AAE 334, Fall 2011, Homework 3 SOLUTION
Due Monday, August 29 at the beginning of class.
Consider a pressure distribution near a leading edge of a symmetric airfoil.
We will do this with
the flow shown in Figure 3.22 of the text and solved on page 248.
We will use
and
.
1
=
∞
V
1
.
0
=
Λ
1.
Plot the airfoil shape near the leading edge.
Hints:
a.
define an angular position vector for points on the body:
thbody = (0.2:0.01:1.8)*pi;
% Theta coordinate
(remember that
thbody=0
is the xaxis, not the leading edge.)
b.
compute for radial coordinate of points on the body
c.
compute (x,y) from (r,
θ
), and plot with
plot( )
d.
to set the correct aspect ratio in your plot, use:
set(gca,
'DataAspectRatio'
,[1 1 1])
after the plot command.
2.
Compute and plot separately a nondimensional quantity
2
2
1
∞
−
V
V
versus angle from the
leading edge.
Top and bottom surfaces in this symmetric flow will have the same result
so expect to see only one curve in this plot.
This
2
2
1
∞
−
V
V
quantity is another
mathematically correct formula for pressure coefficient
()
2
2
1
∞
∞
∞
−
=
V
p
p
c
p
ρ
in an
incompressible flow.
3.
Where is there a favorable pressure gradient for the flow on the surface?
That is, flow
from higher pressure into lower pressure?
4.
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 Fall '09
 COLLICOTT
 Fluid Dynamics, pressure distribution, favorable pressure gradient

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