Abstract
An important criterion in the development of modern aeroengines
is the identification
of the dominant noise sources under typical aircraft take-off and approach
conditions,
and also in ground-based tests in which the engine is stationary. In this
paper, we
develop a theoretical model for unsteady distortion noise, which
results from the
interaction of ingested atmospheric turbulence with the rotating fan, with
a view
to providing a better understanding of the important physical mechanisms
in this
particular aspect of sound generation. The theory, developed in the frequency
domain,
is applicable for any arbitrary spectral form of atmospheric turbulence
upstream of
the fan, and as a simple model we take the von Kármán spectra
for isotropic
turbulence. The key fluid dynamical process in unsteady distortion is the
deformation
of turbulent eddies into long, narrow filaments as they enter the engine,
due to the
strong streamtube contraction experienced by the steady, non-uniform mean
flow
generated by the fan. Simple models of the steady flow fields are provided
for both
open and ducted rotor geometries. The distorted turbulent field at the
fan face can be
obtained using rapid distortion theory, and considerable simplification
is made here
by noting that the number of blades in typical aeroengine fans is large,
allowing the
application of asymptotic analysis and the derivation of closed-form expressions
for
those parts of the turbulence spectrum at the fan face which dominate the
radiation.
The unsteady forces exerted on the rotating fan blades are then calculated
via a
strip-theory approach. The resulting sound scattered to the far field is
then evaluated
using asymptotic theory for open and ducted rotors. Results are presented
in the form
of frequency spectra for the turbulent field at the fan face, the blade
forces and the
radiated sound for typical testing and aircraft operating conditions. High
tonal noise
levels are obtained under static conditions, whereas the sound is generally
broadband
in flight. The dependence on turbulence parameters such as the integral
lengthscale
is highlighted.
