Abstract
The sound generated by the interaction between a turbulent rotor wake and a stator
is modelled by considering the gust response of a cascade of blades in non-uniform,
subsonic mean flow. Previous work by Hanson & Horan (1998) that considers a
cascade of flat plates at zero incidence is extended to take into account blade geometry
and angle of attack. Our approach is based on the work of Peake & Kerschen (1997),
who calculate the forward radiation due to the interaction between a single vortical
gust and a cascade of flat plates at non-zero angle of attack. The extensions completed
in this present paper are two-fold: first we include the effects of small but non-zero
camber and thickness; and second we produce uniformly valid approximations which
predict the upstream radiation near modal cut-off. The thin-airfoil singularity in the
steady flow at each leading edge is crucial in our model of the sound generation.
A new analytical expression for the coefficient of this singularity is derived via a
sequence of conformal mappings, and it turns out that in our asymptotic limit this
is the only quantity which needs to be calculated from the steady flow in order
to predict time-averaged noise levels. Once the response to a single gust has been
completed, we use Hanson & Horan (1998)'s approach to determine the response
to an incident turbulent spectrum, and find that as well as the noise corresponding
to the auto-correlation of the gust velocity component normal to the blade, there is
also a contribution from the cross-correlation of the normal and tangential velocities.
Predictions are made of the effects of blade geometry on the upstream acoustic power
level. The blade geometry can have a very significant effect on the noise generated
by interaction with a single gust, with changes of up to 10 dB from the flat-plate
noise levels. However, once these gust results have been integrated over a full incident
turbulence spectrum the effects of the geometry are rather smaller, although still
potentially significant, leading to changes of up to about 2 dB from the flat-plate
results. The implication of all this is that the blade geometry can have a significant
effect on the tonal noise components generated by rotor–stator interaction (i.e. by
single harmonic gusts), but that the broadband part of the noise spectrum is relatively
unaffected.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
91 articles.
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