Aerodynamics Project (Final)

7/28/2019 Aerodynamics Project (Final)

1/15

MATH 3250Fluid Dynamics 1.

Aerodynamics.


2/15

What is Aerodynamics?

Aerodynamics is a branch of fluid dynamics that deals

with the motion of air and other gaseous fluids.

It deals primarily with the forces in which thesegaseous fluids apply to different bodies moving

through them.


3/15

History The word aerodynamics did not actually come about

until the early 1800s.

For centuries, many philosophers, scientists,mathematicians and great thinkers observed certainbehaviours that occur when objects move through airand other gaseous fluids.

As such, they came up with various theories, conceptsand ideas related to aerodynamics.


4/15

Aristotle Greek Philosopher (350B.C.)

Archimedes Greek Philosopher (250 B.C.)

Leonardo Da Vinci Italian Painter (1490)

Galileo Galilei Italian Mathematician.

Sir George Cayley - English Mathematician .

Dr. Ludwig Prandtl German Scientist.


5/15

Some applications of Aerodynamics

AircraftsWind Turbines

Automobiles (eg. Formula 1 Race cars, Trucks)

Rockets and Missiles

Ships, Sail boats, etc.

Trains

Wind Tunnelling

Calculation of wind loads on Bridges and largebuildings

Kites, Paper Planes, etc.


6/15

The Airfoil.

In the above figure the wing extends in the y direction. This is called the SpanDirection. The freestream velocity V is parallel to the xz plane. Any section of thewing cut by a plane parallel to the xz plane is called an Airfoil.


7/15

Since we are dealing with an Inviscid Flow we are notable to predict aerofoil drag.

Jean LeRond dAlembert obtained a result of zero drag

for the inviscid, incompressible flow over a 2 D body in1744. Then again in 1752 and in 1768. This is the socalled dAlembert Paradox.

dAlembert Paradox says that the drag on the airfoil iszero clearly not the realistic answer.

Viscous flows must be accounted for in order toaccount for drag.

Lift and moments on the airfoil are due mainly to thepressure distribution which (below the stall due toflow separation) is dictated by inviscid flow.


8/15

The first modern configurational aircraft wasconceived and built by the Englishman Sir. GeorgeCayley. It was an elementary hand-launched glider,about a meter in length and had a kite-like shape for awing.


9/15

The first patented airfoil shapes were developed by theEnglishman Horatio F. Phillips in 1884. He also carried

out the first (low speed) wind tunnel experiments onairfoils.


10/15

Assumptions:

The fluid is Newtonian.

Flight path is isolated, meaning external forces likewind is negligible.

Flow velocity around the plane is slow compared to

speed of sound.

Let q = velocity of the airflow, F = external force, p =

pressure, = pressure, and = viscosity of the fluid.


11/15

Then the f low may be governed by the Navier-Stokesequations for a Newtonian incompressible fluid:

(1)

Under the flow conditions described above, we may takethe flow to be steady and irrotational.

Thenand


12/15

Now

Hence equation (1) becomes: (2)

Note that , so the fluid is considered viscous although equation (2)

resembles Eulers Equation of Motion for an inviscid fluid. Finally,

assume that the air density near and around the paper plane isconstant. Then :

Thus, equation (2) reduces to:

=>


13/15

We may assume that the force F acting on the paperplane is comprised of the weightWand lift L. Hence F

=W+ L:

FL = W

FL =

FD =

CD = f(Re)

+ =


14/15

Conclusion:

By assuming that the air around the paper plane

behaves like a Newtonian Fluid and the velocity of

the plane is small we were able to show that under

the assumption of an Incompressible Fluid theNavier-Stokes Equation reduces to the Euler's

Equation of Motion for an Inviscid Fluid when the

flow is steady and irrotational.

Through ideas such as these and through the work

of many Scientists and Engineers the era of

manned flight was born.


15/15

Documents

Aerodynamics Project (Final)