Low and high frequency models for the prediction of noise due to cascade-turbulence interaction

Cascade theory is often used to predict the sound power radiation from a fan subject to incident turbulent flow, but in the high frequency regime it is slow due to the large number of Fourier modes required in the calculations. We demonstrate that the sound power spectrum due to a single isolated airfoil subject to the identical turbulent flow closely matches the equivalent cascade sound power spectrum at suciently high frequency. Several important dierences are apparent in the results and an understanding of these allows the identification of agreement frequencies above which the fast single airfoil theory may be substituted for the computationally expensive cascade theory with negligible dierence to the result.