Chapter Review

This chapter has described the key physical features of the unsteady aerodynamic effects found on airfoils operating under nominally attached flow conditions and away from stall. Unsteady aerodynamic effects have an important role in the prediction of the airloads and performance of helicopter rotors. The contributions of circulatory and noncirculatory effects to the unsteady airloads have been described, and their effects have been explained through the use of classical unsteady aerodynamic theories. These theories have their origin in thin-airfoil theory, with allowance for a shed vortical wake of nonzero strength down­stream of the airfoil. Of primary significance is that unsteady effects manifest as phase differences between the forcing function and the aerodynamic response; these are func­tions of the reduced frequency, the Mach number and the mode of forcing. While most of the classical unsteady aerodynamic theories are elegant in mathematical form, they are restricted to fully incompressible flows. This is an assumption that is hard to justify for helicopter problems, where both the local Mach numbers and effective reduced frequencies are generally high enough to render incompressible flow assumptions invalid, at least under the strictest terms. However, sometimes even some allowance for unsteady effects provides a better predictive capability than if quasi-steady flow alone is assumed.

flows no exact analytic solutions are available for unsteady airfoil problems, at least not over the entire time domain, and numerical solutions must be sought. However, the extension of the classical incompressible methods to subsonic compressible flows can be approached using many of the same fundamental principles as for incompressible flow, albeit using certain levels of approximation. It has been shown that compressibility effects generally manifest as increased phase lags between the forcing function and the unsteady aerodynamic response. For some transient problems, such as blade vortex interactions and unsteady trailing edge flap motions, the treatment of compressibility proves essential if the correct amplitude and phasing of the aerodynamic loads are to be predicted. Validation of the various methods have been conducted with experimental results. Unfortunately., many of the problems of interest are difficult to simulate experimentally, and recourse to indirect validation has been the only choice. However, the recent advent of nonlinear methods based on CFD solutions to the Euler or Navier-Stokes equations has provided a new standard that now helps define the limits of applicability of the classical theories.

The problem of understanding and predicting rotor noise continues to be a challenging one for the analyst. While much progress has been made, the significant reduction of heli­copter noise is an illusive goal. To this end, the accurate modeling of unsteady aerodynamic forces on the blades continues to be fundamental to the prediction of rotor noise. While the better use of CFD methods is often held out to be the answer, good acoustic results are still possible within the framework of linear unsteady aerodynamic theories, albeit with proper correction for compressibility effects. These types of models are also amenable for inclusion in comprehensive rotor analysis, such as those including rotor blade dynamics and aeroelastic response, and perhaps also flight dynamics simulations. Acoustic tools such as wave tracing also provide good insight into the acoustic directivity produced by BVI phenomena and can be used to augment FW-H or other solutions in terms of understanding