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

摘要

Analytical expressions for the axial and transverse acoustic radiation forcesas well as the radiation torque per length are derived for a rigid ellipticalcylinder placed arbitrarily in the field of in plane progressive,quasi-standing or standing waves. The rigid elliptical cylinder case isimportant to be considered as a first-order approximation of the behavior of afluid particle suspended in air, because of the significant acoustic impedancemismatch at the particle's boundary. Based on the partial-wave series expansionmethod in cylindrical coordinates, non-dimensional acoustic radiation force andtorque functions are derived and defined in terms of the scatteringcoefficients of the elliptic cylinder. A coupled system of linear equations isobtained after applying the Neumann boundary condition for an immovable surfacein a non-viscous fluid, and solved numerically by matrix inversion afterperforming a single numerical integration procedure. Computational results forthe non-dimensional force components and torque, showing the transition fromthe progressive to the (equi-amplitude) standing wave behavior, are performedwith particular emphasis on the aspect ratio a/b, where a and b are thesemi-axes of the ellipse, the dimensionless size parameter, as well as theangle of incidence ranging from end-on to broadside incidence. The results showthat the elliptical geometry has a direct influence on the radiation force andtorque, so that the standard theory for circular cylinders (at normalincidence) leads to significant miscalculations when the cylinder cross-sectionbecomes non-circular. Moreover, the elliptical cylinder experiences, inaddition to the acoustic radiation force, a radiation torque that vanishes forthe circular cylinder case. The application of the formalism presented here maybe extended to other 2D surfaces of arbitrary shape.