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16.100 Homework Assignment # 3
Due: Monday, September 26
th
, 9am
Problem 1 (70%)
Useful reading: Anderson: Section 3.14, 3.16, 4.5, 4.10
•
nodes where vortices
are located
X control points where
is enforce
0
=
⋅
n
u
v
v
d
Γ
2
X
Γ
3
V
∞
X
0.12c
X
α
Γ
1
c
Consider the isosceles triangle airfoil with 12% thickness as shown above.
A simple potential
flow model for the flow over the triangle is to place point vortices at each of the three nodes and
then determine the strengths (i.e. the circulations
Γ
i
) which satisfy flow tangency at three control
points.
For this model, let the control points be located at the midpoints of the three edges of the
triangle.
a) Setup the 3x3 system of equations that expresses
0
=
⋅
n
u
v
v
at the control points.
b) Show that the 3x3 matrix for this system is singular (i.e. it has at least one zero eigenvalue).
c) The singularity of the matrix can be removed by applying another condition in addition to
flow tangency.
Since the solution that is often of interest is attached flow in which the flow
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 Fall '03
 willcox
 Dynamics, Aerodynamics

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