Fluid Mechanics and
Aerodynamics Refresher
Dr Nick Lavery
403 Engineering North
2021-22
Contents of this lecture
1 Fluid mechanics refresher
– Navier-Stokes equations
– The Reynolds number
– Laminar or turbulent flow
– Other non-dimensional numbers
– Analytical solution for flow in a pipe
– Lift/Drag over bodies in relation to Reynolds number
– Wind tunnels - flow over bodies (e.g. aerofoil)
– Characteristics of flow
– Derivation of lift/drag from
2 The Aerofoil Experiment
– The subsonic AF100 wind tunnel
– Measuring pressure
– NACA foils
– Experimental measurement of pressure over the NACA0012 aerofoil
– Measurement of Lift & Drag using force transducers
• Kahoot quiz (10 mins)
Components of Fluid Mechanics
3
Fluid
Mechanics
Inviscid
Compressible
(air, acoustic)
Incompressible
(Water)
Viscous
Laminar Turbulent
Internal
(pipe/valve)
External
(aerofoil, ship)
Governing Equations (Navier-Stokes)
4
Continuity
Momentum
(F=ma)



+


+


+


= −


−


+


+


+


+


+


+


= 0
The NS equations completely describes the flow of all fluids (steady or unsteady,
compressible or incompressible, turbulent or laminar) – however numerically the
size of the grid and the time step required are too small to resolve some of the
physics.



= −∇ + ∇2 +


+


+


+


= −


+
2
2
+
2
2
+
2
2
+



+


+


+


= −


+
2
2
+
2
2
+
2
2
+



= − + 2
Lets look at the N-S equations again with = (, , ) the velocity vector and ignoring
gravitational terms



= − + 2
For steady flow, the LHS (inertial terms) can be estimated as
Inertial terms of LHS =


=


+ ∙ ~
2

While for the RHS, the viscous terms can be estimated as
Viscous terms of RHS = 2 ~

2
Therefore the ratio of LHS/RHS can be estimated as
Ratio =
∙
2
~

2



2
=
2

×
2

=


=
The ratio of the inertial to the viscous terms is called the Reynolds number and is dimensionless
=


=

3
×


× ×


The significance of the Reynolds number
=


Osborne Reynolds (1883) determined
by experiments in pipes that the flow
could remain Laminar if Re<2100, but
was inevitably turbulent if Re>4000.
These numbers are not absolute, and
there will always be some variation
from experiment to experiment.
Laminar or turbulent flow
Reynolds number
=


Ratio of inertial to viscous forces
Characteristic length taken as
• Sphere (diameter)
• Oblong (axis of length)
Similarity of flows need same geometry
and equal Reynolds number
But could change L, density and dynamic
viscosity http://en.wikipedia.org/wiki/Reynolds_number
What is the characteristic length for the Reynolds number of a foil?
Similarity and non-dimensional numbers
Reynolds number
Mach number
Prandtl number
Rayleigh number
Darcy number
Lift coefficient
Drag coefficient
http://en.wikipedia.org/wiki/Dimensionless_quantity
Laminar flow in a pipe (analytical solution)
There is only one known analytical solution of the Navier-Stokes equations
and that is for laminar flow in a pipe.
Starting with N-S equations in cylindrical coordinates (r,θ,z), so velocity
has (, , ) terms.
Continuity
1



+
1



+


= 0 →


= 0
Thus u=u(r) only, i.e., = 0 and = 0 .
From the z-momentum NS equations:



+


+




+


= −


+ +
1






+
1
2
2
2
+
2
2
1




=
1



[Eq. 1]
The only non-zero other momentum equation is the r-momentum equation,
which gives,


= 0
Boundary conditions
1. u=0 at r=R (wall)
2. du/dr=0 at r=0 (symmetry)
Assumptions
1. Pipe infinitely long in z-direction
2. Flow is steady (


= 0)
3. This is parallel flow only (so = 0)
4. Incompressible/Newtonian/Laminar
5. Constant pressure gradient
6. Velocity field axisymmetric/no swirl
7. Ignore effects of gravity
z
r
Laminar flow in a pipe (analytical solution)
Therefore, P=P(z) i.e. the only pressure changes are in the z-direction,
and [Eq. 1] can be integrated in r after multiplying both sides by r.



=
2



+ 1 →


=




+
1

Thus, integrating again with r, gives
=
2
4


+ 1 ln + 2
Where C1 and C2 are constants of integration.
From the boundary conditions (1) implies that c1=0.
Boundary condition (2) implies C2 = −
2
4


This gives us the classical parabolic velocity profile:
=
2
4


2 − 2
This will be used in Tutorial 4 next week.
Boundary conditions
1. u=0 at r=R (wall)
2. du/dr=0 at r=0 (symmetry)
z
r
Turbulent Flow Representation
(K-e as an example)
11
ui = u + u′ Where:u′ = deviating velocity,u = constant net velocity
in the direction of flow, and ui = instantaneous velocity
Reynolds Averaged Navier-Stokes Equations
More about this in the lecture on CFD ...
Lift and Drag
When body moves through fluid forces occur at solid-fluid interface:
• Wall shear stresses due to viscosity
• normal stresses due to pressure.
The resultant force in upstream direction is termed the drag, and
the resultant force normal to the upstream velocity is the lift.
If Re is large, then inertial terms are much larger than viscous
terms ∙ ≫ 2 , we can ignore them in the NS
momentum equation, so
∙ = −
∴
∆

~
2

Thus the pressure differences scale as 2 and the drag force is
roughly the size of 2 (Force=pressure X area).
Conversely, if Re is small, 2 ≫ ∙ , then
2 = −
∴
∆

~


= 2


=
2

Thus, the drag force scales as the inverse of the Re number (1/Re).
The momentum terms of the Navier-stokes equations are
the fluid equivalent of F=Mass X acceleration.



= − + 2
Wind tunnels
Not just for flow over wings
Also for
• Automotive aerodynamics
• Radiator design
• Fan-blade design
• Turbine blade design
Fluid flow similarity allows us to use
smaller objects and smaller flows to
understand flow over larger objects
and/or higher velocities
But who says it has to be small!
Transonic wind tunnel at NASA's Langley Research
Centre
Bernoulli’s equation
“F=ma” along a streamline
Valid for planar flows, however
• Viscous effects assumed negligible
• Flow assumed to be steady
• Flow assumed to be incompressible
• Only valid along a streamline
+
1
2
2 + = Constant along streamline
Incompressible, steady, no viscous effects
Incompressible, density = constant
A steady flow is one in which flow variables
(pressure, velocity, etc) do not change with time,
and are only dependent of spatial location (x, y,
z).
Compressible flow can be approximated as
incompressible if the Mach number is below 0.3
The mach number M is defined as the local flow-
speed divided by the speed of sound
Viscous effects are negligible within some
regions – but not all regions, fluid is not inviscid
Fig 1 – from Fluid Mechanics
by Frank White
Flow outside the boundary layer
What is the Mach number?
Derivation of lift equation
For small α < 20°, sin α << cos α
(trigonometry)
Assuming thin foil (t/c<12%), tan φ <<1
= cos = = ℎ
Total normal pressure force:
= cos − cos
= − = ( − )
Total pressure for parallel to chord:
= sin − sin
= tan − tan
= ( tan − tan)
Total lift force is:
= න cos −න sin
Total lift force is:
= න cos =න( − ) cos
Where
= gauge pressure measured lower surface of foil
= gauge pressure measured upper surface of foil
Measuring pressure
Piezometer tube manometer
U-tube manometer
Inclined-Tube manometer
Pitot tube
Pressure taps
Coefficient of lift
Dimensionless coefficient
Used to compare similar foils
=

1
2
2()
What happens to the coefficient of lift as the AoA is increased from 0?
What causes this event?
NACA0012 AEROFOIL EXPERIMENT
EGA324 – Assignment E1
20
EGA324 - Engineering Practice -
Introductory Lecture
The AF100 subsonic Wind Tunnel
Working section:
305 mm x 305 mm, and 600 mm long.
Air velocity: 0 to 36 m.s–1
Noise levels: 80 dB(A) at operators ear
level
The AF100 (now called the 1300) is used
for various experiments including
• AF102 – NACA0012 aerofoil
experiment
• AF106 – Flat Plate Boundary layer
experiment
Data is collected via the Versatile Data
Acquisition System (VDAS-F).
AF102 – 150mm chord
NACA0012 aerofoil experiment
The main aim of this assignment is to
obtain experimental pressure
distributions, as well as lift and drag
coefficients, for a NACA0012 aerofoil
at a range of angles of attack. The
second part of the assignment is to
use validate the experimental data
through the use of computational fluid
dynamics.
EGA324 Assignment C5
AF102 – 150mm chord NACA0012 aerofoil
EQUIPMENT AND METHODOLOGY
The following is available: For this experiment you will
be using the AF100 Subsonic wind tunnel fitted with
the 150mm chord NACA0012 airfoil. This foils has
pressure taps and the machine is set-up to display
both pressure at the tapped locations, as well as a
recording lift and drag forces.
For the report, give a brief describe how the wind
tunnel works and include a picture schematics of the
rig including the instrument panel and how the data is
collected.
In the appropriate sections of the report you will need
to describe the experimental methodology and health
and safety requirements of this test.
Answer the following questions:
• Why is the fan positioned at the outlet and not the
inlet?
• Why is there a grid at the entrance of the wind
tunnel?
• Why is the entrance designed much wider than
the middle section?
RESULTS/DISCUSSION REQUIRED
During the experiment, you will
have experimented with different
flow rates in the wind-tunnel (e.g.
U=10,20,30m/s), and changed the
angle of attack of the aerofoil
between 0° and 18°, in 2° interval
stages.
The data will be saved and emailed
to you by the student demonstrator
at the end of the practical session.
Notes on data handling htm output from
VDAS can be imported into excel
Tim
e
AFA2 Basic
Balance AFA4 Encoder Input
AFA5 DP Cell
1
AFA5 DP Cell
2
Manual Angle
Input
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
(s) (N) (N) (N) (Nm) (Degrees) (Pa) (Pa) (mm) (mm) (mm) (mm) kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa (Degrees) (C) (mbar) (kg.m-3) (m.s-1)
0 -- 18.74 8.13 0.9 -- 246 360 -- -- -- -- -0.24 -1.93 -0.06 -1.25 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.5 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
2 -- 18.75 8.13 0.9 -- 250 361 -- -- -- -- -0.23 -1.92 -0.06 -1.24 -0.17 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
4 -- 18.71 8.12 0.9 -- 240 353 -- -- -- -- -0.24 -1.92 -0.06 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0.01 0 0.01 0 0.01 12 15 1013 1.23 19.79
6 -- 18.68 8.13 0.9 -- 245 359 -- -- -- -- -0.25 -1.92 -0.06 -1.24 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.57 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
8 -- 18.72 8.12 0.9 -- 250 360 -- -- -- -- -0.24 -1.92 -0.06 -1.24 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.38 -0.61 -0.39 -0.55 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
10 -- 18.76 8.12 0.9 -- 245 358 -- -- -- -- -0.25 -1.92 -0.06 -1.23 -0.18 -1.07 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
12 -- 18.54 8.13 0.9 -- 243 357 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.67 -0.39 -0.61 -0.39 -0.55 -0.42 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.91
14 -- 18.59 8.12 0.9 -- 246 358 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
16 -- 18.68 8.12 0.9 -- 239 353 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.75
18 -- 18.68 8.13 0.9 -- 238 357 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.71
Pressures (kPa)
Manual Angle
Atmospheric
Temperature Atmospheric Pressure
Ambient Air
Density
Calculated
WindspeedPressure Pressure Gauge 1 Gauge 2 Gauge 3 Gauge 4
Tim
e Force Lift Drag
Pitching
Moment Angle
AFA3 Balance DTI Inputs AFA6 Multi-Channel Pressure System Operating Conditions
Tim
e
AFA2 Basic
Balance AFA4 Encoder Input
AFA5 DP Cell
1
AFA5 DP Cell
2
Manual Angle
Input
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
(s) (N) (N) (N) (Nm) (Degrees) (Pa) (Pa) (mm) (mm) (mm) (mm) kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa (Degrees) (C) (mbar) (kg.m-3) (m.s-1)
0 -- 18.74 8.13 0.9 -- 246 360 -- -- -- -- -0.24 -1.93 -0.06 -1.25 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.5 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
2 -- 18.75 8.13 0.9 -- 250 361 -- -- -- -- -0.23 -1.92 -0.06 -1.24 -0.17 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
4 -- 18.71 8.12 0.9 -- 240 353 -- -- -- -- -0.24 -1.92 -0.06 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0.01 0 0.01 0 0.01 12 15 1013 1.23 19.79
6 -- 18.68 8.13 0.9 -- 245 359 -- -- -- -- -0.25 -1.92 -0.06 -1.24 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.57 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
8 -- 18.72 8.12 0.9 -- 250 360 -- -- -- -- -0.24 -1.92 -0.06 -1.24 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.38 -0.61 -0.39 -0.55 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
10 -- 18.76 8.12 0.9 -- 245 358 -- -- -- -- -0.25 -1.92 -0.06 -1.23 -0.18 -1.07 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
12 -- 18.54 8.13 0.9 -- 243 357 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.67 -0.39 -0.61 -0.39 -0.55 -0.42 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.91
14 -- 18.59 8.12 0.9 -- 246 358 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
16 -- 18.68 8.12 0.9 -- 239 353 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.75
18 -- 18.68 8.13 0.9 -- 238 357 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.71
Pressures (kPa)
Manual Angle
Atmospheric
Temperature Atmospheric Pressure
Ambient Air
Density
Calculated
WindspeedPressure Pressure Gauge 1 Gauge 2 Gauge 3 Gauge 4
Tim
e Force Lift Drag
Pitching
Moment Angle
AFA3 Balance DTI Inputs AFA6 Multi-Channel Pressure System Operating Conditions
Tim
e
AFA2 Basic
Balance AFA4 Encoder Input
AFA5 DP Cell
1
AFA5 DP Cell
2
Manual Angle
Input
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
(s) (N) (N) (N) (Nm) (Degrees) (Pa) (Pa) (mm) (mm) (mm) (mm) kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa (Degrees) (C) (mbar) (kg.m-3) (m.s-1)
0 -- 18.74 8.13 0.9 -- 246 360 -- -- -- -- -0.24 -1.93 -0.06 -1.25 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.5 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
2 -- 18.75 8.13 0.9 -- 250 361 -- -- -- -- -0.23 -1.92 -0.06 -1.24 -0.17 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
4 -- 18.71 8.12 0.9 -- 240 353 -- -- -- -- -0.24 -1.92 -0.06 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0.01 0 0.01 0 0.01 12 15 1013 1.23 19.79
6 -- 18.68 8.13 0.9 -- 245 359 -- -- -- -- -0.25 -1.92 -0.06 -1.24 -0.18 -1.09 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.57 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
8 -- 18.72 8.12 0.9 -- 250 360 -- -- -- -- -0.24 -1.92 -0.06 -1.24 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.38 -0.61 -0.39 -0.55 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.2
10 -- 18.76 8.12 0.9 -- 245 358 -- -- -- -- -0.25 -1.92 -0.06 -1.23 -0.18 -1.07 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20
12 -- 18.54 8.13 0.9 -- 243 357 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.67 -0.39 -0.61 -0.39 -0.55 -0.42 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.91
14 -- 18.59 8.12 0.9 -- 246 358 -- -- -- -- -0.24 -1.9 -0.06 -1.23 -0.18 -1.07 -0.23 -0.94 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.41 -0.5 -0.41 -0.46 0 0.01 0.01 0 0 0.01 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 20.04
16 -- 18.68 8.12 0.9 -- 239 353 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.75
18 -- 18.68 8.13 0.9 -- 238 357 -- -- -- -- -0.26 -1.92 -0.07 -1.23 -0.18 -1.08 -0.23 -0.95 -0.35 -0.78 -0.36 -0.68 -0.39 -0.61 -0.39 -0.56 -0.42 -0.51 -0.41 -0.47 0 0.01 0.01 0 0 0.02 0.02 0 0 0.01 0 0.01 12 15 1013 1.23 19.71
Pressures (kPa)
Manual Angle
Atmospheric
Temperature Atmospheric Pressure
Ambient Air
Density
Calculated
WindspeedPressure Pressure Gauge 1 Gauge 2 Gauge 3 Gauge 4
Tim
e Force Lift Drag
Pitching
Moment Angle
AFA3 Balance DTI Inputs AFA6 Multi-Channel Pressure System Operating Conditions
Time series – take
Averages and SD
Make sure you know exactly
what tapings relate to which
locations on the foil.
Calculated windspeed depends on environmental
temperature and pressure so record this prior to
starting using handheld device provided
Part 1 – Pressure distributions Analysis of
experimental data
From the experimental data, enter the
pressure tap values into excel with a table
such as the one below (also provided as
a template excel spreadsheet on
blackboard) on the at four angles of
attack (α=2°, α =8°, α =14°, α =17°).
Include one of these (α =8°) into the
report, and number and label the table.
Plot the pressure distributions at α =8°, α
=14° and α =17° for the aerofoil, using the
distance from the leading edge (in mm)
as the x axis, and the pressure on the
vertical axis (in kPa). Use different colour
curves for the upper and lower surfaces,
clearly identifying which one is which.
Explain the shape of the graph using
Bernoulli’s equation.
-0.29 kPa -290 Pa
8 degrees
Ambient temperature, Ta = 21 °C 294.15 °K
Ambient pressure, Pa = 1021 mbar 102.1 kPa
1.209414 kg/m^3
Wind tunnel velocity = 20.72 m/s
Tapping
Number
Distance
from
leading
edge x
(mm)
x/c
Pressure
display,
PT (kPa)
Local
Relative
Static
Pressure
(kPa)
Cp
START 0 0.000 0 0 0
1 0.76 0.005 -1.18 -0.89 -3.42819
3 3.81 0.025 -0.76 -0.47 -1.8104
5 11.43 0.076 -0.77 -0.48 -1.84891
7 19.05 0.127 -0.65 -0.36 -1.38669
9 38 0.253 -0.53 -0.24 -0.92446
11 62 0.413 -0.45 -0.16 -0.6163
13 80.77 0.538 -0.4 -0.11 -0.42371
15 101.35 0.676 -0.37 -0.08 -0.30815
17 121.92 0.813 -0.33 -0.04 -0.15408
19 137.16 0.914 -0.29 0 0
END 150 1.000 0 0 0
START 0 0.000 0 0 0
2 1.52 0.010 -0.03 0.26 1.001495
4 7.62 0.051 -0.09 0.2 0.770381
6 15.24 0.102 -0.16 0.13 0.500748
8 22.86 0.152 -0.19 0.1 0.38519
10 41.15 0.274 -0.24 0.05 0.192595
12 59.44 0.396 -0.22 0.07 0.269633
14 77.73 0.518 -0.27 0.02 0.077038
16 96.02 0.640 -0.27 0.02 0.077038
18 114.3 0.762 -0.27 0.02 0.077038
20 129.54 0.864 -0.29 0 0
END 150 1.000 0 0 0
Wall pressure upstream, PW =
Angle of attack (AoA), α=
Air density =
U
p
p
er
s
u
rf
ac
e
Lo
w
er
s
u
rf
ac
e
A note on NACA foils …
The NACA 4-Series airfoil designations are
codes that give airfoil shapes.
The two most common are the NACA 0012
and NACA 2412.
The first digit is the maximum camber in
units of c/100.
The 0012 is symmetric, that is, it has no
camber.
The 2412 only has 2% camber.
The last two digits give the maximum
thickness in units of c/100.
Both these airfoils have a maximum
thickness of 12%.
The second digit is the location of
maximum camber in units of c/10.
http://airfoiltools.com/airfoil/details?airfoil=naca2412-il
http://airfoiltools.com/airfoil/details?airfoil=naca0012h-
sa
What to expect?
Pressure profile current experiments
Datalo
gger
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Foil 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 20 N/A N/A N/AN/AN/AN/AN/AN/AN/AN/A
The pressure taps on the NACA0012 aerofoil are numbered as given in the
AF-102 manual and shown below, with odd numbers on the upper surface
and even numbers on the lower surface.
However, in the raw data that comes directly from the datalogger, the
numbers 1-10 of the recorded pressures correspond to the even
numbered taps, and numbers 11-20 correspond to the odd numbered taps
on the lower side of the foil.
Upper Lower
Upstream
Wall pressure
Downstream
wall pressure
Wind tunnel 1 Wind tunnel 2
Experimental data (spot the difference)
Experimental data is not always perfect or what you might expect, and working
out why can be challenging
LHS has incorrect tap locations for 1st and 2nd and 3rd & 5th tap points
Part 2 – Experimental lift and drag
Low-Speed Aerodynamic Characteristics of NACA 0012
Aerofoil Section, including the Effects of Upper-Surface
Roughness Simulating Hoar Frost • By N. GREGORY
and C. L. O'REILLY • Aerodynamics Division, N.P.L.
Reports and Memoranda No. 3726, January, 1970
Lift and drag forces are readily available from the
exported data, and the first thing to do is create 3
plots of lift and drag forces as a function of the AoA,
for each of the velocities tested. Remember that the
data is recorded at a number of sampling times (10)
for each AoA, and you can take and average of the
sample data set, with an associated standard
deviation.
Are there any appreciable fluctuations in either the
recorded pressures or velocities? Is there any reason
to doubt the accuracy of the measured lift and forces?
For each of the velocities tested (U=10,20 and 30
m/s), calculate the corresponding Mach and Reynolds
number.
For U=20m/s, convert the lift and drag forces into lift
and drag coefficients, and plot these as a function of
AoA on a separate graph. Give the equations you
have used to calculate the coefficients.
Explain your results.
Expected results put together …
Note: missing units and error bars
LIFT DRAG
1. Do we have to calculate the CL from the graph or can we use the lift values given in the experiment data sheet?
• CL values are based on Lift force and aerofoil data therefore the CL value will come from experimental data.
2. If yes, what do I have to do further? Talk about the difference and compare between the Gregory O riley experiment and my experiment,
and find the stall angle?
• Yes definitely the CL values should be compared directly (extract the data from Gregory et al) and put both on the same graph. This
experiment is just as much about doing some research into results from previous workers as it is about your own results.
3. If I should Calculate CL values from the graph, can I use trapezoidal or rectangular form of approximation to calculate values?
• This is unnecessary – the lift data to get the CL is in the datasheet
4. I am using column 22 to calculate wall pressure, is this correct?
• Yes
5. The pressure tappings are given in the template as odd-even, when I tried using the pressures associated with the numbers, I am getting
a different graph(sort of sinosodial), should I consider the first 10 values as upper and last 10 as lower surface values?
• No – the tap settings are different from those in the manual, as indicated earlier in this lecture the first 10 are the upper, and the last
10 the lower tappings
6. In the user guide given, the lower surface Cp values are given as positive and upper surface Cp values are given as negative, however in
my graph it is coming in the opposite way. Will I get a positive lift coefficient?
• Should be the same
7. I have given the Velocity of wind values as 30, which is not accurate, so can I take the average value of windspeed or just discuss it as an
error?
• Work out standard deviation, if it is significant add it has error bars on your plots
FAQ
Things you need to find out
What are your Re numbers?
What is your Ma number?
Potential/ideal flows=inviscid & irrotational, under what conditions
are these valid in the context of Re/Ma?
Are the pressure measurement methods appropriate?
Can you find other work at the same Re numbers?
How do your results compare to previous experimental work E.g.
NASA reports for NACA aerofoils?
Did you have enough data points?
What discrepancies did you find?
How could these be minimised?
What is the difference between kinematic and dynamic viscosity?
Aerofoil Experiment (YouTube link)
https://youtu.be/f06wf27MwTg
https://create.kahoot.it/share/ega324-fluid-mechanics-
and-aerodynamics-refresher/87c080b8-ad84-48df-acf0-
0df36e20b457
https://canvas.swansea.ac.uk/courses/16061
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