TY - JOUR
T1 - A uniform asymptotic approximation for high-frequency unsteady cascade flow
AU - Peake, N.
AU - Kerschen, E. J.
PY - 1995/1/1
Y1 - 1995/1/1
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)
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U2 - 10.1098/rspa.1995.0038
DO - 10.1098/rspa.1995.0038
M3 - Article
AN - SCOPUS:0029136807
VL - 449
SP - 177
EP - 186
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 0962-8444
IS - 1935
ER -