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
A uniform asymptotic approximation for high-frequency unsteady cascade flow. / Peake, N.; Kerschen, Edward J.
Proceedings - Royal Society of London, A. Vol. 449 1935. ed. 1995. p. 177-186.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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 -