Aerodynamics 1 Pr1

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Aerodynamics 1AE 302

Department of Aeronautical Engineering

Faculty of Engineering

University of Tripoli

March 2014


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Aerodynamics

Ludwing Prandtl, 1949 defined aerodynamics as The termaerodynamics is generally used for problems arising from flight andother topics involving the flow of air.

The American Heritage Dictionary of the English, 1969 definedaerodynamics as the dynamics of gases, especially atmosphericinteraction with moving objects.


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Fluid Dynamics is subdivided into three areas as follows:Hydrodynamics : Flow of liquidsGas Dynamics : Flow of gases

Aerodynamics : Flow of air

In those three areas there are many similarities and identicalphenomena between them.

Applications:External aerodynamics: Deals with external flow over a body.Internal Aerodynamics: Deals with flows internally within ducts.

In addition to forces, moments and aerodynamics heatingassociated with a body, we are frequently interested in thedetails of flow field away from the body.


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Progression of airplanes over the 70 years

Douglas DC-3: One of most famous aircraft of all time, is low speedsubsonic transport designed during 1930s. Without a knowledge of

low speed aerodynamics, this aircraft would have never existed.

The Being 707: Opened high-speed flight to millions of passengersbeginning in the late 1950s. Without a knowledge of high speed

subsonic aerodynamics, most of us would still be relegated to groundtransportation.

The Bell X-1 became the first piloted airplane to fly faster than sound,1947. Without a knowledge of transonic aerodynamics, neither the X-1, nor any other airplane, would have ever broken sound barrier.


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The Lockheed F-104 was the first supersonic airplane designed to flyat twice the speed of sound, accomplished in the 1950s.

The Lockheed-Martin F-22 is a modern fighter aircraft designed forsustained supersonic flight. Without a knowledge of supersonicaerodynamics, these supersonic airplanes would not exist.

Finally, an example of an innovation new vehicle concept for highspeed subsonic flight in the blended wing body. Blended wing bodypromises to carry from 400 to 800 passengers over long distance withalmost 30% percent less fuel per seat mie than a conventional jet

transport.


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This course

The goal of this course is to introduce the fundamental ofaerodynamics and to give the student a much deeper insight totechnical applications.


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Aerodynamics Forces and Moments

Aerodynamics Forces and Moments on the Body are only due to:

1. Pressure distribution2. Shear Stress distribution

R : Resultant aerodynamics forces

M: Resultant aerodynamic moments


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.

. .

.

. .


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How do we compute the aerodynamic forces and moments

Stress on Airfoil

N- Total normal force per unit span

A- Total axial force per unit span


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On the upper surface

= = + ( +ive cw from vertical line tothe direction of p and Horizontal

line to direction of )

On the lower surface

= = +


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= sin + cos + sin + cos

Substitute Nand Ainto

=

= +

To compute the lift and drag per unit span for a body with arbitrary shape

= + +


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Aerodynamic Moments

( ) ( )

= + + +

= + + +


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Integrating from the LE to the TE we get

= +

+ + + +

Where , x andyare known functions of sfor a given body shape. pu,pl, u, and l are also functions of sfrom theory or experiment.

Hence L, Dand Mcan be computed.

Dynamic Pressure: , Lift Coefficient: ,Drag Coefficient: and Normal force Coefficient: .


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Axial Force Coefficient: , and Moment Coefficient: .Where Sis reference area and lis reference length.

Example: S - planform area of the wing

- d2/4 for cylinder

l - chord c for a wing /airfoil

- diameter for a cylinder

For 2D bodies, the forces and moments are per unit span, hence

,, ,

and ,


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The Momentum EquationThe momentum equation is given by

.


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Surface forces on the control volume

1. Due to Pressure distribution over abhior - Also important are:

Pressure Coefficient: and Skin Frication Coefficient:

The equations for the force and moment coefficient in integral for are

= ,, ,, = ,, ,,


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Where dx= ds cos

and dy= -ds sin

.

2. The surface, forces on defdue to the presence of the airfoil:

Shear stresses on aband hiare neglected.

Since cdand fgare next to each other all force on one is cancelled byforces on the other.

,= ,, ,, ,, ,,


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.

.


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Flow exertsp and leading Body exerts equal and opposite

to a resultant force R reaction Ron the control Volume

Hence total surface force on the control volume is


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From the integral momentum equation we have

Assume steady flow, then

= . Taking the x-component of the above eqn.

= .

Where Dis the aerodynamic drag per unit span, which is the x-comp. of R.

+ . =


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Sincepis constant along abhithen

Hence

Where dsis perpendicular to CS evaluated over the closed surface ofthe CV.

The section ab, hi and defare streamlines. Hence

= 0along these.

cdand fgare very close to each other, hence their net contribution iszero.

= 0

= .


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The only contribution to the above integral is from aiand bh. Hence

(*)

From the continuity equation . = 0Applying this equation to CV leads to

or substitute in (*)

or, =

= .

= +

+ = 0

+ = 0

= = 0


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Flow is incompressible, 2D, steady, find Drag.

At the upstream end = At the down stream end:

0 = +

H 2 = + 0 = 2H =

Where vand v0are not measured


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only the x-comp.

as u1=u2

= + +

=

, = =

. = 0.01667

=


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Pressure CoefficientPressure Coefficient: From Bernoullis equation (incompressible flow):

+ or =

=

or =

Condition on Vfor incompressible flows

From the continuity equation:

Continuity Equation for incompressible Flow: .= 0

.= 0

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Aerodynamics 1 Pr1