A three-dimensional (3D) gradient-augmented level set (GALS) two-phase flow model with a pretreated reinitialization procedure is developed to simulate violent sloshing in a cuboid tank. Based on a two-dimensional (2D) GALS method, 3D Hermite, and 3D Lagrange polynomial schemes are derived to interpolate the level set function and the velocity field at arbitrary positions over a cell, respectively. A reinitialization procedure is performed on a 3D narrow band to treat the strongly distorted interface and improve computational efficiency. In addition, an identification-correction technique is proposed and incorporated into the reinitialization procedure to treat the tiny droplet which can distort the free surface shape, even lead to computation failure. To validate the accuracy of the present GALS method and the effectiveness of the proposed identification-correction technique, a 3D velocity advection case is first simulated. The present method is validated to have better mass conservation property than the classical level set and original GALS methods. Also, distorted and thin interfaces are well captured on all grid resolutions by the present GALS method. Then, sloshing under coupled surge and sway excitation, sloshing under rotational excitation are simulated. Good agreements are obtained when the present wave and pressure results are compared with the experimental and numerical results. In addition, the highly nonlinear free surface is observed, and the relationship between the excitation frequency and the impulsive pressure is investigated.

Proper evaluation of forces exerted on a solid boundary by liquid sloshing is difficult. If the free board in a liquid storage tank is insufficient, the sloshing waves caused by seismic excitation will collide with the tank roof and may cause major damage. The current study investigated the sloshing wave impact force (SWIF) in full-scale liquid storage tanks using numerical simulation based on the lattice Boltzmann method (LBM). Several shaking table tests have been conducted on a small-scale rectangular tank to validate the numerical model. The results of a standard dam break test have been used to express the validity of the proposed numerical model. This comparison confirms the validity of the numerical strategy for simulating the effect of sloshing. After validating the numerical model, it has been applied to a practical parametric study of SWIF in full-scale liquid tanks. The results of numerical simulation indicate that the simplified method recommended by related codes and standards for calculating SWIF in liquid tanks significantly underestimates the sloshing force. This confirms that the dynamic nature of sloshing should be considered in the design process of liquid storage tanks.

A numerical model of a rectangular tank containing a layered liquid is modeled for studying layered sloshing wave. The Arbitrary Lagrangian Eulerian method is used to track the development for both the interfacial and free surface of the fluid domain. A series of cases are simulated for baffled and unbaffled sloshing with various excitation frequencies and various baffle configurations. A case containing a submerged block is also simulated to observe the interfacial wave interaction with the block structure and to observe how the position and size of the block affect the interfacial wave in a fluid. Velocity screenshots are analyzed for observing the velocity distribution in the layers and to observe the behavior of the interfacial layer for baffled and unbaffled tank cases. A fast Fourier transform spectral analysis of the layered liquid sloshing time series for both the interfacial layer and free surface layer is presented to observe the energy in the fluid layers as well as to observe the dominant peak frequency for both the layers.

Simulations of oscillatory motion in partially filled rectangular tanks with different tank geometries, fullness ratios, and motion frequencies are presented. Smoothed particle hydrodynamics (SPH) method is used to discretize the governing equations together with new velocity variance-based free surface (VFS) and artificial particle displacement (APD) algorithms to enhance the robustness and the accuracy of the numerical scheme. Two-dimensional (2D) oscillatory motion is investigated for three different scenarios where the first one scrutinizes the kinematic characteristics in resonance conditions, the second one covers a wave response analysis in a wide range of enforced motion frequencies, and the last one examines the dynamic properties of the fluid motion in detail. The simulations are carried on for at least 50 periods in the wave response analysis. It is shown that numerical results of the proposed SPH scheme are in match with experimental and numerical findings of the literature.

Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

Tuned liquid dampers (TLDs) are considered economical and effective dynamic vibration absorbers. They are increasingly being used to mitigate the dynamic resonant response of tall buildings and it is often designed to reduce the structure's acceleration at a serviceability limit state. Slat screens can increase the inherent damping factor of TLDs. They have been used as a common flow damping device in TLDs because of the simplicity of using them and also the ability to control their effects on the performance of a TLD. Two slat screens with the same solidity ratio and different patterns could have different effects on the TLD's performance. Many former numerical researches used the potential and linear theory as a base to describe the fluid flow behavior inside the TLD. The applicability of the linearized flow models was for the condition of the low amplitude of excitations. Under large excitation events such as high return period wind storms or earthquakes, the assumptions of linear theory are no longer valid. Moreover, in the linearized model, screens were modeled as a hydraulic resistance point as a function of the screen solidity ratio without the ability to consider the effect of screen pattern. In the present study, a numerical algorithm has been developed which can handle both the small and large amplitude of excitations. In this algorithm, the fluid flow through the screen is fully resolved and it can take into account the effect of the screen pattern on the TLD's performance. The major focus of this paper is to use this developed algorithm and conduct a numerical investigation to study the effects of the slat screen pattern on the inherent damping and natural frequency of the TLD, as the design parameters of the TLD. In this numerical investigation a selected TLD outfitted by different slat screens and interacted with the structure is exposed by both harmonic and random external excitations. The numerical results have been validated against experimental work. The effect of slat screen pattern on the damping effect and natural frequency of a TLD has been presented. Also in this study, two new parameters termed as slat ratio (SR) and effective solidity ratio (Seff) are presented to imply the physical significance of screen pattern.

This paper presents a model to describe the behavior of sloshing in a general tank with a uniform fluid depth. An equivalent linearized mechanical model is developed for a tuned liquid damper (TLD) with arbitrary tank geometry. The finite element method is employed to determine the mode shapes of the sloshing fluid. In general, the mode shapes of arbitrary tanks will have response components in the x - and y -directions. The mode shapes enable the generalized properties of the sloshing fluid to be determined; these properties are subsequently used to establish equivalent mechanical properties. The nonlinear damping of slat-type damping screens is linearized, permitting it to be included in the model as amplitude-dependent viscous damping. The proposed model is in excellent agreement with existing linearized models for the special cases of rectangular and circular tanks. Sinusoidal shake table tests are conducted on tanks with chamfers placed in selected corners. In the literature, no experimental testing has focused on tanks of arbitrary shape with a constant fluid depth. The proposed model is in good agreement with the experimental results for the mode dominated by motion in the direction of excitation. However, the model is found to underestimate the response of the mode which is dominated by motion perpendicular to the excitation direction. The linearized mechanical model developed can serve as a useful preliminary TLD design tool.

This article reports on an experimental study conducted to investigate slosh forces and moments caused by fluid slosh within a partly-filled tank subjected to lateral and longitudinal excitations applied independently. The experiments were performed on a scale model cleanbore and a baffled tank with laterally placed single- and multiple-orifice baffles. The experiments were conducted for three different fill volumes and different types of excitations: continuous harmonic and single-cycle sinusoidal excitations of different amplitudes and discrete frequencies. The dynamic forces and moments caused by fluid slosh with the baffled and cleanbore tank configurations were measured for different fill volumes and excitations using three-axis dynamometers. It is shown that the resulting forces and moments comprise many spectral components that can be associated with the excitation, resonance, and vibration and beat frequencies. Modulation of excitation frequency with the resonant frequency was also evident for all fill conditions and tank configurations when the two were in close proximity. The results also showed that the peak amplifications of forces and moments occur in the vicinity of the resonant frequency. At higher frequencies, the peak magnitudes of the forces, however, reduced significantly to values lower than the inertial forces developed by an equivalent rigid mass. At a given excitation condition, the slosh force amplitude increased with a decrease in the fill volume. It was also observed that the presence of baffles has negligible effect on the lateral slosh force and the corresponding resonant frequency. However, it caused a significant increase in the longitudinal mode resonant frequency. The baffles greatly reduced the amplifications in longitudinal force and pitch moment under longitudinal acceleration excitations.

The present study is concerned with liquid tank sloshing at low filling level conditions. The volume of fluid method implemented in a Navier–Stokes computational fluid dynamics code is employed to handle the free-surface flow of liquid sloshing. The geometric reconstruction scheme for the interface representation is employed to ensure sharpness at the free surface. The governing equations are discretized by second order accurate schemes on unstructured grids. Several different computational approaches are verified and numerical uncertainties are assessed. The computational results are validated against existing experimental data, showing good agreement. The capability is demonstrated for a generic membrane-type liquefied natural gas carrier tank with a simplified pump tower inside. The validation results suggest that the present computational approach is both easy to apply and accurate enough for more realistic problems.

A numerical investigation on Glimm’s method as applied to water sloshing and impacting is carried out. Emphasis is given to the handling and predicting hydraulic jumps. The effects of the spatial and temporal discretizations are examined. Three shallow water problems, 1) dam-breaking problem, 2) water sloshing in a rolling tank, and 3) impact of breaking of a water reservoir, are studied. It is shown numerically that Glimm’s method is stable and converged solutions can be obtained. The characteristics of the hydraulic jumps are well captured by the numerical calculations. The numerical results are in good agreement with either analytical solutions or experimental data.

The sloshing of liquids in tanks that use a flexible, inextensible bladder to contain the liquid is investigated experimentally and theoretically. The bladder affects both the configuration of the liquid in the tank and the sloshing frequencies and motion. The governing equations of liquid sloshing coupled to the structural dynamics of the bladder are formulated and examined to determine the interaction between the body forces of the liquid and the stiffness of the bladder and to show that the slosh dynamics can be represented by equivalent mechanical models. Tests are conducted to establish such mechanical models for normal and low-gravity conditions. For an inverted tank (liquid above the bladder), the sloshing is sufficiently different from conventional sloshing that the form of the equivalent mechanical model as well as the numerical values of the model parameters must be derived from the test results.

This paper presents an overview of the current state-of-the-art in scale modeling of liquefied natural gas sloshing in ship tanks. The numerous potentially significant scaling parameters are discussed in detail and laboratory test data illustrating the effects of the important scaling parameters are presented. In view of current knowledge, an indication of appropriate scaling criteria is presented and recommendations for additional research efforts are outlined.

The coupled oscillations of a liquid partially filled container having an elastic bottom or elastic walls have been studied. Two different tank configurations, a rectangular and a circular container both with flat bottoms are considered. For the cases where the flexibility of the container walls of a rectangular tank are taken into account, the lowest frequency of the system occurs when the tank is completely filled. The frequency increases as the depth of the liquid decreases. The corresponding natural frequencies for a rectangular tank having one flexible wall only are slightly higher. The effect of flexibility of the bottom of a rectangular tank shows a reduction of natural frequencies of the system. The frequency increases as the depth of the liquid increases and gradually approaches to the value corresponding to that of the rigid container. The more flexible the bottom, the lower the frequency will be. For a circular cylindrical container the frequency increases with increasing wall thickness and exhibits lower values for larger liquid heights.