Multiple scattering field and derived acoustic interaction force and torque for multiple non-spherical axisymmetric objects

Abstract

While analytical theories exist for the acoustic radiation force and torque on single irregular geometries, dealing with multiple objects subject to non-orthogonal and inseparable boundary conditions remains a challenge. Here, we present a calculation method to formulate the interaction effects of multiple axisymmetric geometries with irregular cross-section excited by a time-harmonic external wave in the inviscid fluid. The approach utilizes the translation addition theorem to incorporate the interaction effects among different objects and the conformal transformation approach to capture the non-spherical geometric features. This facilitates the separation of variables for solving the corresponding Helmholtz wave equation, subject to spherical boundary conditions in the mapping coordinate system. As a result, the multiple scattering fields can be determined. Subsequently, the acoustic interaction force and torque can be derived using the scattered pressure field. The validity of the method is demonstrated through comparisons with numerical simulations based on finite element method across a wide range of frequencies and various geometric combinations. The proposed method shows strong agreement with the traditional finite element method while requiring much less computational time.