On the spectra of aerodynamic noise and aeroacoustic fatigue

The aim of the present paper is to obtain the spectra, for the energy and cross-correlation, of waves in random media, comparing with experimental data on the acoustics of turbulent flows. Since the scattering of sound by turbulence (Fig. 1) and by irregular interfaces in motion (Fig. 2), involves deterministic amplitude changes and random phase shifts, we start with the statistics of the latter, both for single and multiple scattering (Fig. 4); the ergodic and central limit theorems, are used to show that the statistics of random phase shifts are Gaussian, as supported by experimental evidence (Fig. 3). A group of applications concerns aerodynamic noise, namely the transmission of sound through the turbulent shear layer of a jet, for which a family of correlation functions for phase shifts is proposed, including Gaussian and volume conserving forms (Fig. 5); the latter is confirmed by direct experimental evidence (Fig. 6) and also by calculation of one-dimensional power spectra of sound (Figs 7-10), and comparison with measurements of aerodynamic noise (Figs 11 and 12). Another class of applications is aeroacoustic fatigue, namely the prediction of the correlation of acoustic pressure loads, for direct (Fig. 13) or indirect comparison with experiment; the latter approach, for the acoustic fatigue due to the turbulent wake of a flap (Fig. 14), involves the calculation of multi-dimensional spectra (Figs 15 and 16), which may have corrections due to edge and finite-span diffraction effects, and lead to predictions of panel response which can be compared with experiment (Fig. 19). The applications of the present theory of waves in random media, to the acoustics of turbulent flows, include not only aeroacoustic fatigue (Fig. 19) and aerodynamic noise (Fig. 18), but also rotor noise (Fig. 17); the corresponding spectra are included in a classification of 32 types, for which analytical calculation is most appropriate, since numerical methods would have the problem (Fig. 20) of summing large quantities with alternating signs, leading to large relative errors. (C) 1997 Elsevier Science Ltd.