AERO2358 Review of Key Concepts 2015
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Transcript of AERO2358 Review of Key Concepts 2015
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School of Aerospace, Mech. & Manuf. Eng.
Aerospace & Aviation Discipline
AERO2358 Advanced Aerodynamics, 2015
Review of Key Concepts learned in AERO2356
Dr. Jon Watmuff Room 251.3.08 Bundoora East
A copy of these Lecture Notes is available on the AERO2358 Blackboard Site.
Version Date & Time: 3-Mar-2015 12:04 AM
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Slide 1 of 39
The following slides are mostly taken from AERO2356 Course notes
They contain critically important information on Airfoils and Wings
These are KEY concepts required to understand the material
further developed in this course associated with Flight Dynamics
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Slide 2 of 39
Basic Fluid Mechanics Fluid Forces acting on a surface
All aerodynamic forces result from the action of the air on surfaces, which can be: 1) Force locally perpendicular to the surface, which is the result a fluid pressure, p, and 2) Force locally tangential (parallel) to the surface, which is the result of fluid shear stress, ,
which arises because of the fluid viscosity, e.g. surface0y
dUdy
=
= .
Note that surface 0 = for an inviscid fluid (since inviscid means that 0 = )
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Slide 3 of 39
Wall Shear Stress is due to Boundary Layer Pressure is always acting on a surface, both for stationary and moving fluid
However, shear stress requires (1) Relative fluid motion, and (2) Fluid viscosity
Shear stress at a surface (wall) occurs because of the boundary layer.
The concept of the boundary layer was created by Ludwig Prandtl (1904).
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Slide 4 of 39
Airfoil Terminology We will consider airfoils as 2D sections through a wing,
Chord, (c): Length of a straight line connecting the leading edge and the trailing edge Mean Camber Line: Line passing through points midway between upper and lower surfaces
Camber: Maximum perpendicular distance between chord line and mean camber line.
Thickness (t): Maximum thickness of the airfoil
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Slide 5 of 39
Lift and Drag Forces on an Airfoil Integrating the forces resulting from fluid pressure and shear stress over the entire surface of an airfoil will lead to a Resultant Aerodynamic Force, R, and a Moment, M.
is defined as the
angle-of-attack
Resultant Aerodynamic Force, R, acts through Aerodynamic Centre which is approximately at the chord point
Lift, L, is defined as the component of R perpendicular to U and Drag, D, is defined as the component of R parallel to U, where U is the freestream velocity (located far away from the aircraft)
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Slide 6 of 39
Aerodynamic Center The pressure distribution over the airfoil changes with angle of attack,
Therefore the resultant lift and drag forces change in both magnitude and direction with
As a result, the pitching moment changes
A point can be found where the pitching moment does not change with
This point is called the Aerodynamic Center of the airfoil
For many airfoils the Aerodynamic Center is located near the quarter chord point
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Slide 7 of 39
How is Lift generated? Even today, scientists and engineers still debate the best explanation for how lift is generated.
1) Pressure acts mainly in the lift direction and shear stress acts mainly in the drag direction. It is reasonable to conclude that lift is mainly due to the pressure difference between the top and bottom surfaces of an airfoil.
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Slide 8 of 39
But WHY is the pressure lower on top and higher on bottom of an airfoil?
Lift cannot exist without viscosity!
Lift is zero in potential flow (=0)
2) Viscosity is responsible for creating a net Circulation, , around an airfoil. Lift is then given by the KuttaJoukowski theorem: L V= The KuttaJoukowski theorem also applies to rotating objects:
Magnus effect (e.g. deflection of spinning ball from flight path)
Kutta condition can used in Potential flow to create Circulation and hence generate airfoil lift
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Slide 9 of 39
Kutta condition As shown below, a trailing edge can have a finite angle or it can be cusped
1) For finite angle: the only way for V1 and V2 to be parallel to the top and bottom surfaces as shown in the figure is for the magnitude of each velocity to be zero.
This means that trailing edge must be a stagnation point, since 1 2 0V V= =
2) For cusped trailing edge for V1 and V2 are in the same direction, so they can be finite. However, the pressure must be the same at each region, and applying Bernoulli equation to upper and lower surface means that V1 = V2. So velocities are finite and equal in magnitude and direction.
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Slide 10 of 39
The role of viscosity There is a singularity at the trailing edge.
If the trailing edge is infinitely sharp then without any viscosity there would be infinite velocity gradient at the trailing edge.
Fluid viscosity prevents this from happening which creates Circulation around the airfoil which is responsible for the lift.
TALAY, T. A. Introduction to aerodynamics of flight. NASA SP-367, 1975
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Slide 11 of 39
There would not be any lift without viscosity Viscosity is responsible for ensuring satisfaction of the Kutta condition
Lift, Drag and Moment Coefficients Nondimensional coefficients allow characterization independent of body size and flow velocity.
Dynamic pressure is appropriate quantity, since it is the maximum pressure available from flow.
212q U =
Need to use a force for nondimensionalization, i.e. need to use an area (since F P A= ) For a wing, use the total surface area, S, and use chord, c, for length in Pitching Moment
Drag Coefficient 212
DDCU S
=
Lift Coefficient 212
LLCU S
=
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Slide 12 of 39
Pitching Moment Coefficient 212
MMCU Sc
=
We can use Dimensional Analysis to derive the following dimensionless coefficient:
1 ( , ,Re) LC f M=
2 ( , ,Re) DC f M=
3 ( , ,Re) M f M=
Where is angle of attack, M
is freestream Mach number and Re is Reynolds number
The physical complexity of flow field around an airfoil is contained in these coefficients
The key for predicting performance is to determine how these coefficients vary with , ,ReM
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Slide 13 of 39
Compressibility: Freestream Mach number Compressibility is a property of a fluid, independent of any motion.
In a compressible flow there is a significant fractional change in density, /d that occurs as a result of pressure, p, fluctuations.
Important parameter is the freestream Mach number, /M U a
= where a
is speed of sound
Liquid flows, and Gas flows with 0.3M
< can both be approximated as incompressible,
For example, for an air flow at sea level with freestream V = 20 ms-1
then the fractional change in density is really small ( )max
/ 0.1%
and the flow can be assumed to be incompressible.
We will consider Compressible Flow in more detail in AERO2358
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Slide 14 of 39
Reynolds number, Re Reynolds number is a measure of the ratio of inertial forces to viscous forces,
inertial forcesReviscous forces
=
Reynolds number is calculated using a length-scale, L, and the freestream values of , ,U
Re U L U L
= =
Exact similitude will only exist between a wind tunnel model and a real aircraft at same Re
Matching Re is very difficult and very expensive but considered necessary for accurate test results
Examples: (a) Match model size, L, leads to extraordinarily large wind tunnels (b) Pressurized wind tunnel to get larger
(c) Cryogenic wind tunnel to get smaller
(d) Fluid other than air, such as Freon, to get larger
and smaller
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Slide 15 of 39
Airfoil as a 2D section through a real (3D) wing We will consider airfoils as 2D sections through a wing.
Use lower case nomenclature to
define sectional properties of an airfoil
, ,l d mc c c
From Anderson, Introduction to Flight
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Slide 16 of 39
Potential flow method Thin Airfoil Theory Developed by German-American mathematician Max Munk and refined by others in 1920s.
Predicts the Lift versus Angle-of-Attack for an Airfoil in incompressible inviscid uniform 2D flow
The airfoil is assumed to have zero thickness but it can have can have camber (and flaps too).
Potential Flow: model airfoil as vortex sheet, i.e. distribution of infinite array of vortex elements
Fourier series solution obtained by determination of the strength of the vortex element distribution to ensure zero flow normal to airfoil and to ensure the Kutta condition at the trailing edge.
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Slide 17 of 39
Predictions from Thin Airfoil Theory (TAT) Example: NACA2412 airfoil
( )0 1
1 2
2 ( )1( )4 4
l
m l
c B B
xc x c B B
c
pi pi
pi
= +
= + +
, where 0B , 1B and 2B depend on airfoil geometry
Lift curve slope: 2 ldcd
pi
Aerodynamic Center: /414 ( ), i.e. for cmc f x c =
These are general results from Thin Airfoil Theory (independent of airfoil geometry)
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Slide 18 of 39
Comparison of Thin Airfoil Theory with 2D Airfoil Data (wind tunnel tests)
Ira H Abbott, Albert E Von Doenhoff, and Louis Stivers, Jr.
SUMMARY OF AIRFOIL DATA
NACA Report No. 824 (1945)
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Slide 19 of 39
Further comparisons between theory and experiment for lift coefficient and moment coefficient
for 2D NACA2412 airfoil wind tunnel tests
From Anderson, Fundamentals of Aerodynamics
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Slide 20 of 39
Lift coefficient versus angle-of-attack for a real physical 2D airfoil
It is the Boundary Layer separation that causes the stall of the airfoil
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Slide 21 of 39
From Anderson, Introduction to Flight
Cambered airfoils have finite lift at zero angle of attack
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Slide 22 of 39
Trailing Edge Flap
From Anderson, Introduction to Flight
Downward flap deflection leads to increase in effective camber. Lift Coefficient increase at fixed
Flap on a Conventional Horizontal Tailplane is called an Elevator
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Slide 23 of 39
Leading Edge (LE) Devices for high lift
From Anderson, Introduction to Flight
Devices delay boundary layer separation on upper surface by reducing adverse pressure gradient Leads to larger angle-of-attack for stall and consequently a larger
maxlc
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Slide 24 of 39
Combination of LE slats (or flaps) with TE flaps
From Anderson, Introduction to Flight
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Slide 25 of 39
Streamline pattern with LE and multi-element TE flaps
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Slide 26 of 39
Typical application Why is highest possible CL required for landing?
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Slide 27 of 39
Real 3D Wings The lift curve slope LdC
d of a finite aspect ratio 3D Wing is
always less than LdCd
of a 2D Wing with same airfoil section.
The flow rolls up at the tips to produce Trailing Vortices for finite aspect ratio wings
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Slide 28 of 39
Downwash causes induced drag The trailing vortices will induce a downwards velocity at the wing centreline, called downwash.
There will also be downwash at other parts of the wing but less than at the centreline.
Effect of downwash is to reduce the local angle of incidence.
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Slide 29 of 39
Induced Drag The Lift for an airfoil section will act normal to the local flow direction but this is deflected down from the freestream direction by the downwash
Overall lift and drag still defined relative to the freestream flow direction,
Wing cos iL L L=
Wing sini i iD D L L = =
Downwash introduces an additional drag which is called induced drag or lift dependent drag or vortex drag
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Slide 30 of 39
Elliptic Lift Distribution The most efficient lift distribution (producing the least induced drag) is an elliptical lift distribution.
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Slide 31 of 39
Properties of the Elliptic Lift Distribution (1) It can be shown that the downwash is constant over the entire span of
an elliptic lift distribution, 02
wb
=
(2) The induced angle of attack for an elliptic lift distribution is given by, 0
2iw
U bU
= =
which is also constant over the entire span
(3) The total lift force, L, can be determined from the circulation distribution
the Kutta-Joukowski theorem (slide 13), i.e. ( ) ( )L y V y =
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Slide 32 of 39
Hence the TOTAL lift is given by 2/2
0 2/241
b
byL U dy
b
=
Using the transformation ( / 2)cosy b =
then 20 00 sin2 4b bL U d U
pi pi
= =
Hence ( )212
0
4 24 L LU SC U SCLU b U b b
pi pi pi
= = =
So the induced angle of attack for an elliptic lift distribution is given by
022L
iSC
bU b
pi
= =
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Slide 33 of 39
An important geometric property of a finite wing is the Aspect Ratio
which may be defined as the ratio of width to chord of the wing
However, for most wings, the chord is not constant, but varies along the wing, so the Aspect Ratio is better defined as:
2
RbAS
= where S is the wing area
Hence the induced angle of attack for an elliptic lift distribution is given by,
Li
R
CA
pi
=
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Slide 34 of 39
(4) The elliptic spanwise lift distribution has minimum induced drag. We know from Slide 25 that sin Li i i
R
CD L L LA
pi
= = ,
It follows that 2
i L L
R R
D C CLq S q S A Api pi
= = i.e. 2
iL
DR
CCApi
= ,
The Total Drag is 02L
D DR
CC CApi
= + , where
0DC is the zero lift constant component.
(5) The Lift curve slope of 3D wing is given by
1
l
L
l
R
dcdC d
dcddA
pi
=
+
,
where ldcd
is the lift curve slope of the 2D airfoil section
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Slide 35 of 39
Wings with non-elliptical lift distribution
0
0
2
1
iL
DR
l
L
l
R
CCA
dcdC d
d
e
e
cdd
A
pi
pi
=
=
+
where 0e is known as the Spanwise Efficiency Factor
and 00.8 0.95e< <
Note that for 0
, 0 and lLR DdcdCA C
d d
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Slide 36 of 39
Requirements for Trimmed Flight
Consider a tail-less wing-body combination
The vertical forces acting on the wing body are the lift, LWB and the weight, mg.
Unless these forces are coincident the wing body will not be in equilibrium.
Additional Vertical Force required for Trimmed Flight
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Slide 37 of 39
Requirements for Longitudinal Static Stability For trim, = 0
MC , and this is shown in plot
with values A = and = AL LC C
If the incidence is increased so that
=B
and =B
L LC C
then the pitching moment coefficient
will change to the value < 0BM
C .
This is a nose down pitching moment
which acts to reduce the incidence.
Characteristics of a Wing alone and a Complete Aircraft with a fixed Elevator
The reverse happens if the incidence is reduced,
i.e. the pitching moment becomes positive (i.e. nose up) and the incidence will tend to increase.
0M LC C < is required for Longitudinal Static Stability
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Slide 38 of 39
Configurations for Trimmed Flight
Main consideration in AERO2358: Conventional Aircraft with Tailplane