A Model for Fan Broadband Interaction Noise in Nonuniform Flow

Abstract

A three-dimensional model is presented for fan broadband interaction noise based on the spectral representation of the impinging upstream turbulence and a multiple scale analysis for the evolution of turbulence in a nonuniform swirling ∞ow. The analysis is based on the fact that, for typical fans, the turbulence integral scale ⁄ is much smaller than the vane chord c or the duct radius rt. The fan is modelled as a three-dimensional annular cascade in a nonuniform swirling ∞ow and its aerodynamic{acoustic response to every upstream Fourier disturbance is calculated using the linearized Euler equations. The broadband noise power radiated is then calculated by summing the spectral density weighted contributions of all Fourier components. Since most of the turbulence spectrum is in the high frequency range, an asymptotic analysis shows that the acoustic response of the cascade will be dominated by the local blade geometry. This suggests that a simplifled two-dimensional cascade model may be adequate for calculating the fan acoustic response at high frequency. This conclusion is conflrmed for unloaded blades by a comparison of the numerical results of the radiated noise spectra of a 3D annular cascade and a 2D linear cascade. Finally, turbulence distortion by swirl over a distance of O(rt), evaluated by calculating the velocity covariance, shows a rise in turbulence intensity, thus modifying the blade upwash and suggesting an increase of the radiated noise power.