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

Kenneth S. Brentner, F. Farassat

Research output: Contribution to journalReview article

424 Citations (Scopus)

Abstract

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 primary advantage of the Kirchhoff formulation (namely, that 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 to be impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based on the conservation laws of fluid mechanics rather than on the wave equation. Thus, the FW-H equation is valid even if the integration surface is in the nonlinear region. This advantage is demonstrated numerically. With the Kirchhoff approach, substantial errors can result if the integration surface is not positioned in the linear region, and these errors may be hard to identify. Finally, new metrics, based on the Sobolev norm, are introduced that may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Original languageEnglish (US)
Pages (from-to)1379-1386
Number of pages8
JournalAIAA journal
Volume36
Issue number8
DOIs
StatePublished - Aug 1998

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Acoustics
Aeroacoustics
Fluid mechanics
Wave equations
Conservation

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering

Cite this

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title = "Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces",
abstract = "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 primary advantage of the Kirchhoff formulation (namely, that 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 to be impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based on the conservation laws of fluid mechanics rather than on the wave equation. Thus, the FW-H equation is valid even if the integration surface is in the nonlinear region. This advantage is demonstrated numerically. With the Kirchhoff approach, substantial errors can result if the integration surface is not positioned in the linear region, and these errors may be hard to identify. Finally, new metrics, based on the Sobolev norm, are introduced that may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.",
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Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces. / Brentner, Kenneth S.; Farassat, F.

In: AIAA journal, Vol. 36, No. 8, 08.1998, p. 1379-1386.

Research output: Contribution to journalReview article

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AU - Farassat, F.

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