Numerical model of energy dissipation and shallow-water sloshing motions in tank under different coupled excitations

Shallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.

Resolving wave and laminar boundary layer scales for gap resonance problems

Free surface oscillations in a narrow gap between elongated parallel bodies are studied numerically. As this represents both a highly resonant system and an arrangement of relevance to offshore operations, the nature of the damping is of primary interest, and has a critical role in determining the response. Previous experimental work has suggested that the damping could be attributed to laminar boundary layers; here our numerical wave tank successfully resolves both wave and boundary layer scales to provide strong numerical evidence in support of this conclusion. The simulations follow the experiments in using wave groups so that the computation is tractable, and both linear and second harmonic excitation of the gap are demonstrated.

Nonlinear Simulation of Wave Train Impact on a Vertical Seawall

A 2D nonlinear numerical wave flume is developed to investigate the wave train impact on a vertical seawall. Fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface. Cases of single-, double- and multi-crest wave trains are discussed. For single-crest wave train cases, the present nonlinear results are compared with the solution of the Serre-Green-Naghdi (SGN) model, showing good agreement. For double-crest wave train cases, the SGN model underestimates the maximum wave run-up along the vertical seawall. Compared with the linear results, the nonlinearity for double-crest cases can lead to an evident increase of the wave run-up and high-frequency free-surface oscillations. Through a fast Fourier analysis, evident nonlinear characteristics of the time series of the wave run-up and wave load during the wave impact process are confirmed. For multi-crest wave train cases, irregular wave run-ups can be observed. In some cases, the wave run-up along the vertical seawall can reach about 6 times that of the incident wave, which should be considered carefully in a practical design.

Dynamic Analysis of Partially Filled Non-circular Cylindrical Shells with Liquid Sloshing

The paper investigates the dynamic behavior of thin-walled reservoirs containing an ideal liquid taking into account the effects of hydroelastic interaction and sloshing. A mathematical statement of the problem is based on the principle of virtual displacements, which accounts for the pre-stressed non-deformed state of the shell caused by various force factors. The behavior of compressible liquid is described by linearized Euler equations, which are transformed by the Bubnov–Galerkin method. The dynamics of partially filled circular and elliptical cylindrical reservoirs are investigated numerically using a finite element procedure. It has been shown that allowing for sloshing considerably reduces eigenfrequencies of vibrations of the examined systems but has inessential effect on the displacements of the structure under non-stationary loads. Based on the modal analysis we present a classification of eigenmodes of free surface oscillations of a liquid in vertical tanks. It has been found that due to consideration of the sloshing effect, the frequency spectrum of the system can split into two parts in the case when the vibration frequencies of liquid differ from the vibration frequencies of an empty shell. Moreover, under harmonic excitation consideration of liquid sloshing leads to a more complicated amplitude-frequency curve characterized by displacement jumps.

ON FARADAY INSTABILITY IN MAGNETIC LIQUIDS: INCE-ERDELYI APPROACH APPLIED TO THE HILL EQUATION DESCRIBING OSCILLATIONS OF A FERROFLUID FREE SURFACE

When an isothermal ferrofluid is submitted to an oscillating magnetic field, the initially motionless liquid free surface can start to oscillate. This physical phenomenon is similar to the Faraday instability for usual Newtonian liquids subjected to a mechanical oscillation. In the present paper, we consider the magnetic field as a sum of a constant part and a time periodic part. Two different cases for the constant part of the field, being vertical in the first one or horizontal in the second one are studied. Assuming both ferrofluid magnetization and magnetic field to be collinear, we develop the linear stability analysis of the motionless reference state taking into account the Kelvin magnetic forces. The Laplace law describing the free surface deformation reduces to Hill’s equation, which is studied using the classical method of Ince and Erdelyi. Inside this framework, we obtain the transition conditions leading to the free surface oscillations.