Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces

Kenneth S. Brentner, F. Farassat

Research output: Contribution to journalConference articlepeer-review

34 Scopus citations


The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects 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 fluid 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 Kirchhoff 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 Kirchhoff noise predictions.

Original languageEnglish (US)
Pages (from-to)687-696
Number of pages10
JournalAnnual Forum Proceedings - American Helicopter Society
StatePublished - 1997
EventProceedings of the 1997 53rd Annual Forum of AHS. Part 1 (of 3) - Virginia Beach, VA, USA
Duration: Apr 29 1997May 1 1997

All Science Journal Classification (ASJC) codes

  • Transportation
  • Aerospace Engineering


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