Category Helicopter Performance, Stability, and Control

As with lift and drag, the change in pitching moment due to stall is delayed if the angle of attack is rapidly increasing as the airfoil goes through its static stall angle

Source: Prouty, “Aerodynamics” column, Rotor & Wing International, Vol. 18, no. 9 (August), 1984.

of attack. Since the dynamic pressure on the retreating blade is small, any pitching – moment characteristics associated with stall would be expected to be of little importance to the aerodynamicist in terms of their effects on performance or stability. The dynamicist, however, has recognized that the delay in the pitching – moment break while going up through stall, and the corresponding delay in returning to unstalled conditions on the downstroke, can lead to negative damping, which may excite the torsional vibration mode of the blade. If the direction of change in pitching moment is nose down while the angle of attack is changing nose up, or vice versa, the damping is positive. The top portion of Figure 6.42 illustrates this with a simple schematic representing an airfoil model mounted on a shaft through a moment balance and restrained by a damper. If the inertia of the model is neglected, the moment measured by the balance is just that caused by the damper, and a plot of moment versus angle of attack as the shaft is oscillated will trace out a counterclockwise hysteresis loop. Thus a plot of aerodynamic pitching moment from an oscillating airfoil test will show positive damping for regions enclosed by counterclockwise loops, but negative damping for regions enclosed by clockwise loops. The lower portion of Figure 6.42 from reference 6.63 shows the hysteresis curves for a NACA 0012 as it oscillates ±6° about mean angles of 0°,

12°, and 24°. The data show positive damping for the low and high mean angles representing nonstalled and fully stalled conditions, but show both positive and negative damping through the stall region. The negative damping region represents a condition where energy is being extracted from the airstream and put into the oscillating blade. This is the source of stall flutter, which, if allowed to persist, could result in serious structural problems. Fortunately, helicopters generally subject their blades to the stalling conditions only during a small portion of the retreating side. For this reason, only a few cycles of oscillation can occur before the angle of attack drops below stall and has positive damping. The phenomenon manifests itself on some helicopters in the form of high control system loads and vibration levels. Detailed discussions of these aspects of stall flutter may be found in references 6.64 and 6.65.

When the speed at a blade element is high enough that shock waves are formed, the resulting effects can drastically change the pitching-moment characteristics.

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

One of the most important changes is the so-called Mach tuck, a sudden nose – down pitching moment that was encountered on airplanes as their dive speeds first approached transonic conditions. When this occurs on the advancing tip of a helicopter rotor, it may produce high enough loads in the blades and control system to effectively limit the maximum allowable forward speed. For most airfoils that have been tested in two-dimensional wind tunnels, the Mach tuck characteristic comes slightly after drag divergence. This does not eliminate the Mach tuck problem, however, since drag divergence may be exceeded in many flight conditions.

Aft-cambered airfoils generally have a worse Mach tuck problem than do forward-cambered airfoils, as illustrated by the pitching-moment coefficient at zero lift shown in Figure 6.39, which is based on curves presented in reference 6.57. The basic source of the nose-down pitching moment is the change in the shape of the pressure distribution as the flow becomes supercritical and shock waves are established, first on the top surface and then on the bottom. This change is illustrated in Figure 6.40. Since the changes in pressure distribution patterns are caused by the shock waves, any reductions in shock wave strength, such as those obtained by supercritical airfoil design techniques, will be beneficial in decreasing the Mach tuck problem.

Trailing edge tabs that are used to adjust the pitching moment at low Mach numbers appear to retain most of their effectiveness at high Mach numbers, according to wind tunnel data presented in reference 6.57.

Symmetrical airfoils, of course, do not exhibit Mach tuck at zero lift, but they do produce compressibility-related pitching moments when developing some

Source: Dadone, “Helicopter Design Datcom,” Vol. I. “Airfoils,” USAAMRDL CR 76-2, 1976.

Source: Hughes, unpublished document.

lift. The presence and relative position of shock waves on both the upper and lower surfaces at about M = 0.9 causes the pitching moment to vary with angle of attack as the shock waves shift position. This produces a definite reversal in pitching-moment characteristics for small angles of attack such that the pitching moment generates an unstable blade twist—that is, an increased angle of attack twists the blade nose up and vice versa. This characteristic was identified in reference 6.61 as the cause of a significant dynamic problem involving an out-of­track phenomenon occurring every other rotor revolution on the Sikorsky NH-3A compound helicopter when the advancing tip Mach number exceeded 0.92. Figure 6.41 from reference 6.62 shows wind tunnel results for the NACA 0012 in the Mach number region from 0.80 to 0.96. It may be seen that at M = 0.90, even the lift curve slope exhibits a reversal. This odd behavior is not limited to symmetrical airfoils. Reference 6.57 shows that the VR-7 also has reversals in both pitching moment and lift at a Mach number of 0.82 and a ct of about —0.3.

The position of the aerodynamic center is important in designing the blade to be free of flutter. The more aft the aerodynamic center is, the less weight will have to be installed in the nose to achieve the proper balance. It has been estimated that

moving the aerodynamic center back 2% of the chord can result in a 10% saving in total blade weight. The positions of the aerodynamic center of NACA airfoils are listed in reference 6.1. For the four – or five-digit airfoils, the aerodynamic center is on or ahead of the quarter chord; for the six-series airfoils, the aerodynamic center is behind the quarter chord. For a given thickness ratio, the position of the aerodynamic center is roughly proportional to the enclosed trailing edge angle, as shown in Figure 6.38. The addition of a flat tab to the trailing edge is an effective way to decrease the trailing edge angle and to move the aerodynamic center aft. The measured effect of tabs on several airfoils is as follows:

Reduction of pitching moments on a given airfoil can be achieved by using a reflex trailing edge either as an integral part of the airfoil design or as an add-on flat tab. Several wind tunnel tests of airfoils with tabs have been made. Figure 6.37 summarizes the results presented in references 6.9,6.10,6.21, and 6.49 in terms of the effect of tab deflection on both cm and c, as a function of the ratio of tab to airfoil chord. The test results for pitching-moment sensitivity correlate well with those obtained from thin airfoil theory as given in reference 6.1. It may be seen that the larger tabs are desirable for their ability to produce a pitching moment

while minimizing the penalty to maximum lift coefficient. Drag penalties of tabs appear to be small—in most cases not much more than the accuracy of the drag measurement.

During the autogiro era of rotary wing flight, some frightening moments resulted from extreme blade twisting and high control loads with cambered blade airfoil

Source: Philippe & Sagner, “Aerodynamic Forces Computation and Measurement on an Oscillating Aerofoil Profile with and without Stall," AGARD CP 111, 1972.

sections that had high aerodynamic pitching moments. In one case, an autogiro with airfoil sections that had nose-down pitching moments entered an unscheduled high-speed dive as the aerodynamic moments twisted the advancing blade nose down and produced effective forward cyclic pitch, even though the pilot had his stick all the way back! Experiences like this led to a period of almost exclusive use of low-moment, symmetrical airfoils. The development of stiffer blades and control systems has alleviated the problem somewhat, so that cambered airfoils with some inherent pitching moment can again be considered. It is noteworthy, however, that even symmetrical airfoils can produce substantial moments at high angles of attack and high Mach numbers. This is illustrated in Figure 6.36, from

Source: Dadone, "Helicopter Design Datcom,” Vol. I. “Airfoils," USAAMRDL CR 76-2, 1976.

reference 6.57, which shows the product of the pitching-moment coefficient and Mach number squared for the symmetrical NACA 0012 airfoil within the Mach number range encountered by rotors. (This presentation has been chosen since the product is directly proportional to the actual moment generated at the blade element.) Also shown are two cambered airfoils, one with forward camber and one with aft camber. It may be seen that forward camber has only a small effect on the pitching moment, whereas aft camber has a large effect.

The amount of aerodynamic pitching moment that can be tolerated in a given helicopter rotor depends on the structural and dynamic characteristics of the blades, hub, and control system. Thus the experience of various helicopter manufacturers has been different. Vertol has found that for their rotors, the value of cm— the pitching moment coefficient at zero angle of attack and low Mach number—should be slightly positive (about 0.01) to maintain a satisfactory control system oscillatory load level. On the other hand, the use of a highly cambered airfoil with а г of about —0.07 on a Hughes tail rotor, reported in reference 6.58, produced only a small increase in oscillatory pitch link loads compared to the symmetrical airfoil it replaced, since the loads due to the aerodynamic pitching moments were out of phase with the existing pitch link loads. Tests of a model rotor using both a NACA 0012 airfoil and the same airfoil with the aft 20% deflected down 5° are reported in reference 6.59. It was found that for cases in which the retreating blade was stalled, the control loads were lower for the blade with the modified trailing edge than for the blade with the standard NACA 0012 airfoil, although below stall the opposite was true. It appears that the component of control and blade loads produced by the various modes of blade deflection can be as high as those due to aerodynamic pitching moments on the airfoil, and that the two can either add or subtract depending on the particular flight condition and the dynamic characteristics of the blade.

At the time of this writing, the accepted limit for cm for main rotors is:

It can be expected that more experience with cambered airfoils on a variety of rotors will lead to the establishment of more rational limits.

For conditions in which there is no separation and no significant compressibility effects, the drag of the airfoil is primarily due to skin friction, whose coefficient is a function of the local velocities on the surface and whether the boundary layer is laminar or turbulent. Figure 6.30, from reference 6.1, shows the effect of Reynolds number on the calculated minimum drag coefficient for fully laminar and for fully turbulent boundary layers. Also shown are wind tunnel results for several airfoils. Laminar flow can usually be maintained only on the nose of the airfoil where the flow is accelerating. Thus no airfoil can take full advantage of laminar flow; but some, such as the six-series airfoils, keep the flow accelerating further back than others and thus have a larger region of laminar boundary layer. As a matter of fact,

Pressure Distributions on Four NACA 64A-Series Airfoil Sections at Angles of Attack as High as 28°,” NACA TN 3162, 1954; Abbott & Von Doenhoff, Theory of Wing Sections (New York: Dover, 1959); Wiesner & Kohler, “Tail Rotor Design Guide,” USAAMRDL TR 73-99, 1973; Davenport & Front, “Airfoil Sections for Helicopter Rotors—A Reconsideration,” AHS 22nd Forum, 1966; Graham, Nitzberg, & Olson, “A Systematic Investigation of Pressure Distributions at High Speeds over Five Representative NACA Low-Drag and Conventional Airfoil Sections,” NACA TR 832, 1945; Gothert, “Airfoil Measurements in the DVL High-Speed Wind Tunnel,” NACA TM 1240.

Droop

the six-series airfoils were originally known as laminar flow airfoils and were especially designed to take advantage of this effect. Wind tunnel tests of these airfoils showed that, compared to other airfoils, the drag coefficient had only a small rise as the angle of attack was increased until at some angle of attack most of the boundary layer suddenly became turbulent. This resulted in the drag bucket illustrated in Figure 6.31. Subsequent use of these airfoils on airplanes in the 1940s and 1950s proved disappolhting from a drag standpoint, since dirt, bugs, and surface imperfections triggered premature transition to turbulent flow and nullified the promising characteristics that had been measured on carefully shaped and polished wind tunnel models.

There is some indication—primarily based on the observations of reference 6.51—that a rotor blade, even one with leading edge erosion, can maintain laminar flow more easily than a wing, possibly because built-in surface imperfections are usually less and also because pitting is less detrimental than protrusions.

Even though the six-series airfoils were disappointing from a skin friction standpoint, it was found that some of them had lower drag characteristics for certain combinations of lift coefficients and Mach numbers than did the older airfoils. Figure 6.32 shows drag data for two 15% thick airfoils, a NACA 23015 and a 66.2-215 taken from reference 6.17. At low lift the drag characteristics of the two airfoils are similar, but at higher lift the six-series airfoil has higher drag at low Mach numbers but dips to lower drag at high Mach numbers. At the time

Source: Graham, Nitzberg, & Olson, “A Systematic Investigation of Pressure Distributions at High Speeds over Five Representative NACA Low-Drag and Conventional Airfoil Sections," NACA TR 832, 1945.

these test results were published (1945), the low drag could not be explained and the dips could only be called "peculiar.” We now know that these dips are characteristic of the class of airfoils that has come to be known as supercritical, which benefit from an advantageous pattern of expansion and compression waves, as shown in Figure 6.16. It is typical of all these airfoils that the region of low drag is limited to a narrow range of operating conditions. The design task for the

airplane aerodynamicist is to design airfoils in which this region coincides with the cruise Mach number and lift coefficient of the airplane. Since the helicopter rotor experiences a much wider range of operating conditions than a wing, it is more of a challenge to adapt this concept to a rotor blade; attempts to do this are outlined in references 6.52 and 6.53. Some whirl tower tests of rotors with six-series airfoils, or modifications of this family, indicate a small but measurable advantage in hover over the older airfoils. These tests are reported in references 6.16, 6.54, and 6.55. It is not known whether these benefits were due to increased laminar flow or to supercritical characteristics. Figure-6.33 shows a comparison of two-dimensional data backing up these whirl tower results.

Comparison of one airfoil with another with respect to drag characteristics should be done at the same Reynolds number if possible. Figure 6.34 shows the results of tests on a single airfoil at several Reynolds numbers. It may be seen that at the same Mach number and lift coefficient, the coefficient of drag decreases as the Reynolds number—or chord—is increased. The effect is present in other sets of wind tunnel data, though usually not as dramatically as in this case. It appears that from the standpoint of minimum profile power, a rotor with a few wide – chord blades is better than one with many narrow-chord blades. It is also evident that those computer programs that use tabulated values of aerodynamic coefficients may introduce sizable errors unless the data are based on the Reynolds number corresponding to the chord of the blade. When new tests in pressurized wind tunnels are being planned, consideration should be given to running at

Source: Benson, Dadone, Gormont, & Kohler, “Influence of Airfoils on Stall Flutter Boundaries of Articulated Helicopter Rotors,” JAHS 18-1, 1973.

Source: Sipe & Gorenberg, “Effect of Mach Number, Reynolds Number, and Thickness Ratio on the Aerodynamic Characteristics of NACA 63A-Series Airfoil Sections,” USATRECOM TR 65-28, 1965.

constant equivalent chords by matching the test Reynolds number to the Mach number whenever possible.

The airplane people have found that a wing can have a blunt trailing edge without a significant base drag penalty if the trailing edge thickness is less than that of the boundary layer on the upper surface. This can result in an allowable trailing edge thickness of about 1% of the chord, as used on the Lockheed S3-A antisubmarine airplane. This feature might be considered for those blades that need high chordwise stiffness.

Effect of Unsteady Aerodynamics on Drag

The oscillating airfoil experiments of references 6.23 and 6.33 used surface – pressure surveys, which are good for measuring instantaneous lift and pitching moment but are not usable to establish the instantaneous drag. Fortunately, another set of tests reported in reference 6.56 used strain gauge balances instead of pressure measurements and thus measured the instantaneous drag. Figure 6.35 shows typical lift and drag loops. It may be seen that the delay in drag corresponds
fairly well to the overshoot in lift and thus can be characterized by the same increase in the stall angle of attack.

The advancing tip operates at nearly zero lift coefficient at high speed, so the drag characteristics of the airfoil in this condition are important. As the free stream

Mach number is increased toward and beyond its critical Mach number, the local velocity on the surface first reaches the speed of sound and then exceeds it, until at some speed and at some position on the airfoil a shock wave is formed through which the velocity decreases to a subsonic value. Tests show that if the shock is weak and close to the nose, there is no significant drag penalty; but as the shock

FIGURE 6.27 Gamma Function as Affected by Mach Number

passes beyond the crest or, for this condition, the position of maximum thickness, the drag increases rapidly as a result of the momentum loss through the shock (wave drag) and m some cases as a result of separation of the boundary layer (shock stall). The free stream Mach number at which the drag coefficient increases significantly is known as the drag divergence Mach number. In many studies, it is defined as the Mach number at which the drag coefficient rises at the rate of 0.1 per unit Mach number. For helicopter applications, however, where the magnitude of the drag change may be more significant than the rate of increase, it is щоге appropriate to define it as the Mach number at which the drag coefficient is twice its incompressible value. Using this definition, the measured two-dimensional drag divergence Mach numbers of a number of airfoils at zero lift as reported in references 6.1, 6.13, 6.17, 6.21, 6.46, 6.47, 6.48, 6.49, and 6.30 have been compiled and are plotted in Figure 6.28a as a function of thickness ratio. It may be seen that the symmetrical airfoils of all families form a reasonably tight grouping, but that

(a)

Sources: Sipe & Gorenberg, “Effect of Mach Number, Reynolds Number, and Thickness Ratio on the Aerodynamic Characteristics of NACA 63A-Series Airfoil Sections,” USATRECOM TR 65-28, 1965; Van Dyke, “High-Speed Subsonic Characteristics of 16 NACA Six-Series Airfoil Sections," NACA TN 2670,1952; Wilson & Horton, "Aerodynamic Characteristics at High and Low Subsonic Mach Numbers of Four NACA Six-Series Airfoil Sections at Angles of Attack from -2° to 31 NACA RM 876 (L53620), 1953; Stivers, “Effects of Subsonic Mach Numbers on the Forces and

the six-series cambered airfoils generally have lower drag divergence Mach numbers. Even these airfoils can be brought into the grouping if the physical parameter is taken as twice the maximum upper ordinate instead of the thickness ratio, as shown in Figure 6.28b.

Just as with the maximum lift coefficient, the scatter of the points in Figure 6.28 represents differences in airfoils and differences in tunnels. Some airfoils have beneficial supercritical characteristics—either by design or by accident—and thus have measurably higher drag divergence Mach numbers than average. For other airfoils, the supercritical characteristics might be detrimental if an expansion wave is located ahead of the shock instead of a compression wave. The difference that a tunnel can make is shown by 5 points for the NACA 0012 airfoil.

A conclusion that can be drawn from Figure 6.28 is that for the same thickness ratio, aft camber as used in the six-series airfoils lowers the drag divergence Mach number, but that forward camber as used in the five-digit airfoils has little effect. This conclusion, however, must be qualified. If the nose is drooped so far that the lower surface becomes concave, the drag curve at zero lift can have the distinct characteristic shown for the 33008 airfoil in Figure 6.29 from reference 6.9. This is known as a “creepy” drag rise and is apparently due to a shock wave formed on the lower surface that locally separates the boundary layer in the concave region. Even airfoils with moderate forward camber may exhibit significant drag creep at small negative angles of attack such as might exist on the advancing tip at high speeds.

The airplane people discovered some time ago that when a wing’s angle of attack is increased rapidly, it can momentarily generate a higher maximum lift coefficient than it could if the angle of attack were increased slowly. This also applies to helicopter blades. A good review of the phenomenon, which is referred to as dynamic stall, will be found in reference 6.27. Figure 6.20 shows this dynamic overshoot as measured during ramp-type angle-of-attack increases in the two- dimensional tests reported in reference 6.28. The overshoot can be related to the change in angle of attack during the time required for the airfoil to travel one chord length. For airfoils that stall first at the leading edge, the dynamic overshoot is attributed to two effects: the delay in the separation of the boundary layer, and the momentary existence of a vortex shed at the leading edge after the boundary layer does separate. These effects are discussed in reference 6.29. The delay in

Source: Lizak, “Two-Dimensional Wind Tunnel Tests of an H-34 Main Rotor Airfoil Section," USA TRECOM TR 60-53, 1960; Davenport & Front, “Airfoil Sections for Helicopter Rotors—A Reconsideration," AHS 22nd Forum, 1966; Racisz, "Effects of Independent Variations of Mach Number and Reynolds Numbers on the Maximum Lift Coefficients of Four NACA Six-Series Airfoil Sections,” NACA TN 2824, 1952.

separation corresponds to the finite time required for the aft edge of the separation bubble to move forward to its bursting position. This time delay is lengthened if the airfoil is pitching nose up, for two reasons. First, the motion raises the position of the stagnation point, as shown in Figure 6.21, and produces an effect similar to drooping the nose, which was shown to be beneficial for static stall. Second, the nose-up pitching motion causes the boundary layer to develop a fuller and more stable profile, which resists separation. A quantitative evaluation of the second effect is given in reference 6.30. If the airfoil has plunging motion instead of pitching motion, the maximum angle of attack occurs while the airfoil is descending, and thus the nose droop and pressure gradient effects are detrimental instead of beneficial. Nevertheless, an airfoil in plunge still exhibits a dynamic overshoot, though not as great as that of the airfoil in pitch.

Even after the leading edge separates, the airfoil can momentarily still generate high lift as a result of a vortex that is shed at the leading edge at the

instant of stall. The vortex travels back over the top of the airfoil at approximately half of the free stream velocity, according to reference 6.31, carrying with it a low – pressure wave that accounts for the very large lift coefficients shown in Figure 6.20.

Airfoils that stall first at the trailing edge also exhibit a dynamic overshoot, though considerably less than those airfoils that have leading edge stall. For example, reference 6.32 shows that a 16% thick airfoil, which would be expected to have trailing edge stall, has approximately half the dynamic overshoot of a 9% thick airfoil, which would be expected to have leading edge stall. The favorable effect of pitching motion for trailing edge stall is apparently the thinning of the boundary layer near the nose, which has a beneficial effect extending to the trailing edge. .

Wind tunnel tests of oscillating, two-dimensional airfoils are reported in References 6.23, 6.33, 6.34, and 6.35. The first set of tests used modified NACA 0012 and 23010 airfoils and oscillated them in sinusoidal pitch and plunge motions at Mach numbers from 0.2 to 0.6; the second set used modified NACA 0006 and 13006 airfoils oscillating only in pitch through the same Mach number range; and the third set used a NACA 0012 in sinusoidal and sawtooth pitch oscillations at a Mach number of about 0.3. The tests of reference 6.35 used several modern airfoils, but at low Mach numbers. Some of the primary effects of varying the test parameters are shown in Figure 6.22. The first set of comparisons shows that oscillations entirely below stall or entirely above stall have only small dynamic effects, but that oscillation through stall produces a hysteresis loop in which stall is

Source: Ham & Garelick, “Dynamic Stall Considerations in Helicopter Rotors," JAHS 13-2, 1968.

reached late on the upstroke and is induced early on the downstroke. Reference 6.36 suggests that the lower limit of stalled lift on the downstroke is approximately the static maximum coefficient of a flat plate. Note that the lift coefficient above the stall angle of attack in Figure 6.22 does not go below 0.6. The second set of comparisons shows that the dynamic overshoot is a function of the frequency of oscillation. The frequency is expressed in terms of the reduced frequency, k: where 0) is the frequency of oscillation in radians per second, c/2 is the semichord, and V is the local velocity. Physically, k is the portion of the oscillation cycle, in radians, which occurs during the time the air travels half of a chord length over the airfoil. For a blade element, the velocity is the tangential velocity, UT. In order to

obtain an understanding of the approximate magnitude of kf assume a rotor in hover is undergoing a once-per-rev pitch change. Then the reduced frequency at the tip is one-half the amount of azimuth subtended by the chord:

k =—1— np 2 (R/c)

or, for the example helicopter with a 30-ft radius and a 2-foot chord:

*rip= 0.033

The reduced frequency will be higher for inboard blade elements, for blade elements on the retreating blade in forward flight, or for blade elements that are being subjected to higher frequencies because they are coming close to a series of vortices shed by the tips of previous blades or being affected by blade torsional oscillations. The effect of increasing the Mach number is shown in the third set of comparisons in Figure 6.22. At low Mach numbers, the airfoil has leading edge stall; thus changes in conditions at the nose are significant in determining the amount of dynamic overshoot. At higher Mach numbers, however, where stall is caused by separation behind a shock wave, the stall occurs before the nose conditions become critical, and thus the pitching motion produces less over­shoot.

A blade element in flight experiences plunge motion where the leading and trailing edges have vertical velocity in the same direction, as well as pitch motion where the leading and trailing edges have vertical velocities in opposite directions. The equation for the local angle of attack is:

Effect of Mean Angle of Attack, ap
M = A, к = .12

Effect of Reduced Frequency, к
M – .4, a0 = 12.5°

Effect of Mach Number, M к = .12

Source: Liiva, Davenport, Gray, & Walton, “Two-Dimensional Tests of Airfoils Oscillating Near Stall,” USAAVLABS TR 68-13, 1968.

a = 0 + tan 1 jy-

U т

and thus the rate of change of angle of attack is:

. a _XU? a = 0 + tan —

и т

where the first term is the rate of pitch (up) and the second is the rate of plunge (down). It is of interest to note that in the third quadrant, where the blade is pitching up, it is also plunging up as a result of the effects of coning and of the longitudinal gradient of induced velocity. Figure 6.23 shows that for the NACA 0012 airfoil, the dynamic overshoot corresponding to plunge is considerably less than that due to pitch.

Sources: Liiva et al., “Two-Dimensional Tests of Airfoils Oscillating Near Stall,” USAAVLABS TR 68-13, 1968: Gray & Liiva, “Wind Tunnel Tests of Thin Airfoils Oscillating Near Stall,” USAAVLABS TR 68-89, 1969.

Sources: Liiva, Davenport, Gray, & Walton, “Two-Dimensional Tests of Airfoils Oscillating Near Stall,” USAAVLABS TR 68-13, 1968; Gray & Liiva, “Wind Tunnel Tests of Thin Airfoils Oscillating Near Stall,” USAAVLABS TR 68-89, 1969.

A limited indication of the effect of the airfoil physical parameters on dynamic overshoot is given by Figure 6.24, which shows test values of dynamic overshoot in both pitch and plunge as a percentage of the static maximum lift coefficient for the four airfoils of references 6.23 and 6.33.

Another set of dynamic test results for a number of modern helicopter airfoil sections oscillating in pitch at a Mach number of 0.3 is reported in reference

6.35. Figure 6.25 summarizes the results. One conclusion that can be drawn is that

Source: McCroskey et al., “Dynamic Stall on Advanced Airfoil Sections,” JAHS 26-3, 1981.

the dynamic overshoot in lift coefficient is nearly independent of the airfoil shape, varying from 0.7 to 0.8 for this group.

A number of ways have been suggested for representing the dynamic overshoot in actual practice. Several sophisticated analytical methods are given in references 6.37, 6.38, 6.27, and 6.39. These use potential flow and boundary-layer equations to predict the separation angle. Although they might be suitable for predicting the performance of an oscillating airfoil in a wind tunnel, they are much too complicated to use in a rotor analysis program. Three simpler methods based on empirical studies of oscillating airfoil wind tunnel data have been used in rotor programs and, at this writing, all must be considered valid, although none of them has undergone rigorous comparison against a wide range of rotor experimental data.

. The method of reference 6.40 as expanded in references 6.31 and 6.41 calculates the overshoot of angle of attack as a function of the pitch rate, which is taken as the rate of change of the calculated angle of attack. The method is based on a series of analogies backed up by the selected test results. It does suffer, however, from a confusing writeup and a lack of explicitly stated correlation factors.

The method of references 6.34 and 6.42 is based on the observation that the overshoot is a function not only of the angle of attack and its velocity, but of the acceleration as well. Tabulated influence factors as a function of these three parameters are stored in the computer, or curve-fitting equations are used based

on analysis of test data. Hints for extrapolation to test conditions or airfoils not tested are given in reference 6.42.

The method of reference 6.43 is also based on test data. It uses the angle of attack and its velocity in empirical equations to approximate the dynamic overshoot. This is the method used for calculations in this book and is explained in detail in Chapter 3 under "Unsteady Aerodynamics and Yawed Flow." This method relies on conclusions derived from wind tunnel results that the angle of attack corresponding to the maximum lift coefficient in a dynamic situation can be directly related to the parameter: уrd/2V. For this purpose, the rate of change of angle of attack, d, is defined as the rate the airfoil had when it reached its maximum lift. To evaluate fcdjw from wind tunnel data of an airfoil oscillating at a frequency, (0, about some average angle of attack, a0, through an amplitude, ± Да, the instantaneous angle of attack is:

а = а0 + Да sin ш and

d = Дат cos (о/

At the instant of stall:

thus

• A • —і I ^stall a0

а = Дао) cos sin 1

From the definition of the reduced frequency, k, previously used:

thus

The test data for four different oscillating airfoils tabulated in references 6.23 and 6.33 include all of the factors required to evaluate у/cd/2V. (Note that the only usable test points are those for which the maximum lift was reached before the maximum angle of attack, since at that point the rate was zero.) Strictly speaking, the dynamic angle of overshoot is the difference between the measured angle of attack at maximum lift for the dynamic and static test conditions, but sometimes the lift curve slope is reduced at high angles of attack so that the magnitude of the angle of attack overshoot is much greater than that

corresponding to the overshoot of maximum lift coefficient. For use in the analysis, which assumes that the increase in maximum lift coefficient is directly proportional to the overshoot of angle of attack, an effective stall angle has been defined based on the measured maximum lift coefficient; the slope of the lift curve; and, in the case of the cambered section, the angle of zero lift:

ci

„ max. „ j

Cl stall ff = + С1ц>

a

In Figure 6.26, the data for the V0011 and the V23010-1.58 are plotted. The slope of the lines through the data points is the function, y, where:

ttstall – dstaU = Ай = Y staueff Staustatic 1

The values of у for pitching oscillations from Figure 6.26 have been plotted on Figure 6.27 as a function of Mach number. Both the values and the trend with Mach number are different from those indicated by reference 6.43 which analysed the same test data. The differences arise primarily from the fact that reference 6.43 plots actual stall angles at which maximum lift is achieved, whereas in Figure 6.26 the effective stall angle is plotted. Another difference is apparently in the interpretation of the test data for Mach number of 0.6. This can be illustrated by examining the dynamic stall hysteresis loop at M = 0.6 in the lower right-hand corner of Figure 6.22. The angle of attack overshoot can be referenced either to the initial static stall at about 6° or to the final static stall at about 15°. In the case of the first, there is considerable angle of attack overshoot; in the case of the latter, none at all as was apparently assumed in the studies of references 6.43 and 6.44. The method used in this book was based on the 6° stall angle as being a more realistic value in light of how the results are used in the analysis.

Confession: The forward flight charts of Chapter 3 were computed before this study was made. The gamma function used was similar to the lines defined by the solid points (and dotted lines) in figure 6.27. Fortunately, the results are about the same for the blade tips at the tip speed ratio range of 0.25 to 0.35, which includes most conventional high-speed flight.

A comparison of the overshoot during pitch oscillations and plunge motions is given in reference 6.45 for M = 0.4. The general conclusion is that at this Mach number the gamma functions are not significantly different for the two types of motion, and thus they do not have to be treated differently in the analysis.

DRAG CHARACTERISTICS

The test results discussed so far are in the Reynolds number range of interest to blade designers but were obtained at essentially zero Mach number, whereas the blade elements that are likely to stall on an actual rotor operate at Mach numbers from 0.25 to 0.5. The effects of compressibility on the lift characteristics of the NACA 0012 airfoil are shown in Figure 6.12 from reference 6.10. Even at relatively low Mach numbers, the local velocity over the surface can exceed the speed of sound, giving supercritical or mixed flow as indicated by the hatched lines. For this condition, the air returns to subsonic flow before reaching the trailing edge by passing through a shock wave. If the velocity is only slightly supercritical, the shock wave will be weak and its primary effect on maximum lift will be to thicken the boundary layer and thus increase the tendency toward early trailing

edge stall. This is shown by the change in stall characteristic between 0.3 and 0.4 Mach number. For high supercritical velocities, the shock wave may be strong enough to cause the boundary layer to separate entirely, thus producing shock stall. Figure 6,13 shows measured pressure distributions for selected angles of attack at

0. 3, 0.4, and 0.65 Mach numbers. It may be seen that at the lower Mach numbers the large pressure peak generated at maximum lift is rapidly destroyed as the airfoil stalls. At higher Mach numbers the height of the pressure peak is limited by the inability of the flow to sustain local Mach numbers above about 1.4. At an angle of attack of 18° and a Mach number of 0.65, the 0012 has extreme shock stall. Despite this, its lift coefficient is high and is still rising, leading to the observation that the term maximum lift coefficient loses its significance in these circumstances. A good survey of the influence of Mach number on maximum lift is presented in reference 6.11.

FIGURE 6.12 Effect of Mach Number on Lift Characteristics of 0012 Airfoil

Source: Lizak, “Two-Dimensional Wind Tunnel Tests of an H-34 Main Rotor Airfoil Section,” USA TRECOM TR 60-53, 1960.

Most modern jet transports cruise at speeds such that a shock wave stands just ahead of the quarter-chord of the wing. The shadow of this shock wave can sometimes be seen when the wing is pointed toward or away from the sun.

Even at high Mach numbers, variations in Reynolds numbers are significant. Wind tunnel tests of several six-series airfoils at various Reynolds numbers and Mach numbers are reported in reference 6.12, and the results for one of these, the NACA 64-210, are shown in Figure 6.14. Since Mach number and Reynolds number are directly related for a given chord, lines of constant chord can be plotted across the family of curves. For sea-level, standard conditions:

.14 R. N./106

M =———————–

Source: Racisz, “Effects of Independent Variations of Mach Number and Reynolds Number on the Maximum Lift Coefficients of Four NACA 6-Series Airfoil Sections,” NACA TN 2824, 1952.

It may be seen that the chord has a strong influence on the effect of Mach number on maximum lift. The larger the chord, the higher is the detrimental effect. As a matter of fact, tests with very small chord models may show beneficial effects. This is illustrated by the test data on Figure 6.15 from reference 6.13 where the effective chord varied from 5 inches at low Mach numbers to 3.8 inches at high Mach numbers. This figure also shows a rather surprising result—that for these test conditions the 64A010 airfoil has a maximum lift coefficient that is somewhat lower than the thinner 64A006 airfoil. The probable reason is that both these airfoils are experiencing pure thin airfoil stall, which is not significantly affected by thickness ratio at low Reynolds numbers. A maximum lift coefficient of 0.8 is typical of a flat plate or of a NACA 0012 tested backwards, according to references 6.14 and 6.15.

The steady reduction of maximum lift coefficient of large chord airfoils with Mach number above.3 shown on Figure 6.14 is not necessarily a trait of all airfoils. The type of airfoil known as supercritical or peaky can actually experience an increase in maximum lift coefficient with Mach number. A supercritical airfoil is one on which the nose is shaped such that the strength of the shock wave is reduced by slowing the air ahead of it through a favorable arrangement of expansion and

Source: Stivers, “Effects of Subsonic Mach Number on the Forces and Pressure Distributions on Four NACA 64A-Series Airfoil Sections at Angles of Attack as High as 28°, NACA TN 3162, 1954.

compression waves, as shown in Figure 6.16. The initial expansion wave is generated by the high nose peak on the pressure distribution, which is reflected from the sonic line as a compression wave and then from the airfoil surface as another compression wave. If the shock wave is located in the region influenced by the second compression wave, its strength will be reduced as a result of the lower local velocity, and its ability to produce shock stall by separating the boundary layer will be correspondingly reduced. If the shock wave lies at some other location, the shock stall may be more severe. Thus the favorable conditions exist only for certain combinations of angle of attack and Mach number, and a penalty may apply to operating at other combinations. The first half of Figure 6.17, from reference 6.16, shows that a 12% thick airfoil with supercritical characteristics has a higher maximum lift coefficient than a 12% thick drooped-nose airfoil only for Mach numbers above about 0.43. At low Mach numbers, the peak on the supercritical pressure distribution—and the corresponding unfavorable pressure gradient behind it—encourages early bursting of the laminar separation bubble. Results for the NACA 0012 from the same series of tests are also shown for comparison. It

may be seen that both of the cambered airfoils are better than the symmetrical airfoil, because the upper surface coordinate at the quarter chord is higher and the corresponding benefit shown in Figure 6.7 applies. Similar results for 15% thick airfoils are also shown in Figure 6.17 from reference 6.17. A complete discussion of supercritical airfoils is given in reference 6.18, and procedures for designing these airfoils for rotors are described in references 6.19 and 6.20.

Figure 6.18 shows the effect of Mach number on the measured maximum lift coefficients of several airfoils with nominal 2-foot chords as reported in references 6.10,6.12, 6.21, and 6.22. Those airfoils that have good characteristics at low Mach numbers appear to retain their relative advantage in the Mach number range of the retreating blade: from 0.25 to 0.5.

Some caution should be exercised in drawing conclusions on the relative merits of the various airfoils shown in Figure 6.18, since the results appear to be affected by the wind tunnel that produced them. Figure 6.19 shows test results for the NACA 0012 airfoil obtained from several tunnels as reported in references 6.9, 6.10, 6.22, 6.23, 6.24, 6.25 and 6.26. It is possible that the difference between tunnels is associated with the thickness of the boundary layer on the side walls and

Sources: Benson, Dadone, Gormont, & Kohler, “Influence of Airfoils on Stall Flutter Boundaries of Articulated Helicopter Rotors,” JAHS 18-1, 1973; Graham, Nitzberg, & Olson, “A Systematic Investigation of Pressure Distributions at High Speeds over Five Representative NACA Low-Drag and Conventional Airfoil Sections,” NACA TR 832, 1945.

the amount of the model affected. In any case, the differences should be resolved for the good of both the helicopter aerodynamicist and the wind tunnel engineer.

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.

• 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

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.

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.

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.

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