Fundmental thoughts

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

1

2Chapter

Fundamental Thoughts

• The flow of air over the surface of an airplane is

the basic source of the lifting force that allows a

heavier-than-air machine to fly

• The science that deals with the flow of air/flow of

any gas is called aerodynamics

• What is aerodynamics?

• The word comes from the Greek words: aeros,

concerning the air, and dynamics, which means

force

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

2

● Aerodynamics is the study of forces and the

resulting motion of objects through the air.■Physical Quantities of a Flowing Gas

Physical quantities in the language of aerodynamics are:

1- Pressure 2- Density

3- Temperature 4- Compressibility

5- Viscosity 6- Flow velocity

and streamlines

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

3

1-Pressure

“Pressure is the normal force due to the time rate of

change of momentum of the gas molecules impacting on

that surface”

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

4

• Mathematically F

Mean pressure P = F/ A

Pressure at point p = dp/ dA A

where p is the pressure

F is the normal force

A is the area

2-Density

Density is defined as the mass of gas divided by its

volume

• Mean density : ρ = m / V

• Density at point : ρ = dm / dV

• Specific volume : v = 1/ ρ

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

5

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

6

3- Temperature

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

7

4- Compressibility

● Compressibility is a measure of the relative

change of a fluid as a response to a pressure

change

● By definition, the compressibility of a fluid β :

β = - (1/V)(dV/dp)

where V is the volume and p is the pressure

p p+dp V V+dV

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

8

• If the temperature of the fluid element in the

Figure is held constant, then β is called

isothermal compressibility βT = - (1/V)(∂V/∂p)T

• If no heat is added to or taken away from the

fluid element, and if friction is ignored, the

compression of the fluid element takes place

isentropically and β is called isentropic compressibility βs = - (1/V)(∂V/∂p)s

• Since m = ρ V then dm = ρ dV + V dρ

But dm = 0 because m = constant

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

9

ρ dV = - V dρ dV/V = - dρ/ρ

Then β = (1/ρ) (dρ/dp)

• Thus, whenever the fluid experience a change in

pressure, dp, the corresponding change in

density, dρ, is : dρ = ρ β dp

• In general, the flow of a gas is a compressible

flow. The exception to this is the low-speed flowof a gas ( at sea-level v ≤ 100 m/s )

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

10

5- Viscosity

● Viscosity is a measure of the resistance of a

fluid to flow.Velocity profile

Boundary Layer

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

11

Newton’s Theory

● In general, in any fluid flow, layers move at different

velocities and the shear stress between the layers, which

opposes any applied force, arises from the fluid’s

viscosity

●Newton postulated that, for straight parallel flow, the shear stress, between layers is proportional to the

velocity gradient, ∂v/∂y, in the direction perpendicular to

the layers

• ∂v/∂y)

The constant µ is known as the coefficient of viscosity/the

absolute viscosity/the dynamic viscosity

N.B. Kinematic viscosity υ =

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

12

6-Flow velocity and streamlines

● The flow velocity, or velocity field, of a fluid is a vector

field which is used to mathematically describe the motion

of the fluid.

● The flow velocity of a fluid is a vector field:

v = v(x,y,z,t)

which gives the velocity of an element of fluid at a

position (x,y,z) and time t .

A

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

13

Velocity field over airfoil

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

14

• Streamline: The path taken by a moving fluid

element ,in steady flow, is called a streamline of

the flow.

• Drawing the streamlines of the flow field is an

important way of visualizing the motion of the

air/gas flow.

Air flow over airfoil

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

15

Air flow about a house

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

16

■Source of Aerodynamic Forces● The four basic aerodynamic flow quantities : p, ρ, T, and v

● A knowledge of p, ρ, T, and v at each point of a flow fully defines the flow field

● For steady flow:

p = p(x,y,z)

ρ = ρ(x,y,z)

T = T(x,y,z)

v = v(x,y,z)

● The primary function of the aerodynamics (theoretical and or experimental) is to calculate or measure the flow field quantities around an aircraft or any flying vehicle

Flow Field

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

17

• The aerodynamic force exerted by the airflow on

the surface of an airplane, missile, etc, results

from only two simple natural sources:

1- Pressure (p) distribution on the surface

2- Shear stress or friction ( distribution on the

surface

Pressure and shear stress distribution

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

18

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

19

Forces, Moments and CoefficientsAerodynamic

• Lift Force L: L = q∞ S CL

• Drag Force D: D = q∞ S CD

• Pitching Moment: M = q∞ S C CM

• Where q∞ is the dynamic pressure

• q∞ = (1/2) ρ∞ v∞2

• S is the planform area of wing

• C is the mean chord of wing

• CL is the lift coefficient

• CD is the drag coefficient

• CM is the moment coefficient

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

20

Equation Of State For A Perfect Gas

• A perfect gas is one in which intermolecular forces are negligible

• Air at standard conditions can be approximated by a perfect gas

• Therefore, we will always deal with a perfect gas for aerodynamic calculations

• Equation of state: The relation between p, ρ, and T for a gas is called the equation of state

• For a perfect gas, the equation of state is:

• P = ρ R T

• Where R is the specific gas constant, the values of which varies from one type of gas to another

• For normal air R = 287 J/(kg)(K)

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

21

Units

• Two system of units are commonly used:

• 1- (SI) system is a metric system based on the meter,

kilogram, second, and Kelvin as basic units of length,

mass, time, and temperature

• 2- English Engineering System of units based on the

foot, slug, second, and Rankine as basic units of length,

mass, time, and temperature

• Force = mass x acceleration

• F = m x a

• In SI units : 1 Newton = (1 kilogram)(1 meter/second2)

• In English Engineering system:

• 1 pound = ( 1 slug )(1 foot/second2)

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

22

Conversion Factors

• 1 ft = 0.3048 m

• 1 slug = 14.594 kg

• 1 Ib = 4.448 N

• 1 oK = 1.8 oR