Hydrodynamic Characteristics of a Plane Wave Interacting with a Spherical Body in a Semi-Infinite Cylindrical Cavity Filled with a Compressible Fluid

A semi-infinite circular cylindrical cavity filled with an ideal compressible fluid and containing a spherical body located near its end is considered. A plain acoustic wave propagates along the axis of the cavity. The hydrodynamic characteristics of the system are determined depending on the frequency of the plane wave and the geometrical parameters. The method of separation of variables, the translational addition theorems for spherical wave functions, and the expressions of spherical wave functions in terms of cylindrical functions are applied. This approach allows satisfying all the boundary conditions and obtaining the exact solution of the boundary problem. The calculations are reduced to solving an infinite system of algebraic equations. Determining the pressure and velocity fields shows that the system has a number of frequencies at which the hydrodynamic characteristics can increase substantially. These abnormal frequencies differ from the frequencies of an infinite cylindrical cavity with a spherical body. Thus, the developed approach can detect anomalous features of the diffraction of a plane wave due to the influence of the end wall.