Generation of discrete frequency tones by the flow around an aerofoil.
University of Bristol, School of Mathematics,
Tonal noise, the self-induced discrete frequency noise generated by aerofoils, is investigated.
It is heard from an aerofoil placed in streams at low Mach number flows
when inclined at a small angle to the stream. The tones are heard as a piercing whistle,
commonly up to 30 dB above the background noise level. The work is motivated
by the occurrence of tonal noise from rotors, fans and recently wind-turbines. Previous
authors have attributed tonal noise to a feedback loop consisting of a coupling
between laminar boundary-layer instability waves and sound waves propagating in the
free stream. The frequency has been predicted by use of various methods based on
In this thesis a review of wind-tunnel results obtained by Dr. E.C. Nash at the
University of Bristol is presented. Boundary-layer measurements show the presence of
tonal noise is closely related to the existence of a region of separated flow close to the
trailing edge of the aerofoil. Highly amplified boundary-layer instability waves were
observed close to the trailing edge of the aerofoil at the frequency of the tone.
A comprehensive analysis of the linear stability of the boundary-layer flow over
the aerofoil is presented. The growth of boundary-layer instability waves over the
aerofoil is calculated. The growth rates of the waves were obtained by solving the Orr–
Sommerfeld problem at several stations on the aerofoil. The Falkner–Skan boundary
layers were found to be a suitable form of velocity profiles to incorporate the adverse
pressure gradients experienced by the flow over an aerofoil. The amplification of the
instability waves is shown to be controlled almost entirely by the region of separated
flow close to the trailing edge. The calculated frequency of the linear modes with
maximum amplification over the aerofoil is found to be close to the observed frequency
of the acoustic tone.
A weakly nonlinear stability analysis was also performed and this appears to be a
suitable description of the boundary-layer instability waves. The results indicate that
the frequency of the tones may commonly be predicted to within 10% by using weakly
nonlinear stability theory.
The generation of sound by diffraction of the boundary-layer instability waves at
the trailing edge of the aerofoil is also discussed as well as the proposed feedback
models. A modified feedback model is proposed, being based on the experimental and
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