Wave Analysis of Liquid Partially Filled in a Rotating Cylinder

Nonlinear Resonance Curve by Shallow Water Theory

Abstract

Wave motion of a liquid in a rotating, axially symmetric container undergoing a whirl motion is investigated. In the analysis, gravity is considered negligible and the liquid motion is taken as being axially uniform. Assuming that the liquid layer is thin, the equations of motion are simplified to one-dimension problem along the circumference of the container by shallow-water theory. The modal coupling equations including the nonlinear effects of the wave motion are presented by applying Galerkin's method. Periodical solutions under harmonic whirl motion, which give resonance curves, are determined by applying the harmonic balance method to the modal coupling equations. The wave height and the fluid force acting on the container obtained from the analysis are compared with the experimental results in the previous works. A good agreement is found between the analysis and the experimental results about the wave height profile and the magnitude of the fluid force by which the asynchronous whirl motion of the container is excited.