Download - Aerodynamics 1 Pr1
-
8/10/2019 Aerodynamics 1 Pr1
1/25
Aerodynamics 1AE 302
Department of Aeronautical Engineering
Faculty of Engineering
University of Tripoli
March 2014
-
8/10/2019 Aerodynamics 1 Pr1
2/25
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.
-
8/10/2019 Aerodynamics 1 Pr1
3/25
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.
-
8/10/2019 Aerodynamics 1 Pr1
4/25
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.
-
8/10/2019 Aerodynamics 1 Pr1
5/25
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.
-
8/10/2019 Aerodynamics 1 Pr1
6/25
This course
The goal of this course is to introduce the fundamental ofaerodynamics and to give the student a much deeper insight totechnical applications.
-
8/10/2019 Aerodynamics 1 Pr1
7/25
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
-
8/10/2019 Aerodynamics 1 Pr1
8/25
.
. .
.
. .
-
8/10/2019 Aerodynamics 1 Pr1
9/25
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
-
8/10/2019 Aerodynamics 1 Pr1
10/25
On the upper surface
= = + ( +ive cw from vertical line tothe direction of p and Horizontal
line to direction of )
On the lower surface
= = +
-
8/10/2019 Aerodynamics 1 Pr1
11/25
= sin + cos + sin + cos
Substitute Nand Ainto
=
= +
To compute the lift and drag per unit span for a body with arbitrary shape
= + +
-
8/10/2019 Aerodynamics 1 Pr1
12/25
Aerodynamic Moments
( ) ( )
= + + +
= + + +
-
8/10/2019 Aerodynamics 1 Pr1
13/25
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: .
-
8/10/2019 Aerodynamics 1 Pr1
14/25
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 ,
-
8/10/2019 Aerodynamics 1 Pr1
15/25
The Momentum EquationThe momentum equation is given by
.
-
8/10/2019 Aerodynamics 1 Pr1
16/25
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
= ,, ,, = ,, ,,
-
8/10/2019 Aerodynamics 1 Pr1
17/25
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.
,= ,, ,, ,, ,,
-
8/10/2019 Aerodynamics 1 Pr1
18/25
.
.
-
8/10/2019 Aerodynamics 1 Pr1
19/25
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
-
8/10/2019 Aerodynamics 1 Pr1
20/25
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.
+ . =
-
8/10/2019 Aerodynamics 1 Pr1
21/25
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
= .
-
8/10/2019 Aerodynamics 1 Pr1
22/25
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
-
8/10/2019 Aerodynamics 1 Pr1
23/25
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
-
8/10/2019 Aerodynamics 1 Pr1
24/25
only the x-comp.
as u1=u2
= + +
=
, = =
. = 0.01667
=
-
8/10/2019 Aerodynamics 1 Pr1
25/25
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