A great deal of progress has been made in the modeling of aerodynamically generated sound of rotors over the past decade. Although the modeling effort has focused on helicopter main rotors, the theory is generally valid for a wide range of rotor configurations. The Ffowcs Williams-Hawkings (FW-H) equation has been the foundation for much of the development. The monopole and dipole source terms of the FW-H equation account for the thickness and loading noise, respectively. Bladevortex-interaction noise and broadband noise are important types of loading noise, hence much research has been directed toward the accurate modeling of these noise mechanisms. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H equation has also been utilized on permeable surfaces surrounding all physical noise sources. Comparisons of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems. Finally, significant progress has been made incorporating the rotor noise models into full vehicle noise prediction tools.

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams{Hawkings (FW{H) equation, is compared with the Kirchho formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchho advantage (namely nonlinear ow eects are included in the surface integration) is also available to the FW{H method if the integration surface used in the FW{H equation is not assumed impenetrable. The FW{H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of uid mechanics rather than the wave equation. This means that the FW{H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchho approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchho noise predictions.

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Three model problems were examined to assess the di culties involved in using a hybrid scheme coupling ow computation with the the Ffowcs Williams and Hawkings equation to predict noise generated by v ortices passing over a sharp edge. The results indicate that the Ffowcs Williams and Hawkings equation correctly propagates the acoustic signals when provided with accurate ow information on the integration surface. The most di cult of the model problems investigated inviscid ow o ve r a t wodimensional thin NACA airfoil with a blu -body vortex generator positioned at 98 percent c hord. Vortices rolled up downstream of the blu body. The shed vortices possessed similarities to large coherent eddies in boundary layers. They interacted and occasionally paired as they convected past the sharp trailing edge of the airfoil. The calculations showed acoustic waves emanating from the airfoil trailing edge. Acoustic directivity and Mach n umber scaling are shown.