Aerodynamics of Rotor Airfoils
It [the Gottingen-429] is a reasonably efficient airfoil, although others give greater lift and a great many different curves [airfoil shapes] are used for designing airplanes. But, the important advantage of this particular type is that its center of lift or pressure is approximately the same at all angles which it may assume in flight. This is not true of other types of airfoil, so that center of pressure travel is a factor to be reckoned with in using them.
Juan de la Cierva (1931; in reference to the twisting moment produced on autogiro blades by a cambered airfoil.)
The goal of this chapter is to review the aerodynamics of airfoils and to discuss their potential impact on helicopter rotor performance. An improved understanding and predictive capability of rotor airfoil characteristics will always lead to an improved analysis capability of existing rotor designs and may ultimately lead to new rotors optimized for greater performance in both hover and forward flight. The selection of airfoil sections for
* о **Vk Г» jA 1 ffl />lllf Л fivA/1 n 1 ІМЛЛЛП ПЛ г» tlrtf ГЧ/М
іиілла id mwit’ uuuv^uu Lixau іш a илл^и-wing anvian іл/tau^ uiv^J uui jpunu
designs; that is, the AoA and Mach number vary continuously at all blade elements on the rotor and one airfoil section cannot meet all the various aerodynamic requirements.
On early helicopters, little attention was paid to the selection of airfoil section because there were just too many other technical problems to solve. Although the NACA had developed some special helicopter airfoils in the late 1940s, it was not until the middle of the 1960s that airfoil sections specifically tailored to meet the special requirements of helicopters became more widely used by manufacturers. Since then, the major helicopter manufacturers and research organizations have developed various families of improved airfoil profiles for use on helicopter rotors. Each airfoil profile within the family will have specific aerodynamic and geometric attributes optimized for different radial positions on the blade. The construction of a blade with multiple airfoil sections along its length is made easier today, mainly because of computer aided design and composite materials manufacturing technology, which makes the design and production costs comparable to one with a single airfoil.
UiofAriPollt/ ilia Koof оігРліІс ога лКіоіпа/^ ЛглппЬ or» m/nlnfiлпor7 пглласс ії;Ьага Клііі
X НОШІІ^ШІ jу Uiv UWOl UiJLJLV/AAO ШЧ/ V/UlUlli^U UJULV/l*gjLl Ш1 vrviuuv/iuu j ^/IVWOO) TVUV1V L/UU1
theory and experiment go hand in hand to meet specific operating requirements. The tools to help design airfoils that have specific aerodynamic characteristics have been available since the 1920s. The development of the thin-airfoil theory by Munk (1922, 1924) and Glauert (1947) led to an understanding of how camber affected the chordwise pressure loading. This allowed the effects of camber to be isolated from thickness, but the effects combined as required by linear superposition. The problem of defining the airfoil pressure distribution for an airfoil of arbitrary shape was tackled semi-analytically by Theodorsen & Garrick (1932). The design of practical airfoil shapes was further aided by methods representing airfoil thickness, such as the conformal transformation method developed by
Prandtl & Tiejens (1934). This made it possible to compute pressure distributions and lift characteristics, at least for some specially shaped “Joukowski” airfoils. The detailed aerodynamic properties of Joukowski airfoils were studied in the late 1920s at Gottingen, Germany and by the NACA. – see Schrenk (1927) and von Mises (1959). Abbott et al. (1945) developed a numerical method to predict chordwise pressure distributions and airfoil characteristics based on an extension of thin-airfoil theory, where the increment in loading distribution associated with camber could be combined with the loading from thickness and angle of attack (AoA).
By the 1960s, surface singularity or “panel methods” coupled with boundary layer displacement corrections were available for airfoil design – see Section 14.7 for details. Much of the pioneering work with panel methods was done by Rubbert (1964) and by Hess & Smith (1967). Inverse panel methods allowed airfoils to be designed meet specific aerodynamic requirements. Kennedy & Marsden (1978) were one of the first to develop such methods. Generally, the airfoil designs were optimized for maximum lift. Eppler & Somers (1980) discuss an alternative method for inverse airfoil design using conformal mapping with boundary layer corrections. Hicks & McCroskey (1980) discuss the numerical optimization of a helicopter airfoil, with experimental validation. The advent of numerical methods for transonic airfoil design also meant that for the first time helicopter airfoil shapes could be more carefully designed to meet advancing blade requirements. Sloof et al. (1975) and Narramore & Yen (1982, 1997) discuss transonic airfoil design methods for helicopter rotors.
While most airfoil designs have been conducted for 2-D flows, the complicated flow near the tip of a helicopter blade demands 3-D prediction methods as well. Caradonna and colleagues (1972, 1976, 1978) were major contributors to 2-D and 3-D transonic flow prediction methods for helicopter blades using finite-difference methods. The advent of finite-difference solvers for the Euler and Navier-Stokes equations has led to increasing sophistication in airfoil design tools – see, for example, McCroskey & Baeder (1985), Malone et al. (1989), Bezard (1992), and Narramore (1994). However, the extreme operating conditions and often highly unsteady flow environment found on helicopters means that rotor airfoils must still be tested in a wind tunnel to fully and accurately assess their aerodynamic performance, mainly because modern computational methods have not yet matured to a level where turbulent flow separation and stall effects can be predicted with acceptable accuracy.