### Abstract

The scattering of harmonic gusts by a two-dimensional, infinite cascade of flat plates is a model problem which is relevant to the prediction of noise generation by rotating turbomachinery. The problem can be solved analytically using the Wiener-Hopf technique, and the key step involves the exact factorization of a certain generic kernel function, K, using infinite products. An approximation factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived. An important limitation of Peake's approximation, however, is that it becomes invalid when any of the acoustic modes in the system are close to cut-off. We therefore present new asymptotic factors which overcome this non-uniformity. The accuracy of this new approximation, across a whole range of operating parameters, is demonstrated by comparison with the exact results. (from Authors)

Original language | English (US) |
---|---|

Title of host publication | Proceedings - Royal Society of London, A |

Pages | 177-186 |

Number of pages | 10 |

Volume | 449 |

Edition | 1935 |

State | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - Royal Society of London, A*(1935 ed., Vol. 449, pp. 177-186)

**A uniform asymptotic approximation for high-frequency unsteady cascade flow.** / Peake, N.; Kerschen, Edward J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Proceedings - Royal Society of London, A.*1935 edn, vol. 449, pp. 177-186.

}

TY - CHAP

T1 - A uniform asymptotic approximation for high-frequency unsteady cascade flow

AU - Peake, N.

AU - Kerschen, Edward J

PY - 1995

Y1 - 1995

N2 - The scattering of harmonic gusts by a two-dimensional, infinite cascade of flat plates is a model problem which is relevant to the prediction of noise generation by rotating turbomachinery. The problem can be solved analytically using the Wiener-Hopf technique, and the key step involves the exact factorization of a certain generic kernel function, K, using infinite products. An approximation factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived. An important limitation of Peake's approximation, however, is that it becomes invalid when any of the acoustic modes in the system are close to cut-off. We therefore present new asymptotic factors which overcome this non-uniformity. The accuracy of this new approximation, across a whole range of operating parameters, is demonstrated by comparison with the exact results. (from Authors)

AB - The scattering of harmonic gusts by a two-dimensional, infinite cascade of flat plates is a model problem which is relevant to the prediction of noise generation by rotating turbomachinery. The problem can be solved analytically using the Wiener-Hopf technique, and the key step involves the exact factorization of a certain generic kernel function, K, using infinite products. An approximation factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived. An important limitation of Peake's approximation, however, is that it becomes invalid when any of the acoustic modes in the system are close to cut-off. We therefore present new asymptotic factors which overcome this non-uniformity. The accuracy of this new approximation, across a whole range of operating parameters, is demonstrated by comparison with the exact results. (from Authors)

UR - http://www.scopus.com/inward/record.url?scp=0029136807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029136807&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0029136807

VL - 449

SP - 177

EP - 186

BT - Proceedings - Royal Society of London, A

ER -