Fluid-Particle Motion During Rotary Sloshing

This paper presents the results of a theoretical and experimental investigation of fluid-particle motion in a partially filled cylindrical tank. The body of fluid is assumed to have a steady-state motion consisting of first nonsymmetric sloshing mode only (lowest J₁ mode), which gives rise to a free-surface wave that rotates around the tank at the sloshing natural frequency. It was found that theory predicts a net transport motion of the fluid particles in the direction of the free-surface waves when nonlinear terms are retained in differential equations that describe the fluid-particle displacements. Experimental measurements of the particle motion are compared with theoretical predictions. Fluid angular momentum was computed using the theoretical fluid motion and compared with the angular momentum that the fluid would possess if the fluid moved as a rigid body at the same rate as the free-surface waves. It was found that an upper bound to the ratio of the transport angular momentum to the rigid-body angular momentum was equal to 0.8 (η/a)², where η is the peak wave height of the free surface waves and a is the tank radius.