Aerodynamic 2

1
Aerodynamics 2
MEC 3706/MEC 3220
Assignment 1
Due Date: 14-1-2010 (11:30 am)
Q1.
Plot the pressure distribution over the symmetrical double wedge, 8 per cent thick supersonic aerofoil shown in figure below when the Mach number meets the upper surface (a) tangentially (b) 12º and (c) .9º. Compare the lift, drag and pitching moment coefficients for these incidents. Assume ε0=6º
Q2
A thin wing can be modeled as a 2m wide flat plate set at an angle of 5º to the upstream flow. If the wing is placed in a flow with a Mach number of 3.5 and a static pressure of
75 kPa, find using linearized theory the pressure on the upper and lower surfaces of the airfoil, lift and drag per span.
(Hint:
2
2∞
∞
∞ q = p M γ , γ=1.4)
2
Q3. a- A thin symmetrical supersonic airfoil has parabolic upper and lower surfaces with a maximum thickness occurring at midchord. Using linearized theory, compute the lift to drag ratio when it is set at an angle of attack of 5º.
Figure 5
[Hint: y = A+ B (αx) + C (αx)2, and dx ε = dy ]
Q4.
Estimate the critical Mach number for NACA 0012 airfoil at 10º angle of attack. The pressure coefficient distribution over this airfoil, measured in wind tunnel at low speed is given in the following figure. Compute and draw the pressure distribution curve at Mach number of 0.75.
0 0.25 0.5 0.75 1
X/c
-0.5
0
0.5
1
1.5
2
2.5
3
Cp
3
Q1.
1- = ∫ ( − ) c
L P PU C c C C dx 0 L for given figure, we obtain
= ∫ − + ∫ ( − ) / 2
0
/ 2
3 1 0 4 2 ( ) c c
L P P p P C c C C dx C C dx
But from linearized theory, we know
1
2
2 −
=
M
Cp
ε then ( ) ( )⎟⎠
⎞
⎜⎝
⎛ − + −
−
= 2 2 3 1 2 4 2
1
1
2 c ε ε c ε ε
M c
CL
1- α = 6
6
12 12 6
6
M=3 c/2 c/2
6 6 0 0 1 ε = − = = radian
6 6 12 0.20933 2 ε = − − = − = − radian
6 6 12 0.20933 3 ε = + = = radian
6 6 1 0.0 4 ε = − + = = radian
( ) (0 ( 0.20933)) 0.148
2
0.20933 (0) 1
2
1
1
2
2
= ⎟⎠
⎞
⎜⎝
⎛ − + − −
−
=
M
CL
0.148
3 1
180
4 6
0.148