Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. I. Theoretical formulation and numerical investigation

A dynamical system involving a driven pendulum filled with liquid is analyzed in the present paper series. The study of such a system is conducted in order to understand energy dissipation resulting from the shallow water sloshing and induced wave breaking. This analysis is relevant for the design of Tuned Liquid Damper devices. The complexity and violence of the flow generated by the roll motion results in the impossibility of using an analytical approach, requiring in turn the use of a suitable numerical solver. In this paper, the coupled dynamical system is thoroughly described, revealing its nonlinear features associated with the large amplitude of the forcing, both in terms of mechanical and fluid dynamical aspects. A smoothed particle hydrodynamics model, largely validated in literature, is used to calculate the frequency behavior of the whole system. For small rotation angles, a semi-analytical model of the energy dissipated by the fluid, based on a hydraulic jump solution, is developed; the energy transfer is numerically calculated in order to extend the analysis to large oscillation angles. The experimental part of the investigation is carried out in Paper II [B. Bouscasse, A. Colagrossi, A. Souto-Iglesias, and J. L. C. Pita, "Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. II. Experimental investigation," Phys. Fluids 26, 033104 (2014)] of this work. © 2014 AIP Publishing LLC.