Maximum Static Lift Coefficient at Low Mach Numbers

A large body of test data exists for airfoils at essentially zero Mach number. Although these data are thus not strictly applicable to rotor blades, the trends demonstrated can be shown to apply at the Mach numbers at which the retreating blade operates in forward flight and are, therefore, of interest. The maximum static lift that can be developed by an airfoil has been found to be related to the type of stall characteristic of the airfoil. Three types of low speed stall have been identified. They are discussed in references 6.2 and 6.3 and are shown pictorially in Figure 6.1. The three types of stall are:

• Thin airfoil stalk Caused by separation of the laminar boundary layer at the nose that produces a bubble whose outer surface is laminar. At moderate angles of attack, the flow reattaches and then may become turbulent before reaching the trailing edge. As the angle of attack is increased, the reattachment point moves aft producing the characteristic long separation bubble until at stall it covers the entire top surface of the airfoil. The characteristics of thin airfoil stall are that it occurs at low Reynolds numbers, has a gentle lift stall but a sharp moment stall, may show a slight jog in the lift coefficient at about 50% of maximum lift, has hysteresis in both lift and moment, and adding leading edge roughness produces either the same maximum lift or an increase.

FIGURE 6.1 Types of Stall

• Leading edge stall. Caused by separation of the laminar boundary layer at the nose that produces a bubble whose outer surface has a transition from laminar flow to turbulent flow. This transition causes the flow to reattach quickly, thus producing a short separation bubble. The bubble effectively blunts the leading edge, giving the air molecules a gentler path. As the angle of attack is increased, the reattachment point moves forward rather than aft as in the case of thin airfoil stall, and the bubble becomes narrower but higher. At some angle of attack, the bubble becomes unstable and bursts—as a result of the unfavorable pressure gradient—separating the flow over the entire top surface. The characteristics of leading edge stall are that it has an abrupt change in both lift and moment, it has hysteresis in both lift and moment, and adding leading edge roughness decreases the maximum lift.

• Trailing edge stall: Caused by gradual separation of the turbulent boundary layer starting at the trailing edge and moving forward. Thickening the boundary layer with surface roughness will produce early stall and thus reduce the maximum lift coefficient. Trailing edge stall is gentle in both lift and moment and has no hysteresis.

Figure 6.2 shows how the measured data of the 63-OXX airfoil family exhibit the clues that typify the various types of stall. Note that it is quite common for the leading edge and trailing edge stall to occur simultaneously.

Source: Abbott & Von Doenhoff, Theory of Wing Sections (New York: Dover, 1959).

The pressure distribution over an airfoil reflects the local velocity. As the air accelerates over the nose, the pressure decreases (almost always plotted upside down on a plot of pressure distribution). Behind the nose, the air must decelerate to reach the free-stream velocity at the trailing edge, thus causing the pressure to rise. This region is called the pressure recovery region and is characterized by an unfavorable pressure gradient. The air can accelerate at almost any rate, but it can decelerate at only a limited rate; that is, it an maintain only an unfavorable pressure gradient up to a certain value, which will depend on the type and thickness of the boundary layer. Attempts to make it decelerate too rapidly will lead to separation and to the establishment of a more comfortable path away from the airfoil surface. This is illustrated by the sequence of Figure 6.3, which shows an

FIGURE 6.3 Upper Surface Pressure Distributions through Stall

Source: McCullough & Gault, “Examples of Three Types of Stall," NACA TN 2502, 1951.

airfoil undergoing leading edge stall during which the increasingly more unfavorable pressure gradient finally causes the leading edge bubble to burst, thus destroying the pressure peak and causing the pressure level over the aft portion of the airfoil to go to a nearly constant value.

Both the type of stall and the maximum lift coefficient are affected by the Reynolds number, as shown in Figure 6.4 from reference 6.3. The same airfoil may give different two-dimensional test results depending on the test Reynolds numbers. For this reason, the same airfoil may also give different results when installed on rotor blades with different chords and tip speeds. Figure 6.5 shows how Reynolds numbers vary. The characteristics of the three thinner airfoils of Figure 6.4 are the results of two trends: (1) at low Reynolds numbers a laminar

Source: Loftin & Bursnall, “The Effects of Variations in Reynolds Number between 3.0 X 106 and

25.0 X 106 upon the Aerodynamic Characteristics of a Number of NACA 6-Series Airfoil Sections,” NACA TR 964, 1950.

Local Velocity, ft/sec FIGURE 6.5 Reynolds Number Conditions at the Blade Element

boundary layer resists natural transition to a turbulent boundary layer; and (2) a laminar boundary layer will tend to separate more easily under the influence of an unfavorable pressure gradient than will a turbulent boundary layer. More specifically, the thinner airfoils exhibit thin airfoil stall at low Reynolds numbers. As long as the outer surface of the separation bubble remains laminar, increases in Reynolds. numbers have little effect on the maximum lift. At some Reynolds numbers, however, the outer surface of the bubble undergoes transition from laminar to turbulent flow, which allows reattachment to occur closer to the nose and thus delays total separation. This is characteristic of leading edge stall. As the Reynolds number is increased further, the transition point and the reattachment point move further forward thus increasing the amount of chord which is influenced by the relatively stable turbulent boundary layer. When the transition point moves to the forward edge of the bubble, the beneficial effects have been exhausted and no further rise in the maximum lift takes place. Designers of low – speed airfoils have developed a technique for changing the type of stall from thin airfoil to leading edge or from leading edge to trailing edge when it is advantageous to do so. This technique involves careful use of a contour change that produces a slightly unfavorable pressure gradient that is just steep enough to

promote transition but not steep enough to cause separation. A discussion of this technique is given by reference 6.4. A less sophisticated method is to trip the boundary layer mechanically with a transition strip consisting of a finite step or distributed roughness. The danger here is that if the tripping procedure is too severe, the resultant turbulent boundary layer will start out with a large initial thickness that will weaken its ability to withstand separation near the trailing edge.

For those airfoils that stall as a result of the separation of the turbulent boundary layer at the trailing edge, an increase in Reynolds number is beneficial in that it results in a thinner boundary layer with respect to the chord. This thinner boundary layer is more resistant to separation. The concept of the thinner boundary layer being more stable can also be used to design airfoils for high maximum lift. This is done by the use of a concave pressure distribution, with the steepest gradient just behind the transition point where the boundary layer can best negotiate it. As the boundary layer thickens, the unfavorable pressure gradient is reduced, producing a condition in which the boundary layer over the trailing edge has everywhere the same margin from separation. Such a pressure distribution is called a Stratford recovery and has been used for the two airfoils of Figure 6.6 which have achieved test values of maximum lift coefficient of over 2.2, as reported in references 6.5 and 6.6. These airfoils stall abruptly, unlike those with the more conventional type of trailing edge stall that progresses gradually from the extreme trailing edge. There is, however, little lift hysteresis as there is with the abrupt leading edge stall.

c/4

c/4 FIGURE 6.6 High Lift Airfoils

Source: Abbott & von Doenhoff, Theory of Wing Sections (New York: Dover, 1959).

Reference 6.1 presents results of the testing of 118 airfoils in the NACA low-turbulence, two-dimensional wind tunnel at test Reynolds numbers of 3 to 9 million, corresponding to the Reynolds numbers existing at the retreating tips of rotor blades with about 1- to З-foot chords. A convenient summary of the stall characteristics of these airfoils is obtained by plotting c/max against the ordinate of the upper surface at the 25% chord station. The types of stall fall into separate envelopes, as shown in Figure 6.7. It may be seen that for those airfoils that have thin airfoil or leading edge stall, the maximum lift coefficient is almost directly proportional to the ordinate at the 25% chord station. Modifying one of these airfoils by extending the trailing edge without changing the leading edge will not significantly increase the maximum lift capability of the blade, since the maximum lift coefficient will decrease as the chord is increased. For those airfoils that stall at the trailing edge, the maximum lift coefficient is nearly constant and is relatively independent of the ordinate of the upper surface.

A study of Figure 6.7 indicates several potential methods for increasing the maximum lift coefficient. One obvious method is to increase the thickness ratio as in the 0006, 0009, 0012 series. Another method is to introduce forward camber, or "droop snoot,” as in going from the 0012 to the 23012. This improvement comes from modifying the path from the stagnation point to the upper surface, as shown

in Figure 6.8. Because of the less violent changes in curvature and direction experienced as the molecules travel over the nose, the local velocities are reduced. This decreases the centrifugal force on the air, delaying the formation of the laminar separation bubble and also decreasing the magnitude of the deceleration required as the air goes toward the trailing edge (where it must slow to free stream velocity), thus decreasing the unfavorable pressure gradient. Figure 6.9 shows pressure distributions of a six-series airfoil and of its drooped nose modification from reference 6.4. The modification resulted in a 40% increase in maximum lift. Reference 6.7 reports on tests of families of airfoils produced by drooping the noses of NACA four-digit symmetrical airfoils. The results of these tests are shown in Figure

6.10, which indicates that drooping the nose is indeed an effective method of in­creasing the maximum lift coefficient. In the airplane industry, airfoils with drooped noses such as the NACA 23012 have bad reputations for abrupt stall. It appears that this is actually a characteristic of what would otherwise be considered a very good airfoil, which achieves its maximum lift coefficient by maintaining attached flow on both the leading and trailing edges longer than other airfoils do. When the flow does separate, the resultant stall is abrupt. This characteristic is not significant on rotors, however, because stall conditions are entered gradually starting with a small portion of the retreating side and also because the stall becomes less abrupt as a result of compressibility effects at Mach numbers about 0.3 or 0.4, as discussed in the next section.

A third potential for improvement is indicated in a negative way in Figure

6.7 by noting that three airfoils with very sharp noses lie below the envelope. This

Source: Hicks, Mendoza, & Bandettini, “Effects of Forward Contour Modification on the Aerodynamic Characteristics of the NACA 64,-212 Airfoil Section," NASA TM X-3293, 1975.

leads to the speculation that airfoils with very blunt noses might lie above. Tests reported in reference 6.8 have shown that blunting can produce a small but measurable improvement if done carefully. Figure 6.11 shows both good and disappointing results of increasing the nose radius. The disappointing result, from reference 6.9, is due to too sudden a change in curvature. In simple terms, the curvature of the surface governs the velocity of the air over the airfoil; thus the change in curvature governs the acceleration. If a sudden change in curvature from high to low demands a higher deceleration than the air can readily accomplish, it will separate. Most successful airfoils have gradual changes in curvature—at least in the first 10% of chord—and any modifications aimed at increasing the maximum lift coefficient should maintain this characteristic.

The final potential that can be inferred from the trends of Figure 6.7 is that the maximum lift coefficient could be increased if the trailing edge stall could be delayed. This path of development leads to the high lift airfoils of Figure 6.6.

FIGURE 6.10 Effect of Nose Droop on Maximum Lift Coefficient

Source: Jacobs, Pinkerton, & Greenberg, "Tests of Related Forward-Camber Airfoils in the Variable-Density Wind Tunnel,” NACA TR 610, 1937.