools.de/airfoils/javafoil.htm.
Background reading
DGSJ sections 6.6, 12.7 – 12.9
2 Theory
Lift on an aerofoil can be explained in terms of the Coanda effect or in terms of bound
vorticity (see lectures); but in practical terms it is the result of a difference in pressures
between the top and bottom surfaces of the aerofoil. A symmetric aerofoil produces zero
lift at zero angle of incidence; as the angle of incidence increases, so does the pressure
difference and resulting lift. Indeed, using potential flow theory it is possible to show that
the lift on the aerofoil varies linearly with angle α, for small angles of attack. However
at larger angles of attack, the flow over the top surface will separate (a boundary layer
effect) leading to a change in the pressure distribution and a drop in the lift coefficient;
a phenomenon known as stall.
2.1 Theory – experiment
Lift on an aerofoil can be determined experimentally by direct measurement, or (as
here) by measuring the pressure distribution around the aerofoil. The aerofoil has twelve
pressure tappings on the surface from the leading to the trailing edge (see appendix for
details). Note that the pressure tappings alternate sides; odd numbered tappings are on
the lower side of the aerofoil and even numbers on the upper. Pressure distributions are
conventionally plotted as a graph of the pressure ratio given in terms of the dimensionless
1
Fluids Practical - Lift Force on an Aerofoil ECM3151
Figure 1: Pressure tappings for AF18 Experiment
coefficient Cp :
Cp =
p− p∞
1
2
ρU2∞
as a function of the position ratio (distance from the leading edge divided by the chord
length x/c). Here p∞ is the static pressure and U∞ the free stream velocity. Determining
the free stream velocity is slightly complex; because the aerofoil is in a duct and there
is a developing boundary layer there is a smaller effective area around the aerofoil itself
and thus a correspondingly higher free stream velocity. To allow for this we must find
the ’effective static pressure’ peff around the aerofoil and then use this to find the correct
free stream velocity. To find the effective static pressure we must interpolate between
the duct inlet pressure (before the aerofoil) and atmospheric pressure (after the aerofoil).
The duct inlet tapping is 135 mm upstream of the exit of the duct. The centre of the
2
Fluids Practical - Lift Force on an Aerofoil ECM3151
aerofoil is 85 mm downstream from this tapping, so
peff = p0 +
85
135
× (pa − p0) (1)
where po = pressure at the duct inlet and pa = atmospheric pressure. We measure this
for each angle and use peff to find the correct free stream velocity
U∞ =

2 × (pairbox − peff )
ρ
(2)
and from this
Cp,n =
pn − peff
1
2
ρu2∞
(3)
for the n’th pressure tapping.
Conventionally, separate curves are plotted for the upper and lower surface; the area
between the two graphs represents the net lift force on the aerofoil, assuming the aerofoil
is sufficiently thin1. This also makes it easier to understand the physics of the flow
above and below the aerofoil. Lift on an aerofoil is usually expressed in terms of the lift
coefficient CL :
CL =
FL
1
2
ρU2A
with A as the plan area of the aerofoil. In mathematical terms this can be evaluated
from the Cp values :
CL =
∫ [
Cpl
(x
c
)
− Cpu
(x
c
)]
d
(x
c
)
i.e. as the area between the upper and lower Cp curves on your graphs, which can be
evaluated numerically from your data (e.g. using Simpson’s rule or the trapezium rule)
for each angle of attack.
2.2 Theory – Panel Method
The Panel Method is a computational method for determining the lift and other charac-
teristics of an aerofoil, based on potential flow theory but including “real fluid” correc-
tions to deal with phenomena such as separation and stall. In potential flow theory, the
flow velocity at any point in space can be determined from the flow potential (and/or
stream function) created as the sum of individual elements such as sources/sinks and
vortex points. In a Panel Method code, the surface of the aerofoil is represented as a
series of discrete sections (lines in 2d, faces in 3d), each with its own associated potential
function, and the potential and velocity at any point is determined by the sum of these
individual scalar potentials. This can be used to calculate streamlines and pressure dis-
tributions around the aerofoil and hence in a very similar methodology the lift coefficient.
1Can you explain why the aerofoil has to be thin?
3
Fluids Practical - Lift Force on an Aerofoil ECM3151
Panel method codes such as XFoil are used extensively in industry as a (relatively) cheap
way to determine aerofoil characteristics and as part of a design process. javaFoil is an
implementation in Java of a 2d panel code, which you can use to simulate the aerofoil
and compare with your experimental results.
3 Methodology
a. Calculate an accurate value for the density of air using room temperature and
atmospheric pressure (Rogers and Mayhew 1992 pp.157-8).
b. With the aerofoil at 0◦ angle of attack, record the pressure measurements from the
video.
c. From the atmospheric and duct inlet pressures calculate the effective static pressure
(equation 1).
d. Using peff and the airbox pressure reading, calculate the actual free stream velocity
(equation 2) and the Reynolds number based on the chord length.
e. For each pressure tapping reading, calculate the corresponding value of Cp,n (equa-
tion 3), and plot these against x/c. You can extend the curves to the zero pressure
coefficient line at a chord ratio of 0 and 1. The resulting curves should be similar
to those shown in figure 11c in the appendix. You should find that the pressure
coefficient near to the leading edge is zero, because the aerofoil forces the air to
stop moving at this stagnation point. The exact position of this stagnation point
changes with incident angle.
f. From your curves of Cp, calculate the lift coefficient by numerical integration.
g. The measurements have been repeated for increasing angles of attack (in steps of
5

) up to 25

, with additional measurements at 17.5

and 22.5

. Calculate the
corresponding lift coefficients and plot a graph of CL vs. α for the aerofoil.
h. Use javaFoil to calculate equivalent results using the panel method and compare
with your experimental results.
Please present your results in the form of a standard experimental report following
the guidelines set out in “Notes on Experimental Reports”. Remember to analyse and
comment on all your results, including an estimate and analysis of the experimental
errors. Near stall, the manometer readings may fluctuate significantly; why is this?
4
Fluids Practical - Lift Force on an Aerofoil ECM3151
Appendix
Aerofoil characteristics.
Aerofoil Type NACA0020
Aerofoil Chord 63 mm
Aerofoil Wing Span 49 mm
Effective surface area 0.0031 m2
Tapping positions :
Tapping Number Tapping Position
From the leading
edge (mm)
1 1.0
2 2.0
3 4.5
4 7.5
5 11.0
6 14.5
7 20.0
8 26.0
9 32.1
10 38.0
11 44.0
12 50.0
5
120
Theory

Pr
es
su
re
Co
ef
fic
ie
nt
x/c
Upper
Surface
Lower
Surface
Pr
es
su
re
Co
ef
fic
ie
nt
x/c
Negative
Pressure UpperSurface
Lower
Surface
Negative
Pressure
Positive
Pressure
Positive
Pressure
Incident Angle = Stall Angle
Incident Angle => Stall Angle
x
c
= distance from leading edge
= chord
Pr
es
su
re
Co
ef
fic
ie
nt
x/c
Upper
Surface
Lower
Surface
Negative
Pressure
Positive
Pressure
Incident Angle < Stall Angle
Airflow
Airflow
Airflow
Pr
es
su
re
Co
ef
fic
ie
nt
x/c
Negative
Pressure
Upper
and lower Surfaces
Negative
Pressure
Incident Angle = 0
Airflow
-
+
-
+
-
+
-
+

Figure 11c. Pressure around a symmetrical Aerofoil


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