Simplified models of acoustic Faraday cage

Abstract

A theoretical framework for modelling the acoustic isolation performance of a bubbly curtain consisting of a circular array of bubbly plumes is proposed. The plumes are considered as cylindrical columns with effective acoustic properties deduced from the conventional formulas for a bubbly medium. The rationale for this design is the ability to engage the collective modes of the plumes leading to favorable low frequency performance, defined by a low insertion ratio. Two analytical models have been evaluated. First, the multiple scattering model expressing the results in terms of the scattering amplitude of individual plumes known from the previous studies and, second, the model of an effective boundary condition imposed on the centreline of the array. It is found that the former model performs better over a broad range of parameters. It is shown that the main parameter controlling the system performance is the reflection coefficient of the array, which can be deduced analytically and used to maximize the suppression of a given frequency of an acoustic noise source. As a demonstration of the predictive capability of the framework, the optimal system parameters are derived and then validated with the results of finite element modelling, showing good agreement.