Acoustic radiation from a turbulent fluid containing foreign bodies

Abstract

The problem of the acoustic radiation from a turbulent fluid containing foreign bodies of arbitrary shape and arbitrary composition is solved formally by the method of Green functions. Particular attention is given to the radiation from the surface of these bodies. A practical advantage of the method is that provided an appropriate Green function can be found, either exactly or approximately, then knowledge of the values on the surface of the fluctuations in only one scalar variable is needed to permit estimation of the radiation from the surface. This variable may be either the pressure, the normal pressure gradient, the density, or the normal density gradient. The pressure fluctuations at the surface, in particular, are relatively easy to measure. It is shown that if fluctuations in the fluid are locally isentropic the volume source distribution of the pressure fluctuations is quadrupole. A proof is given of the proposition that when arbitrary obstacles are immersed in a fluid all dipole radiation must come from surface source distributions on these obstacles. For rigid bodies these distributions represent physically the reaction by the obstacles to the stresses imposed upon them by the fluid. It is pro ved that if the density fluctuations or the normal density gradient fluctuations on these surfaces vanish then there is no dipole radiation. The same result is true for pressure and pressure gradient fluctuations within the limits of validity of the assumption of local isentropy. A brief description is given, together with references to more detailed accounts, of some of the principal features of the behaviour of Green functions which may be useful in practical estimates of aerodynamic surface sound. As a representative example of acoustic radiation from a turbulent boundary layer, the total acoustic power radiated by a turbulent boundary layer on an infinite rigid plane is estimated, using the limited available experimental data on wall pressure fluctuations. For low and moderate subsonic speeds the power radiated per unit wall area covered by the turbulent boundary layer is Kρ 0 a 3 0 M 6 0 , where M 0 is the free stream Mach number, ρ 0 is the density and a 0 the speed of sound in the undisturbed fluid, and the dimensionless parameter K is approximately a constant of order of magnitude 10 -5 .