Lecture Notes Aerodynamics Introductory

7/22/2019 Lecture Notes Aerodynamics Introductory

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1 Dr. Abdullah M. Al-Garni AE Dept., KFUPM

Aerodynamics: Introduction• Aerodynamics deals with the motion of objects in air. These objects

can be airplanes, missiles or road vehicles.

• The Table below summarizes the aspects of vehicle performance

directly influenced by aerodynamic design.

Splash and Spray

Dirt AccumulationVisibility

Wind Noise

Heating, Ventilation and Air ConditioningComfort

Condenser

Brakes

Transmission

Engine

Cooling

Crosswind Sensitivity

Response to Flow Unsteadiness

Directional Stability

Stability

Acceleration

Maximum Speed

Emissions

Fuel Economy

Performance




Aerodynamics: Aerodynamic Forces

• When a body moves in the air, a

pressure and shear (friction)

stresses are produced at every

point of the body.

• The pressure, p, acts normal to

the surface and the shear, τ , acts

tangential to the surface of the

body.

• The sum of the pressure and shear

forces gives the resultant force, R .

• The aerodynamic forces are mainly

due to pressure and shear stress

distribution over the body surface.

τ

p

V ∞ Airfoil





• The resultant force, R , can be resolved into twocomponents along the wind (freestream) axes:

lift = L = component normal to V ∞

drag = D = component along V ∞

or along the body axes axis:

normal force = N = component normal to the airfoil chord

axial force = A = component along the body chord

• The point at which the resultant force acts is called the

center of pressure.

• It is convenient sometimes to specify the aerodynamic

center which is defined as the point at which the

aerodynamic moment, M , is independent of the angle of

attack, α.

N R

V ∞ A

L

D

α

chord line M





• In aerodynamics, we usually deal with aerodynamic forces andmoments coefficients more than forces and moments.

• The freestream dynamic pressure, q∞,

ρ∞ is the freestream density and V ∞ is the freestream velocity.

Pressure Coefficient: ; P ∞ = the freestream pressure

Lift Coefficient:

; S = the reference area

Drag Coefficient:

Moment Coefficient: ; l = the characteristic length.

21

2q V ρ

∞ ∞ ∞=

P

P C

q∞

∞

−=

LC q S

∞

=

DC q S ∞

=

M C q Sl

∞

=





From dimensional analysis, the above coefficients depend on some parameters:

• Mach number , M = V ∞ /a where a is the speed of sound.

• Reynolds number , Re = ρV ∞ l / μ where ρ is the air density and μ is the dynamic

viscosity of the air.

• Angle of attack , α .

• In many practical problems, the lift, drag and moment coefficients are identical

for geometrically similar bodies at the same Mach, Reynolds number and angle ofattack.

(C L)1 = (C L)2

(C D)1 = (C D)2

(C M )1 = (C M )2

1 2




Aerodynamics: Airfoil

• An airfoil is simply a section cut of a wing.

• It is often called infinite wing.

• The flow characteristics around an airfoil are significantly different fromthose around a wing.

• The flow around the airfoil is two dimensional.

lower flow velocity

higher pressure

V ∞ P ∞

higher flow velocity

lower pressure




Aerodynamics: Airfoil

• The pressure and velocity fieldsaround the airfoil are related via

the Bernoulli’s equation

• The pressure distribution over

Joukowski airfoil at α = 10º.

• The pressure coefficient isnegative (means lower than the

freestream pressure, P ∞) over the

top surface and positive (higher

than the freestream pressure, P ∞)

on the bottom surface of the airfoil.

• The net imbalance of pressure

distribution produces the lift.

lower flow velocity

higher pressure

V ∞ P ∞

higher flow velocitylower pressure

2 21 12 2

P V P V ρ ρ ∞ ∞

+ = +

0 0.2 0.4 0.6 0.8 1

-5

-4

-3

-2

-1

0

1

C p

x/c




Aerodynamics: Wings

• Often called finite wing

• The flow around a wing is three

dimensional; there is a flow in the

spanwise direction.

• The mechanism for generating lift is the

same as that for the airfoil, a higher

pressure on the bottom surface and a

lower pressure over the top surface.

• As consequence of the pressure

imbalance between the lower and upper

surface of the wing, the flow near the

wing tips tends to curl around the tips; the

flow is forced from the higher pressureregion just underneath the wing tips to

the lower pressure region on the top of

the wing.

Flow from higher pressure

region (lower surface) tolower pressure region (upper

surface)

•This causes the flow underneath thewing to move along the spanwise

direction from the wing root to the tip

and the flow on top of the wing to move

from the wing tip to the root.




Aerodynamics: Wings

• This flow produced a trailing vortex at both wing tips that trails

downstream of the wing.

• For large airplanes such as the

Boeing 747, these vortices arepowerful enough to cause light

airplanes flying closely behind to go

out of control.

• Accidents due to these vorticeshave occurred and that is one of the

reasons for large spacing between

aircraft during landing and take-off at

airports.

• The vortices draw the air behind the

wind thus inducing a downwash

(downward flow) in the neighborhood

of the wing.

Top view Cross section view




Aerodynamics: Flow Characteristics for Wings

• This downwash results in an increase ofdrag.

• The additional drag is called induced drag,

Di , and is related to the lift by

• The downwash also affects the angle of

attack.The angle of attack actually seen by the

wing is the angle between the chord line

and the local relative wind defined as the

effective angle of attack , α eff .

• The “geometric angle of attack” α and the

“aerodynamic angles of attack” α eff and α i is

given by

Di

V ∞

L

α

αi

αeff

αi

wV ∞

Local relative

wind

Chord linesini i D L α =

eff i

α α α = −




Aerodynamics: Lift on Airfoil

• At small angles of attack thelift coefficient varies linearly

with the angle of attack for

both symmetric and cambered

airfoils.

• The mathematical analysis

shows that for a symmetric

airfoil

•for a cambered airfoil :

•The slopes of the lift

coefficient for symmetric and

cambered airfoils are the

same.

Cambered airfoil

Symmetric airfoil at small α

Symmetric airfoil at high α

α L=0 =0

α L=0 < 0

α

C l

2l C πα =

02 ( )l LC π α α =

= −

/ 2o l dC d η α π = =

l o

dC

d η

α =




Aerodynamics: Lift on Airfoil

Cambered airfoil

Symmetric airfoil at small α

Symmetric airfoil at high α

α L=0 =0

α L=0 < 0

α

C l

l o

dC

d η

α =

• As the angle of attack

increases, an adverse pressure

gradient starts to develop over

the top surface of the airfoilwhich will cause the boundary

layer to separate.

• At a certain angle of attack, this

adverse pressure becomesstrong enough to cause flow

separation over the top surface

of the airfoil.

• Once the flow separates the liftcoefficient drop drastically and as

a consequence stall occurs as

shown in Figure 9.




Aerodynamics: Lift on Wing

• The lift curve for a wing has smaller slope than the corresponding lift curve foran airfoil with the same airfoil cross section.

• The relationship between the two slopes is given by

where η is the slope of a wing, ηo is the slope of the airfoil, is the aspect ratio,

τ is a correction factor.

• The aspect ration is defined as where b is the span and S is the

area of the wing.

1 (1 )

L o

o

dC d

η η

η α τ

π

= =

+ +ℜ

2 /b S ℜ =




Aerodynamics: Lift and Circulation

• The lift per unit span of an airfoil can be related to the intensity of thecirculatory flow or circulation, Γ, via Kutta-Joukowski Theorem

where the L′ is the lift per unit span of the wing.

• This relation shows that the lift per unit span is directly proportional to

circulation.

• It is a pivotal relation in ideal incompressible flow theory often called

potential flow theory.

•Thus, a major propel of the potential flow theory is to calculate circulation.

' L V ρ ∞ ∞

= Γ





• Example of this relation:

flow over a circular cyl inder

• The flow around non-lifting

circular cylinder is symmetric

• Hence one would expect that

the pressure distribution over the

top and bottom surfaces of the

cylinder is also symmetric.

•This results in zero lift for the

cylinder.

•However, if the cylinder rotatesabout its axis, then the flow field

is not symmetric any more.

Flow over Non-lifting circular cylinder

Flow over lifting circular cylinder

L = 0

L > 0





• Why do we have a lift when the cylinderrotates?.

• When the cylinder rotates, this will

increase the flow velocity over the top

surface and decrease it on the bottomof the cylinder.

• As a result, the pressure on the top

surface decreases and the pressure on

the bottom surface increases(Bernoulli’s equation).

•This net imbalance of pressure will

produce a finite lift as sketched in

Figure. This is often called Magnus

effect.

Flow over lifting circular cylinder

L > 0

High speed flow

Low pressure

Low speed flow

High Pressure

V ∞

ω

L′

2 21 1

2 2

P V P V ρ ρ ∞ ∞

+ = +





• Another Example of this relation:

flow over a airfoi l with a

leading-edge rotating cylinder

Leading-edge cylinder is off [α = 0]a) U c /U = 0

b) U c /U = 1

L > 0

L = 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 5 10 15 20 25 30 35 40

α

o

C L

Uc/U=0

Uc/U=1

Uc/U=2

Uc/U=3

Uc/U=4

Leading-edge cylinder rotates




Aerodynamics: Lift and Circulationa) U c /U = 0

b) U c /U = 1

α = 20

e) U c /U = 4




δ

C L

Wing with a trailing-edge flap

Wing without flap and slat

Wing with a leading-edge slat

α

d i n

c r e a s e

s

Aerodynamics: High Lift Devices

• The lifting properties of a givenairfoil can be enhanced by using high

lift devices as shown in the Figure 13.

• The most common of these devices

is the simple flap at the trailing edgeof the wing.

• When the flap is deflected

downward, the camber of the airfoil is

increased.

• This increase is associated with a

dramatic increase in the maximum lift

coefficient, C L,max and a shift of the

zero-lift angle of attack to a morenegative value for the wing.




Aerodynamics: High Lift Devices

• In some airplanes, the flap is designednot only to deflect downward but also to

translate rearward which increases the

wing area and hence increase the lift.

• The flap can increase the maximum liftcoefficient by about 200%.

• High lift devices can also be applied to

the leading edge of the wing with the most

common is the leading-edge slat.

• The leading edge slat can alter the

pressure distribution over the wing, reduce

the pressure on the top and increase the

pressure on the bottom surface. As aresult, a more lift is generated on the wing.

•Another advantage of the leading-edge

slat is the delay of flow separation over

δ

C L

Wing with a trailing-edge flap

Wing without flap and slat

Wing with a leading-edge slat

α

d i n

c r e a s e

s

the top surface of the wing to higherangles of attack and consequently delays

stall of the wing. In modern aircraft a

combination of leading-edge slat and

trailing-flaps is common.




Aerodynamics: Drag

• The drag is an important subject in aerodynamics.

•A reduction in drag can lead to a reduction in fuel consumption and better

performance for a vehicle.

•The drag coefficient varies from one object to another depending on the

particular geometry of that object.

•For streamlined body such as wing and airfoil, the drag coefficient is lowcompared to bluff body such as circular cylinder, sphere or road vehicle.




Aerodynamics: Drag

C D

= 0.017Boeing 747

C D

= 0.037Piper PA-16

Clipper

C D

= 0.4-0.5Pickup

truck

C D

= 1.6Equilateral

triangle

C D = 1.7

Half

Cylinder

C D

= 1.2Half

Cylinder

C D

= 0.12Streamlined

body

C D

= 1.2 at Re =

105

C D

= 0.6 at Re =

107

Circular

Cylinder

C D

= 2.0 Normal

Plate

V ∞

d

V ∞

d

V ∞

d

V ∞

d

V ∞

d

V ∞ d

X

Z




Aerodynamics: Drag for Airfoil vs. Wing

• It is important to note that there is a difference between the drag of an airfoil andthat of a wing.

• The drag acting on an airfoil section is the sum of the skin friction drag , Df , and

the pressure drag , D p, which is due to flow separation. That is,

The sum of the skin friction drag and the pressure drag is called profile drag .

• On the other hand, the total drag of a subsonic finite wing in a real case is the

sum of the induced drag, Di , and the profile drag,

where the subscript D represents the drag of the wing and the subscript d

represent the drag of the airfoil.

f p

d

DC

q S ∞

+=

i

D d

D

C C q S ∞

= +




Aerodynamics: Drag for Airfoil vs. Wing

• Using the lifting line theory it can be shown that for ageneral wing

where is the induced drag coefficient and e is the

span efficiency factor . For elliptical wing, e = 1 and forother platforms, e < 1.

• Therefore, the induced drag is minimum for an

elliptical platform.

• In the past, several aircraft have been designed with

elliptical wings.

• However, elliptical wings are more expensive to

manufacture than other simple platform such asrectangular wings. The rectangular wing is

considered far from optimum. A compromise between

the elliptical wing (manufacturing difficulty) and

rectangular wing (poor efficiency) is the tapered wing.

2

, L

D i

C C

eπ =

ℜ

Tapered wing

Rectangular wing

Elliptic wing




Aerodynamics: Laminar and Turbulent Flows

• The drag coefficient of a body depends on theflow around the body whether it is laminar or

turbulent.

• When the streamlines are smooth and regular and

a fluid element moves smoothly along a streamline

the flow is called laminar.

• On the other hand, when the streamlines break up

and a fluid element moves in a random, irregular,

and tortuous fashion the flow is called turbulent.

• Most of real flows are turbulent flows.

•In turbulent flow, the higher energy fluid elements

from the outer regions of the flow are pumped close

to the surface. Hence, the average flow velocity

near a solid surface is larger for a turbulent flow incomparison with laminar flow. Figure 15 shows the

velocity profile for laminar and turbulent boundary

layers.

Laminar flow

Turbulent flow




Aerodynamics: Laminar and Turbulent Flows

• In turbulent flow, the higher energy fluid elements

from the outer regions of the flow are pumped close

to the surface.

• Hence, the average flow velocity near a solid

surface is larger for a turbulent flow in comparisonwith laminar flow.

• Since the shear stress is proportional to the

velocity gradient along the y-direction

then the shear stress (friction) as well asaerodynamic heating at the wall surface is higher for

turbulent flow than laminar flow.

Turbulent

L a m

i n a r

y

u

/u yτ ∝ ∂ ∂




Aerodynamics: Streamlined vs. Bluff body

• Airfoils, flat plate and wings are considered to be

streamlined bodies. On the other hand, cylinder,

sphere, trucks are bluff bodies.

• The flow around streamlined and bluff bodies is

significantly different.

• The flow over streamlined body is usuallysmooth and the wake behind the body is small.

• The flow over bluff body, however, exhibits a

large wake downstream the body. This wake iscaused by separating flow from the body surface

with a low-energy recirculating flow inside the

wake as shown in the figure below.

Streamlined body- small wake

Bluff body- large wake




Aerodynamics: Streamlined vs. Bluff body

• The skin friction drag is due to the shear forces

acting on the body and the pressure drag is due

to flow separation from the body surface.

• Therefore, if the body is streamlined, the flow

separation is minimal and one would expect thatthe friction drag is much greater than the pressure

drag.

• Since skin friction drag is smaller for laminar

than for turbulent flow, laminar flow is desirablefor streamlined bodies.

•On the other hand, the pressure drag which is

due to flow separation is much greater for bluff

body than skin friction drag.

•In this case, the turbulent flow is desirable

because the pressure drag for turbulent flow is

smaller than for laminar flow.

p D

p f D D

Laminar f low is desirable

Turbulent f low is desirable




Bluff body:

Square Back (SB) Model

X

Y

X Z

Y Z

Model Side View

Model Top View

Cab Back

Wind Tunnel View




PIV Results

0 50 100 150 200 250

-100

-80

-60

-40

-20

0

20

40

60

80

100

x (mm)

y ( m m )

0 50 100 150 200 250

-100

-80

-60

-40

-20

0

20

40

60

80

100

x (mm)

y ( m m )

U = 30 m/s

Mean velocity and vorticity Fields Streamlines of the mean velocity field

Lecture Notes Aerodynamics Introductory

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