Generation of discrete frequency tones by the flow around an aerofoil
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 this model. 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 theoretical results.