Predicting radiated noise of marine propellers using acoustic analogies and hybrid Eulerian-Lagrangian cavitation models

Abstract

Anthropogenic noise from a variety of merchant ships has been reported to be a major factor adversely affecting marine organisms. Consequently, scientists and regulators have become more vocal about encouraging, and possibly enforcing, quieter ships in the future. For this to be feasible from an engineering standpoint, a range of numerical methods must be made available to allow acoustic performance of vessels to be evaluated at the design stage.

Cavitation is a major contributor to the hydroacoustic signature of a merchant vessel. The reason for this is the relatively high drop of pressure induced by the propeller, which in turn promotes the growth of vapour bubbles and cavities, oscillation and collapse of which act as strong acoustic sources. The entire process is made more dynamic by the non-uniform wake of the ship, propeller rotation, as well as the fact that vessels travel in a seaway. Because of its complexity, the problem of marine propeller noise is thus not widely studied numerically, which translates to the lack of tools readily available to designers willing to reduce the noise generated by ships.

A set of numerical utilities are proposed which could be employed at the late design stage of a merchant ship in order to allow the designer to estimate the radiated noise and make informed decisions on how to improve the design. The methodology involves solving the turbulent flow over the propeller using Detached Eddy Simulation (DES) and modelling cavitation using a mass-transfer model. The porous Ffowcs Williams-Hawkings acoustic analogy is used to infer far-field radiated noise caused by the blade rotation, pulsating cavitation, as well as non-linear noise sources in the propeller slip-stream. The cavitation model is also extended to incorporate Lagrangian bubbles dispersed downstream of the large cavities modelled using the baseline Schnerr-Sauer model via the volume fraction equation approach. This allows the broadband nature of cavitation noise to be captured.

The methods are applied to a NACA 66 and the Delft Twist 11 hydrofoil test cases. Although there are limited validation data allowing all of the methods to be validated simultaneously, relatively good agreement is seen at intermediate validation stages. These include comparing the non-cavitating noise of the Insean E779a propeller to reference data, conducting acoustic predictions for idealised acoustic sources, as well as comparing cavitation patterns, cavity cloud shedding frequencies, and induced pressures to experimental data for hydrofoils and propellers.

It is concluded that the presented methodology may be used to predict low-frequency noise due to cavitation in a relatively robust manner, although the method is yet to be tested and validated on more complex geometries. The hybrid Eulerian-Lagrangian model is still at an early stage and a range of areas for improvement have been identified, such as implementation of more realistic cavity break-up models as well as better coupling between the fluid and bubble solvers. Nonetheless, the method is demonstrated to be a promising tool at tackling the broadband cavitation noise components as it can capture the contribution of the mass of small, oscillating bubbles on the radiated pressure which would otherwise be unaccounted for in the baseline Eulerian framework.

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Identifiers

ORCID for Stephen Turnock: orcid.org/0000-0001-6288-0400

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