Study on the attenuation effect of pressure wave by bubble clusters using the compressible multi-scale method

• A compressible multi-scale model for evaluating pressure wave attenuation caused by bubble clusters is proposed. • The propagation process and attenuation mechanism of pressure waves among bubble clusters are presented. • The effects of pressure wave amplitudes and bubbles numbers and bubble sizes on pressure wave attenuation are investigated. Bubble clusters are widely existed in nature and every single bubble will pulsate under its surrounding ambient pressure wave. To simulate the motion of bubble cluster under pressure wave is a great challenge for both algorithm robustness and calculation cost. This paper introduces a multi-scale method to simulate interaction between the pressure wave and bubble clusters comprising several thousand natural bubbles. In this model, the propagation process of pressure waves is simulated within a continuous Eulerian field, while the bubble clusters are depicted as Lagrangian points distributed in this field. The flow field information surrounding the bubbles is acquired by interpolation from the Eulerian field. Bubble oscillation and migration are accurately calculated using bubble theory. The variations of the bubble clusters are incorporated as source terms in the equations to achieve two-way coupling solution, which facilitates a more precise simulation of the interaction between underwater pressure waves and bubble clusters. Comparison with experimental data demonstrates the advantages and effectiveness of the computational model in simulating bubble cluster coupled with underwater pressure wave. Subsequently, this paper investigates the propagation process and attenuation mechanism of pressure waves among bubble clusters, analyzing the effects of pressure wave amplitudes and bubbles numbers and bubble sizes on pressure wave attenuation. Our results indicate that the pressure wave attenuation is dominated by the initial gas volume fraction of the bubble cluster and is not significantly affected by the pressure wave amplitude.