
doi: 10.2514/6.2011-2877
A linearized Euler theory is developed for a fan modeled as a rotating annular cascade. The model fully accounts for three-dimensional efiects as well as the additional centrifugal and Coriolis forces. Computations are carried out for a typical fan geometry in nonuniform in∞ow conditions. The aerodynamic and acoustic results are compared with those of guide vanes with the same relative ∞ow conditions and geometry, as well as a linear cascade using the strip theory. Results show signiflcant difierences for the blade unsteady pressure and acoustic mode intensity with the rotor having stronger responses. Results are also extended to broadband calculations and compare with experiments. In a previous paper, 1 the authors developed a model for the scattering of incident disturbances by a rotor. The rotor is modeled as an annular cascade which accounts for the three-dimensional efiects of the rotor geometry and the radial variation of the incident disturbances. In addition, the model accounts for the centrifugal and Coriolis forces which become signiflcant as the angular velocity of the rotor is comparable to the axial ∞ow velocity. A signiflcant difierence between guide vanes and rotor scattering is that the rotor scatters the incident disturbances and produces acoustic modes of difierent frequencies. The results show that the aerodynamic response of a rotor is afiected by its angular rotation primarily near the tip of the blades. In the present paper, we flrst examine the aerodynamic and acoustic response of a rotor for a typical fan geometry and we compare the results with that of guide vanes with the same relative ∞ow conditions. This comparison will determine the efiects of the centrifugal and Coriolis forces on the rotor response. In addition, we compare the results with those of the popular linear cascade model. As a flrst step, we consider only unloaded cascades. We have also extended the model to calculate the response to incoming turbulence using 2 for isotropic and anisotropic turbulence. As the in∞ow turbulence interacts with the fan blades, it generates tonal and broadband noise. In addition, the ∞ow accelerates in the contracting fan inlet and the turbulent eddies are stretched in the streamwise direction and ∞attened in the lateral directions. This causes the turbulence structure to become anisotropic. It is well known that streamwise eddy stretching reduces the streamwise component of the turbulence velocity and may amplify its lateral components. 3,4 This suggests the need for accurate representation of the turbulence energy spectrum for anisotropic turbulence. A similar approach using asymptotic analysis was developed in. 5 The results in the current work are compared with the Boeing 18 inch fan experiments. 6
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