article · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1995
A uniform asymptotic approximation for high-frequency unsteady cascade flow
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Abstract
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 approximate factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived by Peake, and this approach has the advantages of both providing more physical insight and being significantly easier to compute than the exact factors. An important limitation of Peake’s approximation, however, is that it be comes invalid when any of the acoustic modes in the system are close to cut-off, and in this paper 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, with typical errors of the order of only 3% even for very modest values of the reduced frequency.
Cite this paper
Peake, N., & Kerschen, E. J. (1995). A uniform asymptotic approximation for high-frequency unsteady cascade flow. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 449(1935), 177–186. https://doi.org/10.1098/rspa.1995.0038
Peake, N., and E. J. Kerschen. “A uniform asymptotic approximation for high-frequency unsteady cascade flow.” Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, vol. 449, no. 1935, 1995, pp. 177–86, https://doi.org/10.1098/rspa.1995.0038.
Peake, N., and E. J. Kerschen. 1995. “A uniform asymptotic approximation for high-frequency unsteady cascade flow.” Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 449 (1935): 177–86. https://doi.org/10.1098/rspa.1995.0038.
Peake, N. and Kerschen, E.J. (1995) ‘A uniform asymptotic approximation for high-frequency unsteady cascade flow’, Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 449(1935), pp. 177–186. Available at: https://doi.org/10.1098/rspa.1995.0038.
@article{peake1995uniform,
title = {{A uniform asymptotic approximation for high-frequency unsteady cascade flow}},
author = {Peake, N. and Kerschen, E. J.},
journal = {Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences},
volume = {449},
number = {1935},
pages = {177--186},
year = {1995},
doi = {10.1098/rspa.1995.0038}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.