The Ffowcs Williams–Hawkings equation for hydroacoustic analysis of rotating blades. Part 1. The rotpole

Abstract

This paper deals with the use of the Ffowcs Williams–Hawkings equation for hydroacoustic analysis of rotating blades, and the deep difference between the acoustic fields generated by aeronautical and marine devices in air and underwater. This dissimilarity does not depend on either the different fluid or the (although existing) geometric and structural difference of the blade: it is an intrinsic feature of the generating noise mechanisms related to rotating sources and is essentially due to the remarkable diversity of the rotational speed. It will be shown how the usual assumption of believing the flow nonlinear sources to be negligible for blades rotating at low subsonic speed (coming from decades of research strictly limited to aeroacoustics) is totally wrong when applied to hydroacoustics. Such a goal is achieved through a practical approach, by analysing the general behaviour of the surface integral kernels of the solution for a rotating point source (here named rotpole), and by showing its relationship with a general multibladed device. This analysis suggests that the underwater noise prediction from a marine propeller is an inherently nonlinear problem and, contrary to analogous aeronautical configurations, it always requires an accurate estimation of the nonlinear flow sources just by virtue of the very low rotational speed.