AERO2358 Review of Key Concepts 2015

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

[email protected]

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Cambered airfoils have finite lift at zero angle of attack

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Trailing Edge Flap


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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Leading Edge (LE) Devices for high lift


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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Combination of LE slats (or flaps) with TE flaps


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Streamline pattern with LE and multi-element TE flaps

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Typical application Why is highest possible CL required for landing?

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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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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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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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Elliptic Lift Distribution The most efficient lift distribution (producing the least induced drag) is an elliptical lift distribution.

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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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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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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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(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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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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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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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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Configurations for Trimmed Flight

Main consideration in AERO2358: Conventional Aircraft with Tailplane

Documents

AERO2358 Review of Key Concepts 2015