CAIRO UNIVERSITY

FACULTY OF ENGINEERING

AEROSPACE DEPARTMENT

THIRD YEAR STUDENTS

FIRST TERM

Course Title: AERODYNAMICS (A)

Course Code: AER 301 A

PROF. Dr. MOHAMED MADBOULI ABDELRAHMAN

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Aerodynamics is an engineering science

concerned with the

interaction between moving

bodies and the air or the

atmosphere.

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10/14/2011 3

COURSE OBJECTIVES

External Aerodynamics

External Aerodynamics

Prediction of forces and moments on bodies moving through air

Internal Aerodynamics

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Determination of air properties moving

internally through ducts or blades.

(jet engines)

Aerodynamic applications include:

General aviation (commercial, cargo, and business

aircraft);

V/STOL vehicles (helicopters, some military aircraft, tilt

rotors);

Lighter-than-air vehicles (airships, balloons, aerostats);

Aerodynamic decelerators (parachutes, thrust reversal

devices);

Road vehicles (passenger and racing cars, commercial

vehicles, high speed trains);

Spacecraft, missiles and rockets, low- to high-speed flight

(micro air vehicles to hypersonic wave riders), high altitude

flight, human powered flight, unmanned flight, gliders, energy

conversion systems (wind and gas turbines);

Propulsion systems (propellers, jet engines, gas

turbines). 5

is that science concerned with the

knowledge and understanding of

the aerodynamic loading

(forces and moments)

on the airplane components

(wing, fuselage, vertical and horizontal

tail)

and thus on the whole airplane during

its motion through the earth’s

atmosphere.

Airplane aerodynamics

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Airplane Parts Definitions

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Airplane Aerodynamics

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Prediction of forces and moments on an airplane moving through air

The aerodynamic forces and moments are

L lift force

D drag force

S Side force

MP Pitching moment

MY Yawing moment

MR Rolling moment

These aerodynamic forces and moments are due to Pressure distribution Shear stress distribution

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Forces on an Airplane

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11

Axis of rotation of an Airplane

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Moments on an Airplane

The line arrows represent the

system used in aerodynamics

studies

Z-axis

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The systems of force and moment components

The broad arrows

represent forces used in

aerodynamic studies

The line arrows represent the

system used in control and

stability studies The

moments are common to

both systems Z-axis

The Main Four Forces on an Airplane

The Main Four Forces on an Airplane

The Main Four Forces on an Airplane

The Main Four Forces on an Airplane

What is Weight ?

What is Drag?

What is Thrust?

What is Lift ?

Think About It

The motion of the airplane through the air

depends on the relative magnitude and

direction of the forces we have discussed.

If the 4 forces are balanced, the aircraft

cruises at constant velocity and altitude.

If the forces are unbalanced, the aircraft

accelerates in the direction of the largest force.

Simplified Aircraft Motion

The aerodynamic loading depends in a

quite complex manner on:-

the geometry, speed and motion of the

airplane and on

the properties of the air (pressure,

temperature, density, viscosity, conductivity

and compressibility).

The determination of these relationships is

the object of the study of the airplane

aerodynamics.

Airplane aerodynamics

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The student must carry out the following

steps:

Knowledge of the physical properties of air and of

the atmosphere, and outlines of the basic behavior of

the airplane.

The ability to select the airfoil section from the two

dimensional airfoil theories of compressible flow,

including the influence of friction on the airfoil

characteristics.

The ability to conduct preliminary design analysis

of the wing shape from the three dimensional wing

theory for subsonic and supersonic incident flow.

To achieve the objectives of this course (1)

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The student must carry out the following

steps (cont.): The ability to conduct preliminary design analysis of

the fuselage and the vertical and horizontal tail units and

evaluating there interference effects on the airplane

aerodynamic performance.

The ability to determine all aerodynamic forces and

moments and their derivatives with respect to angle of

attack, side slip angle and control surface deflection

angles (elevator, radar and aileron) for the airplane for

various flight conditions.

Ability to apply mathematical methods for calculation

of aerodynamic loading, analyze results and improve

aerodynamic design shape.

To achieve the objectives of this course (2)

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The student must carry out the following

steps (cont.):

Ability to conduct design experiments and

assess experimental data related to aerodynamic

problems.

The ability to construct numerical codes and to

use the available commercial numerical codes to

conduct a complete simulation of the

aerodynamic problems.

Ability to use the internet and other resources

to collect data and information, communicate

effectively and have efficient presentation skills

To achieve the objectives of this course (3)

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Contents of the AE 301 (A) Course

Introduction

The governing equations of fluid motion Some exact and closed form solutions of

the governing equations Alternative formulations of the

governing equations The two dimensional incompressible

potential flow Introduction to theory of flow over finite

wings 28

– Introduction: Source of aerodynamic forces and moments.

Statistical and continuum approaches, Review of mathematical

tools.

– Governing Equations of Fluid Motion: Control volume and fluid

element approaches. General assumptions in continuum fluid

flow. Derivation of the continuity, momentum and energy

equations (Navier-Stokes equations). Non dimensional form of

the equations. Special forms of the equations.

– Some exact and closed Form Solutions of the Navier-Stokes

equations

COURSE SYLLABUS

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– Alternative Formulations of the Governing Equations:

Conservation forms. Vorticity and stream function formulation.

Euler equations. Potential flow formulation.

– Two Dimensional Incompressible Potential Flow: Elementary

flows and superposition. Complex potential function. Flow

around Rankine body. Lifting and non lifting flow around

cylinder. Complex potential function. Conformal transformation.

Flow past Joukowski airfoil. Thin airfoil theory. Airfoil with flap.

General airfoil. Panel methods.

– Introduction to Theory of Flow Over Finite Wings

COURSE SYLLABUS

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Main Text Book

“Aerodynamics for Engineering Students”

By E.L. Houghton and P.W. Carpenter

Fifth edition published by

Butterworth-Heinemann 2003

(First published in Great Britain 1960,

Fourth edition published in 1993 by

Edward Arnold) 31

Additional References

• “Boundary Layer Theory” by Hermann Schlighting seventh edition by McGraw Hill, 1979.

• “Aerodynamics for Engineers” by John J. Bertin & Michael L. Smith, third edition by Prentice Hall Inc, 1979.

• “Fundamentals of Aerodynamics” by John D. Anderson, Jr., third edition by McGraw Hill, 1984.

• “Foundations of Aerodynamics” by Arnold M. Kuethe & Chuen Yen Chow, fourth edition by John Wiley & sons, 1986.

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Fluid Mechanics

Liquid (water, others)

Gas (Air, others)

Static Dynamic

Aerodynamic is a branch of the fluid mechanics

Aerodynamic

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Methods of Mechanics Analysis

Statistical mechanics approach

Continuum mechanics approach

The fluid molecules are in random motion, and we are interested in the motion of individual molecules.

We are interested with average effects of the many molecules that make up the fluid particle; these average effects are measurable.

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Fluids are composed of molecules that collide

with one another and with solid objects.

The continuum assumption considers fluids to

be continuous. The fact that the fluid is made up of

discrete molecules is ignored.

The properties such as density, pressure,

temperature, and velocity are taken to be well-defined

at small points with averaged values.

These properties are assumed to vary

continuously from one point to another.

Continuum Mechanics Approach

Origin of Fluid Forces

The forces applied to bodies moving through the fluid can be divided into two types: normal forces (due to pressure) and tangential forces (due to shear). Pressure forces (normal forces) are created at the surface of a body due to elastic collisions between molecules of the fluid and the surface of the body. Shearing forces (tangential forces) are produced by fluid viscosity between the adjacent layers of fluid and the body surface.

Pressure forces are usually the dominant type of force.

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Approximations The equations of motion for a general fluid are extremely complex. Thus certain simplifying approximations can be made. These may include the following assumptions:

• Inviscid flow assumption: The effect of viscosity may sometimes be neglected. For many aerodynamic flows of interest, the region of high shear is confined to a thin layer of fluid near the boundary of the solid surface. Outside this layer, the fluid behaves as if it were inviscid.

• Incompressible flow assumption: When the fluid density does not change with changes in pressure, the fluid is incompressible. Air is compressible, but if pressure changes are small in comparison with its nominal value, the incompressible equations work quite well in describing the flow.

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Approximations

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Boundary layer flow means

flow near the solid boundary

Potential flow means

irrotational flow

Derivation of Governing Equations

•We now need to develop a mathematical model of the fluid motion suitable for use in numerical calculations. •We want to find the flow field velocity, pressure, density and temperature distributions. •The mathematical model is based on the conservation laws and the fluid properties. •Two approaches can be used to obtain the mathematical description defining the governing equations (Lagrangian and Eulerian approaches)

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40

Review of

vector

algebra

Definition of nappla operator in cartesian coordinates

Gradient of a scalar p in cartesian coordinates

Divergence of a vector V in cartesian coordinates

where kwjviuV

Review of vector algebra

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kz

jy

ix

kz

pj

y

pi

x

pp

z

w

y

v

x

uV

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Review of vector algebra

kzjyixsd

If “s” is any arbitrary direction where

kds

dzj

ds

dyi

ds

dxe

s

The unit vector in the “ds” direction

The directional derivative of the scalar “p” in the “s” direction

kz

pj

y

pi

x

pp

where

ds

dz

z

p

ds

dy

y

p

ds

dx

x

pep

ds

dps

kz

jy

ix

Curl of a vector V in cartesian coordinates

Curl of a vector

Where

kwjviuV

Review of vector algebra

43

We can prove the following two identities

Curl of a vector

Where V in cartesian coordinates

kwjviuV

Review of vector algebra

kz

jy

ix

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and the operator nappla in cartesian coordinates

VVV

VVVVV

2

2

2

1)(

In any orthogonal curvilinear coordinates where

u1, u2, u3 are the coordinate system

h1, h2, h3 are the scale factor at each direction

e1, e2, e3 are the unit tangent vector

Curl of a vector Review of vector algebra

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For cartesian coordinates

u1 = x , u2 = y , u3 = z

h1 = 1 , h2 = 1 , h3 = 1

e1 = i , e2 = j , e3 = k

For cylindrical coordinates

u1 = r , u2 = θ , u3 = z

h1 = 1 , h2 = r , h3 = 1

e1 = er , e2 = eθ , e3 = ez

For spherical coordinates

u1 = r , u2 = θ , u3 = φ

h1 = 1 , h2 = r , h3 = r sinφ

e1 = er , e2 = eθ , e3 = eφ

Curl of a vector

we can write

the nappla operator

Review of vector algebra

46

In any orthogonal curvilinear coordinates where

u1, u2, u3 are the coordinate system

h1, h2, h3 are the scale factor at each direction

e1, e2, e3 are the unit tangent vector

Laplace operator

33

3

22

2

11

1

uh

e

uh

e

uh

e

33

21

322

31

211

32

1321

2

uh

hh

uuh

hh

uuh

hh

uhhh

1

Curl of a vector Review of vector algebra

47

Gradient of a scalar Φ

In any orthogonal curvilinear coordinates where

u1, u2, u3 are the coordinate system

h1, h2, h3 are the scale factor at each direction

e1, e2, e3 are the unit tangent vector

Divergence of a vector A

332211eAeAeAA

where

333

222

111

euh

1e

uh

1e

uh

1

3

321

2

231

1

132

321u

Ahh

u

Ahh

u

Ahh

hhh

1A

Curl of a vector Review of vector algebra

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Curl of a vector A

332211eAeAeAA

where

In any orthogonal curvilinear coordinates where

u1, u2, u3 are the coordinate system

h1, h2, h3 are the scale factor at each direction

e1, e2, e3 are the unit tangent vector

332211

321

332211

AhAhAh

uuu

eheheh

321 hhh

1A

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END OF THE

INTRODUCTION

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NEXT

Governing

Equations