NACA 0012 at Re=40000

The dependency of lift coefficient on the angle of attack, α, as displayed in Fig. 101 for the NACA 0012 airfoil at Re=40000 for three different levels of the free-stream turbulence. xfoil does allow to vary this via a variable called Ncrit. Ncrit=9 (green) pertains to an "average" (late 1990) wind tunnel while 4-8 represents a "dirty" wind tunnel. Ncrit=9 was our first investigation which as shown in Figure 101 results in cL versus angle of attack behavior which is far away from what we traditionally expect. Out of curiosity we also show the suppression of the influence of laminar separation bubbles due to higher level of free-stream turbulence. The influence is astonishing and might explain while older investigations like Jacobs and Sherman (1937) [6] obtain linear dependency between friction coefficient and angle of attack at the Reynolds numbers under discussion.

Figure 101 : Lift Coefficient versus Angle of Attack

To investigate the case of Ncrit=9 further , we show in Fig. 102 the skin friction factor for the case of Re=40000 and α=1°. It clearly shows a separation bubble ( cF < 0 ) covering the rear half of the air foil. Closer inspection of the numerical data reveals that there is a large separation bubble on the upper side of the airfoil stretching from x/c=0.5422 all the way to the trailing edge and a much smaller one on the underside between x/c=0.9604 and the trailing edge. Both separation bubbles are laminar. (Falkner-Skan flow in program xfoil).

Figure 102 : Skin friction coefficient at &alpha=1°, Re=40000, Ncrit=9

In Table 101 we show the two laminar separation bubbles as they change position and size as function of the angle of attack.

αTop StartTop End Bot StartBot End
0.00.70201.0000 0.70201.0000
0.50.61371.0000 0.81251.0000
1.00.54221.0000 0.96041.0000
2.00.42711.0000 - -
3.00.33121.0000 - -
4.00.22820.7715 0.94671.0000
5.00.12870.5743 0.97441.0000
7.00.03300.3100 - -
9.00.01780.2941 - -
Table 101 : Extent of Laminar Separation Bubbles, Re=40000, Ncrit=9

At α=0 the laminar separation bubbles appear in equal size on the bottom and top of the airfoil in a symmetric fashion and as expected, the bottom bubble quickly vanishes as the angle of attack increases slightly. The re-occurrence of the bottom bubble at around 4 and 5 degrees might be an artifact, the bubble is extremely small in comparison to the separation bubble on the top of the airfoil and probably has negligible influence on the airfoil characteristics.

An alternative way to reduce the influence of laminar separation bubbles or prevent them from forming in the first place is to trip the developing boundary layers into turbulent ones (references needed). xfoil allows to specify trip locations where the boundary layers can change instantaneously from laminar to turbulent. Figure 103 compares the lift coefficient as function of angle of attack for a "dirty" wind tunnel (Ncrit=1) without tripping to the results of a clean wind tunnel (Ncrit=9) with tripping at position x/c=0.1 on the top and bottom side of the airfoil. The effect is rather similar as far as lift coefficient is concerned, but the change to turbulent boundary layer incurs a penalty in the form of a higher drag coefficient, see Fig 104, below.

Figure 103 : Lift Coefficient versus Angle of Attack

Figure 104 : Lift Coefficient versus Drag Coefficient


Zig Herzog; hgn@psu.edu
Last revised: 05/27/11