Computation of Broadband Noise Radiated by a Ducted Fan

Abstract

— Acoustic pressure amplitude Am! a — Speed of sound B — Number of rotor blades b — Rotor blade span C — Blade load constant — Spherical coordinates for free-field radiation D,,# — Cylindrical coordinates of a source on the rotor d,$, y1 y — Blade load, and its azimuthal Fourier transform F,F f — Frequency G — Green’s function I — Sound intensity — Integral on a point source ! — Bessel function of first kind and of order m Jm — Total, transverse, and axial wave-numbers K,kt,kz L — Duct length l — Radial turbulence length scale — Spinning mode (m azimuthal, radial) m,! ! — Axial Mach number in the annular duct in front Max of the rotor — Tip rotational Mach number Mtip — Mach number of the uniform flow in the duct Mz N — Rotor angular rotation speed (either in rpm or in Hz) n — Number of point sources along the blade span in non-compact calculations — Sound pressure in the duct and in the far field, p,P respectively q — Exponent of decrease of the blade pressure fluctuations at high frequency R — Duct radius — Cylindrical coordinates of a point in the duct r,%,x1 x S — Blade surface area — Reception time, emission time t,& — Rotation speed of a point source on a blade Urot W — Sound power — Dirac function ' — Mean fluid density (0 — Fan hub-to-tip ratio ) — -th root of *m! ! Jm ! 0 — Rotor angular rotation speed ( ) + + ! 2,N — Angular frequency ( ) ! 2,f ! aK