Scaling properties of the Ffowcs-Williams and Hawkings equation for complex acoustic source close to a free surface

Abstract

We perform a scaling analysis of the terms composing the Ffowcs-Williams and Hawkings (FWH) equation, which rules the propagation of noise generated by a rigid body in motion. Our analysis extends the seminal work of Lighthill (Proc. R. Soc. Lond. A, vol. 211, 1952, pp. 564–587) and the dimensional analysis of classical sources (monopole, dipole and quadrupole) considering all the FWH integral terms. Scaling properties are analysed in light of perfect/imperfect similarity when laboratory-scale data are used for full-scale predictions. As a test case we consider a hydrodynamic example, namely a laboratory-scale ship propeller. The data, obtained numerically in a previous study, were post-processed according to the scaling analysis presented herein. We properly scale the speed of sound to obtain perfect similarity and quantify the error with respect to the imperfect scaling. Imperfect similarity introduces errors in the acoustic response related both to the linear terms and to the nonlinear terms, the latter of great importance when the wake is characterized by robust and organized vorticity. Successively, we analyse the effect of a free surface, often present in hydrodynamic applications. We apply the method of images to the FWH equation. The free surface may generate a frequency-dependent constructive/destructive interference. The analysis of an archetypal acoustic field (monopole) provides robust explanation of these interference effects. Finally, we find that imperfect similarity and the absence of a free surface may introduce errors when model-scale data are used to obtain the full-scale acoustic pressure. The error is small for microphones placed in the near field and becomes relevant in the far field because of the nonlinear terms.

Hydroacoustic analysis of a marine propeller using large-eddy simulation and acoustic analogy

“…In particular, the comparison in figure 20 shows that the experiment has higher SPL than the simulation. It is likely that the effects of reverberation from the walls of the experimental facility, free-surface (Cianferra & Armenio 2021), self-induced noise from the hydrophone and the background noise in the experiments, all missing in the computations, contribute to higher SPLs. In addition, both experiments and computations were carried out in absence of cavitation phenomena: in such conditions the propeller is quite silent, making even more demanding capturing accurately its acoustic signature.…”

“…Based on the conclusions by Ianniello (2016), Cianferra, Petronio & Armenio (2019 b ) and Cianferra & Armenio (2021) utilised the results of a wall-modelled LES computation on a grid consisting of 3 million volumes to perform the acoustic analysis of the SVA VP1304 propeller. In contrast with earlier studies, the direct approach to the computation of the different terms of the FWH equation was pursued.…”

“…However, the studies by Cianferra et al. (2019 b ) and Cianferra & Armenio (2021) were still based on rather coarse simulations, unable to reproduce the instability mechanisms of the wake, which are expected to enhance the role of the quadrupole terms. In addition, the tractor configuration they considered prevented the generation of the hub vortex.…”

“…In this way they were able to confirm the results of the theoretical study by Ianniello (2016), finding that as one moves away from the propeller, the volume terms become dominant. However, the studies by Cianferra et al (2019b) and Cianferra & Armenio (2021) were still based on rather coarse simulations, unable to reproduce the instability mechanisms of the wake, which are expected to enhance the role of the quadrupole terms. In addition, the tractor configuration they considered prevented the generation of the hub vortex.…”

Vortex structures in the wake of a marine propeller operating close to a free surface

“…in the context of anti-surface warfare where the prediction of propeller-radiated noise based on the nominal wake can lead to misleading conclusions. Recent analyses reported in Cianferra & Armenio (2021) proved that the free surface plays an important role when scaling model-scale data to full scale, even though the air-water interface was considered flat and fixed.…”