On 1 Nov 2000 [EMAIL PROTECTED] wrote:
> So this implies that in steady flight there is more air going under
> the LE than coming out at the TE. (Alternatly more air leaving the
> upper surface past TE than entering) Wouldn't that result in
> continuously increasing density under the wing (or vaccume over) as
> long as it is moving? You might work this into a perpetual motion
> machine.
At the stagnation point where the flows part, the speeds are the same.
At the trailing edge, the speeds are also the same (Kutta condition).
So, if we draw our control volume in front and behind the airfoil,
conservation of mass still applies. HOWEVER, it's in between those two
points that everything interesting happens.
Take a look at this flying wing airfoil pressure plot, I found it through
the UIUC airfoil site. It was done using Dr. Drela's Xfoil code.
http://amber.aae.uiuc.edu/~m-selig/flyingWingAfs/s5010/s5010.html
(It's actually a pressure distribution, but the two are closely
linked.)
First, note that the y-axis is reversed. This is done for the sake of
clarity; speed of the flow is higher on top and lower on the bottom, so
pressure is lower on top and higher on the bottom (Bernoulli's law).
The stagnation point is that place on the lower surface where Cp = 1.
This is the high-pressure spike on the lower left of the plot. Cp=1
implies the flow velocity is zero, which is why it's called 'stagnation'.
The Kutta condition is that place at the trailing edge where the flows
come back together. It's a bit of a mess on this plot due to boundary
layer interactions, but it's that place at x = 1, y ~ 0.1.
(For most airfoils it'd be less than 0, but this is a flying wing airfoil.
The reflex trailing edge pushes the pressure up, to counter the airfoil
pitching moment.)
You can see that the speed increases dramatically as the pressure rounds
the leading edge. All that curvature acts like a big ol' waterslide for
air. After that high point at x ~ .05, the air spends the rest of the
airfoil slowing back down to the Kutta condition.
On the bottom, you can see that the air takes its own sweet time speeding
up to the Kutta condition. After about x ~ .5, it hardly changes speed at
all. And never does it get going as fast as the freestram air (Cp=0).
(The reason the Cp can be allowed less than the freestream speed at the
trailing edge is that the plot is the x-component of the Cp. If both x
and y components are taken into account, the speed at the TE is equal to
the freestream. The y-component of Cp is what gives you pressure drag.)
Daniel O. Miller
BRAIN: Pinky! Are you pondering what I'm pondering?
PINKY: I think so, Brain, but three men in a tub? Ewww, that's unsanitary.
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