### 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 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 language | English (US) |
---|---|

Pages (from-to) | 687-696 |

Number of pages | 10 |

Journal | Annual Forum Proceedings - American Helicopter Society |

Volume | 1 |

State | Published - 1997 |

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### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Transportation

### Cite this

*Annual Forum Proceedings - American Helicopter Society*,

*1*, 687-696.

}

*Annual Forum Proceedings - American Helicopter Society*, vol. 1, pp. 687-696.

**Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces.** / Brentner, Kenneth Steven; Farassat, F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces

AU - Brentner, Kenneth Steven

AU - Farassat, F.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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M3 - Article

VL - 1

SP - 687

EP - 696

JO - Annual Forum Proceedings - American Helicopter Society

JF - Annual Forum Proceedings - American Helicopter Society

SN - 0733-4249

ER -