On the hydroacoustics of a trailing edge with a detached flap

An analysis is made of production of sound by low Mach number turbulent flo w over the trailing edge of a hydrofoil with a single detached flap. Follow ing the approach advocated by Professor Doak in 1960 (Proceedings of the Ro yal 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 alpha (alpha (2)much less than1) when the chord of the flap is acousticall y compact. The Green function can be used with data derived from direct num erical simulations of the unsteady hydrodynamic flow, and provides an effec tive means of calculating the radiation from a knowledge of the incompressi ble component of the flow in the edge region. The results permit a comparis on to be made of the separate contributions to the production of sound by t urbulence 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 noi se 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 inte racting with the flap leading edge is expressed in terms of an equivalent d ipole 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 o f 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 much less than 1 is the chara cteristic edge flow Mach number, and modifies the directivity of the sound. (C) 2001 Academic Press.