Download Aerodynamics Notes 2

Reynolds Numbers
Osborne Reynolds was responsible for discovering many of the
principles of fluid viscosity and boundary layers. He discovered
that the condition of the boundary layer, laminar or turbulent,
depend on the fluid velocity, the distance downstream, and a
characteristic of fluid known as kinematic viscosity. Reynolds
numbers are used to measure the viscous (Having a thick, sticky
consistency between solid and liquid) qualities of a fluid. The
symbol Re is used for this number and can be expressed as the
equation:
Re = V x s
√
Where V = Fluid velocity
d = distance downstream from leading edge
√ = kinematic viscosity of the fluid (these are standard
figures which are given with respect to air temperature)
Figure: (Scott, 2005)
At low Reynolds numbers the flow is laminar,
and at high Reynolds numbers it is turbulent.
Interested fact: Spheres are not a good shape for
aerodynamics. A blade or fin or wing works
much better at controlling air flow for flight by
maximizing lift and minimizing drag forces.
Dimples on a ball help reduce drag, while spin
mostly promotes lift. Without dimples, golf balls
wouldn't fly half
as far as they do.
Form Drag
The figure to the right shows how form drag (also known as
pressure drag) is affected by the streamlined shape of the
body. For a flat blocky shape, the form drag will be high and for
a streamlined low-profile body, the form drag will be
minimized. The separation of the fluid creates turbulence and
results in pockets of low and high pressure that leave a wake
behind the body, thus the term pressure drag. The pressure drag
opposes forward motion and is a component of the total drag.
Wake
A wake is the region of recirculating flow immediately behind a
moving or stationary solid body, caused by the flow of surrounding fluid around the body.
The figure below shows the large wake generated behind the a small boat. This wake is in
essence "wasted" energy that the ship generates. This wasted energy was not used to propel the
boat forward, but rather to generate waves.
Figure: (Cortana, 2006)
Wake Turbulence
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Wake turbulence forms behind an aircraft as it passes through the air. This turbulence includes
various components, the most important of which
are wingtip vortices and jetwash. Jetwash refers
simply to the rapidly moving gases expelled from
a jet engine; it is extremely turbulent, but of short
duration. See image below.
Figure: (Edmont, 2009)
Figure: (NASA, 1990)
Drag Coefficient
The amount of drag on an object is proportional to the dynamic pressure times the area and will
vary with the shape of the body, the roughness of the surface, and other factors. Drag, like lift, is
proportional to the dynamic pressure of the air and to the area on which it is acting. Therefore, a
drag coefficient is used to describe how much of the dynamic pressure is converted into drag. The
equation looks a lot
like
the
lift
equation, except that
it measures the
force in a stream
wise
direction,
which is parallel to
the airflow.
Drag=Cd x (1/2 p V2)
Where:
Figure: (Aquaphoenix, 2012)
- Cd= Drag
-
xA
coefficient
P=
Density
V= Velocity
A= Area
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The term ½ p V2 , remember, is the dynamic pressure, referred to by the symbol q. Thus, using this
notation:
Drag= Cd x q x A
There is a similarity between lift coefficient and drag coefficient
in that the lift coefficient, CL , is a measure of how much of the
dynamic pressure gets converted into lift, and the drag coefficient
is a measure of how well a wing (or other body) converts dynamic
pressure force into drag.
Both are an indication of efficiency. When generating lift, however, we want as much as possible,
but, when generating drag, we want the least possible.
A low drag coefficient, then, is what we want. The efficiency is determined by how little of the
pressure force is turned into drag.
The drag coefficient can also be expressed as
the ratio of drag force to dynamic pressure
force, or:
C
d=
Drag/q
xA
This is the formula that is used to calculate CD from wind
tunnel tests. The drag force is measured using some sort of
scale or balance. The force is then divided by q x A which is
determined from a measurement of the air speed, density, and
the area of the body.
Figure: (Magda, 2006)
Testing the Racer Shapes in a Wind Tunnel
Using a wind tunnel to test different shapes and designs of our
racer is a fantastic way to predict how our racer is likely to
behave in an F1inSchools race. If we test our models in our
wind tunnel and determine the different racer’s Reynolds
numbers we can determine the designs which create the least
turbulence and therefore move with the best laminar airflow.
Figure: (PITSCO, 2002)
Obviously the designs with the lowest Reynolds numbers will
then potentially be the fastest cars. Of course all other
contributing factors between cars would have to be equal. We
can use the Pitsco Scout, to test our racer designs. We can read
the Reynolds number directly from the digital readout which
makes this very useful for determining which of our designs is
the best aerodynmically.
Bernoulli's principle
The production of the lift force by an aerofoil is explained by
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Bernoulli's principle. Daniel Bernoulli (1700-82) was a Swiss scientist who discovered that the
total pressure in a fluid remained constant. This total pressure consists of:
• static pressure (the weight of the molecules) • dynamic pressure (due to motion)
Figure: (OTEN, 2002)
If air was accelerated through a shaped tube called a `venturi', then at the narrowest point, where
the speed of the flow was fastest, the static pressure was least. The relationship between the
velocity and pressure exerted by a moving fluid is described by Bernoulli's principle (OTEN,
2002):
as the velocity of a fluid increases, the pressure exerted by that fluid decreases.
See Bernoullis’s Principle Experiments YouTube
http://www.youtube.com/watch?v=P-xNXrELCmU&feature=related
Air foils and Lift
Air foils are the wings on aeroplanes and the spoiler type sections on cars. In planes we all know
that the wings allow the plane to be supported in the air, however on cars they are not just for
show they have a very important purpose.
In the diagram to the left differences in shape and the direction of the force produced is shown
when the wing is inverted in powered car racing where the aim is to produce down force (so that
the cars can “stick “ to the road and grip so that the power produced by the engine can be
transferred to the track). This is the direct opposite to a plane wing where the aim is to create lift
to keep the plane in the air.
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