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Decomposition of modal acoustic power due to cascade–turbulence interaction

Decomposition of modal acoustic power due to cascade–turbulence interaction
Decomposition of modal acoustic power due to cascade–turbulence interaction
This paper investigates the modal acoustic power (MAP) generated by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. The basic formulation for the upstream and downstream acoustic power based on the analytical theory of Smith [Discrete frequency sound generation in axial flow turbomachines, Reports and Memoranda no. 3709, Aeronautical Research Council, 1972] and its generalization to broadband noise due to Cheong et al. [High frequency formulation for the acoustic power spectrum due to cascade–turbulence interaction. Journal of the Acoustical Society of America 119 (2006) 108–122]. The MAP has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a term that specifies the wavenumber distribution of mean square velocity, a sound power factor that specifies the efficiency of radiation, and an acoustic blade response function. The effect of these terms on the MAP is discussed in detail in this paper. The acoustic blade response functions are found to determine the modal lines of minimum sound power in mode-frequency maps of the MAP. The upstream sound power factor is less than the downstream power factor, which is generally large, especially away from the cut-off frequency. Both power factors are small for modes close to cut-off. Modes close to cut-off, therefore, do not contribute significantly to the radiated acoustic power in the downstream direction, even though the modal pressure amplitude for these modes is high since they are excited close to resonance. For an isotropic turbulent gust, the mean square velocity wave number spectrum reduces only the magnitude of the MAP without altering the distribution of power in the frequency-mode map
0022-460X
57-73
Cheong, Cheolung
8891ef93-d484-4d86-b50d-db37154ab922
Jurdic, Vincent
482e51b2-d6f0-4720-86ce-444fc4415085
Joseph, Phillip F.
9c30491e-8464-4c9a-8723-2abc62bdf75d
Cheong, Cheolung
8891ef93-d484-4d86-b50d-db37154ab922
Jurdic, Vincent
482e51b2-d6f0-4720-86ce-444fc4415085
Joseph, Phillip F.
9c30491e-8464-4c9a-8723-2abc62bdf75d

Cheong, Cheolung, Jurdic, Vincent and Joseph, Phillip F. (2009) Decomposition of modal acoustic power due to cascade–turbulence interaction. Journal of Sound and Vibration, 324 (1-2), 57-73. (doi:10.1016/j.jsv.2009.01.059).

Record type: Article

Abstract

This paper investigates the modal acoustic power (MAP) generated by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. The basic formulation for the upstream and downstream acoustic power based on the analytical theory of Smith [Discrete frequency sound generation in axial flow turbomachines, Reports and Memoranda no. 3709, Aeronautical Research Council, 1972] and its generalization to broadband noise due to Cheong et al. [High frequency formulation for the acoustic power spectrum due to cascade–turbulence interaction. Journal of the Acoustical Society of America 119 (2006) 108–122]. The MAP has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a term that specifies the wavenumber distribution of mean square velocity, a sound power factor that specifies the efficiency of radiation, and an acoustic blade response function. The effect of these terms on the MAP is discussed in detail in this paper. The acoustic blade response functions are found to determine the modal lines of minimum sound power in mode-frequency maps of the MAP. The upstream sound power factor is less than the downstream power factor, which is generally large, especially away from the cut-off frequency. Both power factors are small for modes close to cut-off. Modes close to cut-off, therefore, do not contribute significantly to the radiated acoustic power in the downstream direction, even though the modal pressure amplitude for these modes is high since they are excited close to resonance. For an isotropic turbulent gust, the mean square velocity wave number spectrum reduces only the magnitude of the MAP without altering the distribution of power in the frequency-mode map

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Published date: 10 July 2009
Organisations: Fluid Dynamics & Acoustics Group

Identifiers

Local EPrints ID: 154073
URI: https://eprints.soton.ac.uk/id/eprint/154073
ISSN: 0022-460X
PURE UUID: 73dcd304-95bf-4cfb-ad1b-02d9a3ba6e88

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Date deposited: 24 May 2010 13:39
Last modified: 16 Jul 2019 23:58

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