Unsteady Airfoil Behavior

The addition of the dimension “time” to steady aerodynamics has far-reaching effects, both practical and theoretical. There is the practical necessity for coping with many important problems involving nonsteady phenomena such as nutter, buffeting, transient flows, gusts, dynamic response in flight, maneuvers, and stability. Apart from the many applications, theoretical nonsteady aerodynamics embraces and sheds light on the realm of steady aerodynamics and introduces interesting new methods.

I. E. Garrick (1957)

Introduction

The confidence levels in the design of new helicopters are greatly improved by the ability to predict accurately the aerodynamic behavior of the rotor system at all comers of the operational flight envelope. One difficulty and uncertainty in this process is to fully account for unsteady aerodynamic effects, especially when the helicopter is in high-speed forward flight and during flight maneuvers. In the previous chapter, the quasi-steady aerodynamic characteristics of rotor airfoils have been discussed in detail. Yet, these attributes alone are not necessarily the best indicator as to whether a given airfoil will operate successfully in the rotor environment or will meet the requirements of a given rotor design. The next level of consideration is to examine unsteady aerodynamic effects and to strive to assess their potential impact on the prediction of the airloads and performance of helicopter rotors.

In the context of rotor airloads prediction, the mathematical modeling of unsteady airfoil behavior is one of formidable complexity. While the absence of significant flow separation reduces somewhat the complexity of the problem, a complete understanding of unsteady airfoil behavior even in attached flow has not yet been obtained. The additional problem of dynamic flow separation[27] is still the subject of ongoing research, and completely satisfactory predictive models of the problem have not yet been developed. This is particularly true for the rotor case, where the rotor blades encounter a broad spectrum of unsteady effects from a number of different sources. The most obvious are the excursions in AoA resulting from blade flapping and pitch control inputs. The additional effects of the rotor wake, with its embedded concentrated tip vortices, lead to regions of the rotor disk that can experience large perturbations in AoA over very short time scales. The problems are compounded by the 3-D effects found at the blade tips, which can be locally transonic during forward flight. Therefore, the problems of defining accurately the unsteady aerodynamic flow field on the rotor is really rather formidable.

The principal focus of the present chapter is to describe the key physical features and techniques for modeling the unsteady aerodynamic effects found on airfoils operating un­der nominally attached flow conditions away from stall. The essential physics of nonsteady airfoil problems can be observed from idealized 2-D experiments, and interpretations of

the behavior can be supported by theoretical or numerical models. The “classical” unsteady aerodynamic theories describing the observed behavior have formed the basis for many types of rotor analyses. The tools for the analysis of 2-D, incompressible, unsteady aerody­namic problems were laid down by 1940, with the extension to compressible flows complete by 1950. The most authoritative source documenting these theories is Bisplinghoff et al. (1955). Lomax and his colleagues (1952,1968) have provided a basis from which to develop linearized unsteady aerodynamic models applicable to compressible flows. The mathemat­ical elegance and computational simplicity of these linearized approaches are attractive to the helicopter rotor analyst. Although there have been a plethora of “new” unsteady aerodynamic theories developed over the years for helicopter applications, most still have their roots in the classical theories. Also, while the classical theories assume linearity in the airloads, the assumption of linearity can probably be justified for many of the problems encountered on the rotor, in practice. The proof of this latter statement is not always easy to justify, mostly because of other uncertainties in the problem such as those resulting from the rotor wake. The advent of nonlinear methods based on CFD solutions to the Euler and Navier-Stokes equations has provided new results that help the rotor analyst justify and define the limits of the parsimonious, linear models and may give guidance in developing improved and more practical unsteady aerodynamic models for future use in helicopter rotor blade airloads prediction, aeroelastic analysis, and rotor design.