The aim of this work is to show the potential of the Acoustic Analogy in the analysis of the underwater noise generated by a marine propeller. In particular, some formulations proposed by Feri Farassat are used to conduct an investigation on an interesting and rather unknown aspect of the problem: the identification of the most significant noise generating mechanisms taking place underwater and related to the propeller. Sample numerical results are presented, that were obtained by coupling an incompressible hydrodynamic code to an acoustic solver based on the Ffowcs Williams-Hawkings (FWH) equation, suitably designed to manage the huge set of data from the hydrodynamic simulation. A surprising outcome is that, contrary to popular belief and regardless of the low blade rotational speed, a reliable hydroacoustic analysis of a marine propeller seems to require the computation of the FWH equation's nonlinear quadrupole sources and cannot leave apart an accurate estimation of the three-dimensional turbulence and vorticity fields.
The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.
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