Decomposition of modal acoustic power due to cascade–turbulence interaction

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.