Analysis using xfoil Sivaranjani H

AE - 221, Aerodynamics SC18B039

Question 1
Three NACA airfoils namely, NACA 0010, NACA 2412 and NACA 6412 were analysed at Re =
3×106 for angles of attacks from −5o to 24o with a step of 0.2o . The airfoils and their properties
are listed in Figure 1. The cl –α, cm –α curves and drag polar are shown below in Figure 2 and
Figure 3.

(a) NACA 0010 Max camber: 0%, Max thickness : 10% at 30% chord

(b) NACA 2412 Max camber: 2% at 40%chord , Max thickness : 12% at 30% chord

(c) NACA 6412 Max camber: 6% at 39.6%chord , Max thickness : 12% at 30.1% chord

Figure 1: Airfoils and their important characteristics

1. The symmetric airfoil NACA0010 had an αL=0 = −0.00009o that can be taken as zero
for practical purposes and is exactly as what we would expect. The NACA2412 airfoil
has a αL=0 of −2.1475o because of its camber of 2% (max) at 40% the cord length. The
NACA6412 has the most negative value of αL=0 at −5.5535o due to its high camber of
6%. Thus it is evident that the value of αL=0 becomes more negative as max camber
increases. This is as expected because an airfoil with more camber would generate more
lift at zero AoA. Thus, to nullify the lift a greater negative AoA is necessary.

2. The symmetric airfoil was found to have a mean cm of 0 for small AoA (−5o < α < 5o ) be-
yond which it begins to oscillate. The airfoil with intermediate camber, the NACA2412 has
a mean cm = −0.055 which indicates the presence of a restoring pitching moment, aimed
at bringing the airfoil back to the old AoA in case of any disturbance. The NACA6412
with the greatest camber has the greatest -ve cm of −0.15. All these indicate that cm

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 Figure 2: Plots of cl –α and cm –α (cm has been scaled up ×10 )

is strongly influenced by the maximum camber and greater camber generally indicates a
greater -ve value of cm .

3. On inspecting the drag polar and finding the drag for cl = 0, it can be seen that NACA2412
has a slightly lower drag than the other two airfoils and hence is considered to be ideal
for low-drag cruise conditions. This also happens to have a favourable AoA of 2.37o , as
compared to the 4.62o of NACA0010 and −2.13o of NACA6412.

4. The lift-curve slope seems to have similar behaviour in all three airfoils at different AoAs.
For low AoAs from -4 to +8 or +9, the slope does not change at all and remains constant.
Once the AoA increases and the boundary layer begins to separate, the lift decreases in

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 Figure 3: Drag polar with cd vs cl

an almost quadratic way. The slope changes continuously, going from a positive number
to zero to a -ve value. A -ve value of slope indicates that any further increase in AoA
reduces the lift generated due to excessive flow separation.

Question 2
The NACA4412 was analysed for an AoA of −4o to 24o at different reynolds numbers of 3×103 ,
3×104 and 3×106 . The analysis was also carried out by modifying the defaullt panel settings.
The non-uniform panel placing as shown in 4(a) was modified to make it uniform like in 4(b).
The values obtained were plotted in the same graph in order to see the effect panel bunching
had on the numerical estimations. The cl –α curve and drag polar are shown below in Figure 5
and Figure 6
At low Reynolds number where, viscous forces dominate over inertial forces, cl increases
gradually with AoA without a definite lift curve slope (as predicted by inviscid, thin airfoil
theory). The increase in cl is slightly greater for low angles of attack than for larger angles
but there’s no definite boundary between the two. Most importantly, there’s no characteristic
stalling AoA in the analysed region. There could be one at higher AoA’a but the stall is not
expected to be steep as in case of high Re’s. In other words, the dome might be more spread

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 (a) NACA 4412 with more panels near the leading (b) NACA 4412 with uniformly distributed panels
edge

Figure 4: Difference in panelling

Figure 5: Plots of cl vs α

out and cl drops gradually over a large value of AoAs. For high Reynolds number, the slope is
around 0.1/o which roughly matches the one predicted by thin airfoil theory of 2pi/rad.
The drag polar also shows no characteristic change in L/D to indicate separation. However,
the general trend observed is that for a particular value of cl , drag is always higher at low
Reynolds numbers, indicating the role played by viscosity in increasing skin friction drag.

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 Figure 6: Drag polar

The dotted lines represent the numerical results done when the panel density was kept
uniform at the body and edges. This didn’t affect the results significantly except at stall
conditions when there’s high Reynolds number. The estimated drag was also lower when there
were more panels concentrated in the leading edge. This is because, smoothening out the
geometry and allowing a much more gradual acceleration helps reduce the pressure and skin
friction drag a little.

Question 3
A GOE-496 (Figure 7) was used along with the 3 NACA airfoils from Q1. Their co-ordinate
data files were taken in excel in the order of starting at the trailing edge, travelling to the
leading edge from top to bottom and reaching the trailing edge again. All files were ensured to
have the same number of control points (200). Then, the average of the four was calculated and
stored in a separate file. This was loaded into xfoil and its pressure distribution was obtained
for the conditions of Re = 3 × 106 and α = 3. The following Cp distribution, 9(a) was obtained.

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Figure 7: GOE 496 airfoil max camber: 5% at 50% chord, max thickness: 10% at 30% chord

Figure 8: Inverse design of the airfoil

This airfoil was loaded into the mdes menu and its velocity distribution was generated. Then
it was used to inverse design the airfoil as shown in Figure 8. The generated airfoil was observed
to have very minor changes in the positions of the points, and its properties too didn’t change
much. Below(9(b)) is the Cp distribution plotted for the same Re = 3 × 106 and α = 3.

(a) Cp distribution of averaged airfoil (b) Cp distribution of generated airfoil

Figure 9: Cp distributions before and after inverse design