Cavitation Acoustic Perturbation Equations: A Computational Framework for Source-Resolved Multiphase Hydroacoustics

Abstract

This work develops a cavitation-consistent acoustic perturbation framework for predicting sound generation and propagation in cavitating flows. Unlike conventional acoustic perturbation equations for single-phase or weakly compressible flows, the proposed formulation embeds cavitation physics directly into the acoustic equations. The cavitation acoustic perturbation equations (CAPE) incorporate vapor mass transfer, mixture compressibility, and pressure-rate effects within a unified formulation, allowing cavitation-induced noise sources to be resolved in the computational domain. The numerical framework is verified using one-dimensional wave-propagation problems. The solutions become insensitive to further mesh and time-step refinement, the perfectly matched layer suppresses boundary reflections, and the predicted attenuation over a range of source frequencies follows Stokes' sound attenuation law. The framework is then applied to cavitating flow past a circular cylinder and a NACA hydrofoil. The non-cavitating benchmark shows dipole-like radiation associated with unsteady loading, whereas cavitating cases exhibit monopole-like or geometry-modulated radiation caused by volumetric phase change. Source-term analyses identify tonal frequencies associated with vortex shedding, cavity shedding, and collapse-induced excitation. The phase-change terms provide a direct volumetric contribution to the monopole-like source, while localized collapse events appear through amplification of the pressure-rate source. The proposed framework extends acoustic perturbation methods to cavitating multiphase flows and provides an efficient tool for hydroacoustic prediction, source localization, and mechanism analysis in marine and hydraulic applications.