High frequency formulation for the acoustic power spectrum due to cascade-turbulence interaction

This paper investigates the noise radiated by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. An analytic formulation for the spectrum of acoustic power of a two-dimensional flat-plate is derived. The main finding of this paper is that the acoustic power spectrum from the cascade of flat airfoils may be split into two distinct frequency regions of low frequency and high frequency, separated by a critical frequency. Below this frequency, cascade effects due to the interaction between neighboring airfoils are shown to be important. At frequencies above the critical frequency, cascade effects are shown to be relatively weak. In this frequency range, acoustic power is shown to be approximately proportional to the number of blades. Based on this finding at high frequencies, an approximate expression is derived for the power spectrum that is valid above the critical frequency and which is in excellent agreement with the exact expression for the broadband power spectrum. The formulation is used to perform a parametric study on the effects on the power spectrum of the blade number, stagger angle, gap-chord ratio, and Mach number. The theory is also shown to provide a close fit to the measured spectrum of rotor-stator interaction.