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ON THE HYDROACOUSTICS OF A TRAILING EDGE WITH A DETACHED FLAP

Abstract An analysis is made of production of sound by low Mach number turbulent flow over the trailing edge of a hydrofoil with a single detached flap. Following the approach advocated by Professor Doak in 1960 (Proceedings of the Royal Society A 254 , 129–145), an aeroacoustic Green function is derived for a hydrofoil of large chord with a detached flap at relative angle of attack α ( α 2 ⪡1) when the chord of the flap is acoustically compact. The Green function can be used with data derived from direct numerical simulations of the unsteady hydrodynamic flow, and provides an effective means of calculating the radiation from a knowledge of the incompressible component of the flow in the edge region. The results permit a comparison to be made of the separate contributions to the production of sound by turbulence interacting with the trailing edge of the hydrofoil, the trailing edge of the flap, and with the leading edge of the flap. The side-edge noise of part-span flaps is not discussed. Formulae are given for calculating the “self-noise” produced at trailing edges by boundary layer instability; the efficiency of sound generation at the edge of the hydrofoil is shown to be typically at least 7 dB larger than that produced at the trailing edge of the flap. The impingement noise generated by small-scale turbulence interacting with the flap leading edge is expressed in terms of an equivalent dipole source equal to the fluctuating flap-lift force, acting at a distance l F to the rear of the main hydrofoil; l F is determined as a function of the flap dimensions, and does not normally exceed about twice the width h of the slot separating the hydrofoil and flap. The proximity of the dipole to the edge of the hydrofoil increases the efficiency of sound production by a factor proportional to h /( l F M ) where M ⪡1 is the characteristic edge flow Mach number, and modifies the directivity of the sound.