An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

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 e ects 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.