Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence

TL;DR

This paper derives analytical expressions for acoustic radiation forces and torque on a rigid elliptical cylinder in various wave fields, highlighting the impact of elliptical geometry and incidence angle on these forces.

Contribution

It introduces a novel analytical framework for calculating radiation forces and torque on elliptical cylinders in acoustic fields, extending previous circular cylinder models.

Findings

Elliptical geometry significantly affects radiation force and torque.

The radiation torque vanishes for circular cylinders but not for elliptical ones.

Transition from progressive to standing waves influences force and torque behavior.

Abstract

Analytical expressions for the axial and transverse acoustic radiation forces as well as the radiation torque per length are derived for a rigid elliptical cylinder placed arbitrarily in the field of in plane progressive, quasi-standing or standing waves. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a fluid particle suspended in air, because of the significant acoustic impedance mismatch at the particle's boundary. Based on the partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross-section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape.