Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. Part I: Theoretical formulation and Numerical Investigation

TL;DR

This paper develops a comprehensive theoretical and numerical framework to analyze energy dissipation caused by sloshing and wave breaking in a liquid-filled pendulum system, with implications for designing Tuned Liquid Damper devices.

Contribution

It introduces a coupled nonlinear model combining semi-analytical and numerical methods to study energy dissipation in large amplitude oscillations, validated through SPH simulations.

Findings

Validated SPH model for system frequency response

Semi-analytical hydraulic jump model for small angles

Numerical extension to large oscillation angles

Abstract

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 Part I, 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 (SPH) 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 Part II of this work.