Pengenalan Aerodinamika

AERODINAMIKA TEKNIK

Textbook(s) and/or other required material

Textbook: J. D. Anderson, Fundamentals of Aerodynamics, Wiley, 1992

References: – Ira H. Abbott and Albert E. Von Doenhoff, Theory of Wing Sections, Dover, 1959. – J. J. Bertin and M. L. Smith, Aerodynamics for Engineers, Prentice-Hall, 1998. – Arnold M. Kuethe and Chuen-Yen Chow, Foundations of Aerodynamics: Bases of

Aerodynamic Design, 5th edn., Wiley, 1998. – Barnes Warnock McCormick, Aerodynamics, Aeronautics and Flight Mechanics, Wiley,

1995.

• Course objectives • Course Objectives: It is the instructor's intention to...

– teach students the fundamentals of potential flow. – teach students the fundamentals of wing theory in both 2D and 3D. – teach students some of the fundamentals of propeller theory. – convey to the students the notion that mathematics is the only language suitable to describe the physics of

aerodynamics. – show students the direct application and physical significance of the formalism of calculus learned during the first

years of their undergraduate education. – convey to the students a knowledge of the limits of analytical solutions and the necessity, usefulness and accuracy of

computational methods. – provide an opportunity for the students to improve their team-work and report-writing skills.

• Course Outcomes: Students must be able to... – use superposition of the solutions to Laplace's equation for some simple, fundamental flows to model more

complicated ones. – explain the concept of circulation and its relationship to the lift on an airfoil. – use a vortex sheet and vortex filament to model a 2D airfoil and wings of finite span. – explain the concept of lift-induced drag.

Contribution of course to meeting the professional component • This course contributes primarily to the students' knowledge of engineering topics, but does

not provide design experience. • The following statement indicates which of the following considerations are included in this

course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.

• Focuses primarily on the theory of wings and the lift and drag associated with airflow over those structures. It is primarily a technical course and does not cover any of supplemental topics (economics, environmental, etc).

Silabus1. Fundamental principles

– Introduction– Fundamental principles and equation

2. Inviscid, incompressible flow– Fundamental of inviscid, incompresible flow– Incompressible flow over airfoils– Incompressible flow over finite wings– 3-D incompressible flow

3. Inviscid, compressible flow– Preliminary aspects– Normal shock wave and related topic– Oblique shock and expansion waves– Compressible flow through nozzles, diffuses and wind tunnel– Subsonic compressible flow over air foil: linear theory4. Viscous flow

Introduction to fundamental principles and equations of viscous flowSome special casesIntroduction to boundary layers

Fundamental principlesIntroduction

Aerodynamics ?

The term of “aerodynamics” is generally used for problem arising from flight and other topics involving the flow of air.

Ludwig Prandtl, 1949

Aerodynamics: the dynamics of gases, especially of atmosphere interaction with moving objects.

The American Heritage Dictionary of the English Language, 1969


Aerodynamics , Historical examples:

• August 8, 1588: Spanish armada vs English fleet.• 1687: Principia by Isaac Newton.• Jean Le Rond d’Alembert (1777) and Leonhard Euler (1781):

Invconsistency of Newton’s model.• 1901: Wilbur and Orville Wright• 1939-1945: World War II• 1951: H. Julian Allen , blunt reentry body.


Classification• Hydrodynamics : flow of liquid• Gas dynamics : flow of gases• Aerodynamics : flow of air

Practical objectives:• The prediction of forces and moments on, and heat transfer

to, bodies moving through a fluid (usually air) : external aerodynamics

• Determine of flow moving internally throught duct. We wish to calculate and measure the flow properties inside rocket and air-breathing jet engines and to calculate the engine thrust: internal aerodynamics.




Fundamental aerodynamic variables1. Pressure: normal force per unit area exerted on a surface due to the time

rate of change of momentum of the gas molecules impacting on that surface.

Consider point B in volume of fluid, the pressure at point B in the fluid is defined as

2. Density

3. Temperature

dAdFp lim 0dA

dvdmlim 0dv

kTKE23

KE: mean kinetic energyk : Bolttzman constant


Fluid element

Velocity

Stream line

velocity


Aerodynamics forces and moments2 basic sources:1. Pressure distribution over the body surface, p2. Shear stress distribution over the body surface, τp act normal to the surface, and τ tangenttial to the surface.

The net effect of the p and τ distribution integrated over the complete body surface is resultan aerodynamic force R and moment M on the body. p

s

RM

V


L= lift= component of R perpendicular to V∞ (free stream)

D=drag= component of R parallel to V∞ (free stream)

Or N=normal force=component of R perpendicular to cA=axial force=component of R parallel to c

L= N cos α – A sin αD= N sin α + A cos α

V

N

AD

L R

c

(1.1)(1.2)


cossin

sincos'

'

uuuuu

uuuuu

dsdspdA

dsdspdN

cossin

sincos'

'

lllll

lllll

dsdspdA

dsdspdN

l

TE

LE llu

TE

LE uu

l

TE

LE llu

TE

LE uu

dspdspA

dspdspN

cossincossin

sincossincos

'

'

s us

usp

A

ls lsp

V

Leading edge (LE)

Trailing edge (TE)

y

x

(1.3)

(1.4)

(1.5)

(1.6)

(1.7)

(1.8)


lllllll

uuuuuuu

ydspxdspdM

ydspxdspdM

cossinsincos

cossinsincos'

'

u

TE

LE uuuuLE dsypxpM cossinsincos'

l

TE

LE llll ydsypxp cossinsincos

(1.9)

(1.10)

(1.11)


• Free stream dynamic pressure

2

21

Vq

lM

A

N

D

L

SqMC

SqAC

SqNC

SqDC

SqLC

Lift coefficient

Drag coefficient

Normal force coefficient

Axial force coefficient

Moment coefficient

2

'''

;;cq

Mccq

Dccq

Lc mdl

2 dimensional bodies, force and moment perunit span, reference area S=c(1)=c

Pressure coefficient:

Skin friction coefficient:

qppC p

q

c f

lcSdsdydsdx ;sin;cos

c c

lfufl

lpu

upa

c c llf

uufuplpn

dxccdxdxdyC

dxdyC

cc

dxdxdyc

dxdycdxCC

cc

0 0 ,,,,

0 0 ,,,,

1

1

Substituting above equation into eqs. (1.7), (1.8) and (1.11), dividing by and S, we obtain

c c llf

uuflpupm xdx

dxdyc

dxdycxdxcc

cc

LE 0 0 ,,,,2

1

c c

llfl

lpuufu

up dxycdxdyCdxyc

dxdyC

c 0 0 ,,,,2

1

cossinsincos

and

anl

cccccc

y

x

c

ds

ds

dxdy

q


'

'

''

NM

NM

LEcp

cpLE

''

1cos0sin

NL

'

'

LM LE

cp

Center of Pressure

''4/

''

4LMLcM cpcLE

cpx

'N

'A'LEM

'A'LEM

4c

'A

'

4cM

cpx

'A

'N 'N'N

Center for pressure for an airfoil

R at LE R at quarter –chord point R at center of pressure

Dimensional analysisBuckingham pi theorem

acVfR ,,,, Dimensional analysis is based on the obvious fact that in equation dealing with the real physical world, each term must have the same dimensions.

1

K: number of fundamental dimension required to describe the physical variables(mass, length, and time , hence K=3)

0,.....,, 211 Npppf 0,......,, 212 KNf

NKKN

KK

KK

ppppf

ppppfppppf

,,......,............................................

,,......,,,......,

215

22142

12131

0,,,,, acVRg K=3; m = dimension of mass, l = dimension of length, and t = dimension of time

1

11

1

3

2

lta

tml

lcltV

ml

mltR

N=6

N-K=6-3=3

0,, 3212 f

acVfcVfRcVf

,,,,,,,,,

53

42

31

2131

1

mltlltml

RcVebd

ebd m : d+1=0l : -3d+b+e+1=0t : -b-2=0d=-1, b=-2, and e=-2

221

2211

cVR

cVR

RC

SqR

SV

R

cV

R

222

1

21

21

jih

jih

tmllltml

cV1113

2

2

m : 1+j=0l : -3+h+i-j=0t : -h-j=0j=-1, h=1, and i=1

cV2 Free stream Reynolds number

srk

srk

ltlmllt

acV131

3

3

m : k=0l : 1-3k+r+s=0t : -1-s=0k=0, s=-1, and r=0

aV

3 Free stream Mach number

0Re,,

0,,

21

2

22

MCf

aVcV

SV

Rf

R

MfCMfCMfCMfC

M

D

L

R

Re,Re,Re,Re,

9

8

7

6

,Re,,Re,,Re,,Re,

9

8

7

6

MfCMfCMfCMfC

M

D

L

R


• Flow Similarity• 2 different flow fields over2 different bodies are dynamically similar if:1. The streamline pattern are geometrically similar2. The distribution of V/V∞, p/p∞, T/T∞ , etc throught the flow field are the same

when plotted against common nondimensional coordinates.3. The force coefficients are the same

The flow will be dynamically similar if:1. The bodies and any other solid boundaries are geometrically similar for both flows.2. The similarity parameters are the same for both flow.

Non-Dimensional Number

Reynolds Number, Re

Mach Number, M

Froude Number, Fr

Prandtl Number, Pr

Ratio of Specific Heats, k

Roughness Ratio

Pressure Coefficient, Cp

Drag Coefficient, CD

Lift Coefficient, CL

Skin Friction, cf

Definition Significance

All branches of fluid dynamics

Compressible flow

Free surface flow

Heat transfer

Compressible flow

Turbulent flow

Aerodynamics,Hydrodynamics



Boundary layer flow

Application


y

x

z

p1,h1

p2,h2

h

dxdzdydydpp

pdxdz dxdydzg

dxdy

dz

1

2

dxdzdydydppdxdzp

dxdydzdydp

Net pressure force

Gravity force

gdxdydz

Fluid element is stationary (in equilibrium)

dygdp

dxdydzgdxdydzdydp

0 hghhgpp

dygdph

h

p

p

1212

2

1

2

1

= constant

cghpghpghp

1122

Fluid Static


y

x

z

1p

2p

1h

2h l

dy

Solid or hollow body

Element of fluid

1

1

2

2

1

2

1

1

2

1

1

12

12

h

h

p

p

h

h

h

h

gdylF

gdygdydppp

lppF

Buoyancy force on body = weight of fluid displaced by body

Buoyancy Force


• Continuum versus Free Types of Flow• Molecule Flow• Inviscid versus Viscous Flow• Incompressible versus Compressible Flow• Mach Number Regimes• Subsonic if M<1• Sonic if M=1• Supersonic if M>1

Types of Flow

Low Chamber -Low Drag-High Speed-Thin Wing Section-Good For Racing aircraft, Fighters and Interceptor Planes.

Deep Chamber-High Lift-Low Speed-Thick Wing Section-Good For Transport, Freighters and Bomber Planes.

Deep Chamber-High Lift-Low Speed-Thin Wing Section-Good For Transport, Freighter and Bomber Planes.

Low Lift-High Drag-Reflex Trailing Edge Wing Section.

Very Little Movement Of Center Pressure. Good Stability.

Symmetrical (Cambered Top and Bottom) Wing Section-Similar To Above.

GA(W)-1 Airfoil-Thicker For Better Structure and Lower Weight-Good Stall Characterististics- Chamber Is Maintained Farther Rearward Which Increases Lifting Capability Over

More Of The Airfoil and Decreases Drag.

Documents

Pengenalan Aerodinamika