### Abstract

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the governing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Original language | English (US) |
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DOIs | |

State | Published - Jan 1 1998 |

Event | 4th AIAA/CEAS Aeroacoustics Conference, 1998 - Toulouse, France Duration: Jun 2 1998 → Jun 4 1998 |

### Other

Other | 4th AIAA/CEAS Aeroacoustics Conference, 1998 |
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Country | France |

City | Toulouse |

Period | 6/2/98 → 6/4/98 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering
- Aerospace Engineering

### Cite this

*A study of supersonic surface sources—The Ffowcs Williams-Hawrings equation and the Kirchhoff formula*. Paper presented at 4th AIAA/CEAS Aeroacoustics Conference, 1998, Toulouse, France. https://doi.org/10.2514/6.1998-2375

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**A study of supersonic surface sources—The Ffowcs Williams-Hawrings equation and the Kirchhoff formula.** / Farassat, F.; Brentner, Kenneth Steven; Dunn, M. H.

Research output: Contribution to conference › Paper

TY - CONF

T1 - A study of supersonic surface sources—The Ffowcs Williams-Hawrings equation and the Kirchhoff formula

AU - Farassat, F.

AU - Brentner, Kenneth Steven

AU - Dunn, M. H.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the governing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

AB - In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the governing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

UR - http://www.scopus.com/inward/record.url?scp=84894597126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894597126&partnerID=8YFLogxK

U2 - 10.2514/6.1998-2375

DO - 10.2514/6.1998-2375

M3 - Paper

AN - SCOPUS:84894597126

ER -