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The purpose of this paper is to analyze the liquid sloshing behaviors in two-dimensional tanks with various porous baffles under the external excitation.

Adopting the finite element method (FEM) and control variable method to study the impacts of the height, length, number, location, shape, porous-effect parameter of the porous baffle, the external load frequency and the shape of the tank on the liquid sloshing response.

The amplitude of the free surface can be reduced effectively when the baffle opening is appropriate. The anti-sway ability of the system increases in pace with the baffle’s height growing. Under the same conditions, the shapes of the baffles have an important effect on improving the anti-sway ability of the system.

As there exist the differences of the velocity potential between each side of the porous baffle, which means that there are two different velocity potentials at a point on the porous baffle, the conventional finite element modeling technologies are not suitable to be applied here. To deal with this problem, the points on the porous baffle are regarded as two nodes with the same coordinate to model and calculate.

The paper aims to present a numerical modeling procedure for the analysis of liquid sloshing in a flexible tank subjected to an external excitation, with taking into account the effects of fluid–structure interaction (FSI).

A numerical model based on coupling a two-phase flow solver and an elastic solid solver is developed in OpenFOAM code. The Arbitrary Lagrangian–Eulerian formulation is adopted for the two-phase Navier–Stokes equations in a moving domain. The volume of fluid (VOF) method is applied for the air–liquid interface tracking. The finite volume method is used for the spatial discretization of both the fluid and the structure dynamics equations. The FSI coupling problem is solved by an explicit coupling scheme. The model is validated for linear and nonlinear sloshing cases. Then, it is used to analyze the effects of the liquid sloshing on the dynamic response of the tank and the effects of the tank flexibility on the liquid sloshing.

The obtained results show that the flexibility of the tank walls amplifies the amplitude of the sloshing and increases the fluctuation period of the air–liquid interface. Furthermore, it is found that the bending moment acting on the tank walls may be underestimated when rigid walls assumption is adopted as usually done in sloshing tank modeling. Also, tank walls flexibility causes a phase shift in the free surface dynamic response.

A review of previous studies on liquid sloshing in flexible tanks revealed that FSI effects have not been clearly and comprehensively analyzed for large-amplitude liquid sloshing. Many physical and numerical aspects of this problem still require clarifications and enhancements. The added value of the present work and its originality lie in the investigation of large-amplitude liquid sloshing in flexible tanks by using a staggered coupling approach. This approach is carried out by an original combination of a linear solid solver with a two phase fluid solver in OpenFOAM code. In addition, FSI effects on some response quantities, identified and analyzed herein, have not been found in the previous works.

The present work involves analytical and experimental investigation of sloshing in a two-dimensional rectangular tank including the effect of porous baffles to control and/or reduce the wave motion in the sloshing tank. The purpose of this study is to assess the analytical solutions of the drag coefficient effect on porous baffles performance to track free surface motion variation in the sloshing tank by comparison with experimental shake table tests under a range of sway excitation.

The linear second-order ordinary differential equations for liquid sloshing in the rectangular tank were solved using Newmark’s beta method and obtained the analytical solutions for liquid sloshing with dual vertical porous baffles of full submergence depths in a sway-oscillated rectangular tank following the methodology similar to Warnitchai and Pinkaew (1998) and Tait (2008).

The porous baffles significantly reduce wave elevation in the varying filled levels of the tank compared to the baffle-free tank under the range of excitation frequencies. It is observed that the Reynolds number-dependent drag coefficient for porous baffles in the tank can significantly reduce the sloshing elevations and is found to be effective to achieve higher damping compared to the porosity-dependent drag coefficient for porous baffles in the sloshing tank. The analytical model’s response to free surface elevation variations in the sloshing tank was compared with the experiment’s test results. The analytical results matched with shake table test results with a quantitative difference near the first resonant frequency.

The scope of the study is limited to porous baffles performance under range sway motion and three different filling levels in the tank. The porous baffle performance includes Reynolds number dependent drag coefficient to explore the damping effect in the sloshing tank.

The porous baffles with low-level porosities in the sloshing tank have many engineering applications where the first resonant mode of sloshing in the tank is more important. The porous baffle drag coefficient is an important parameter to study the baffle’s damping effect in sloshing tanks. Hence, obtained analytical solution for liquid sloshing in the rectangular tank with Reynolds number as well as porosity-dependent drag coefficient (model 1) and porosity-dependent drag coefficient porous baffles (model 2) performance is discussed. The model’s test results were validated using a series of shake table sloshing experiments for three fill levels in the tank with sway motion at various excitation frequencies covering the first four sloshing resonant modes.

The purpose of this paper is to develop the numerical simulated methodology for sloshing motion of fluid inside a two dimension rectangular tank, and parametric studies were performed for three parameters – excitation frequency, excitation amplitude, and liquid depth.

A numerically simulated methodology by using the cell‐centered pressure‐based SIMPLE scheme and level set method for the sloshing motion of fluid in a rectangular tank has been developed. The convection term in the Navier‐Stokes equations and the equations used in the level set method were treated by the second‐order upwind scheme. The temporal derivative terms were solved by the three‐level second order scheme. The diffusion term in the Navier‐Stokes equations alone was solved by the central‐difference scheme. All algebraic equations were solved by the point Gauss‐Seidel method. A fully implicit scheme to treat the level set distancing equation, written as the advection equation, was developed. In addition, the level set distancing equation was solved by the iterative procedure to determine the variation of free surface.

For given excitation amplitude together with a liquid depth, the free surface displacement increases when the excitation frequency is less than the resonance frequency of tank. However, the free surface displacement decreases when the excitation is greater than the resonant frequency of the tank. It is noted that the maximum free surface displacement is generated under the circumstance for which the excitation frequency approaches the resonant frequency. The excitation amplitude and the excitation frequency have a substantial effect on the impact pressure on the wall of the tank being investigated.

The sloshing motion of fluid in a rectangular tank has been studied by researchers and scholars using many numerical methods; however, literature employing the level set method to study the sloshing motion of fluid is limited. In this study, the cell‐centered pressure‐based SIMPLE scheme and level set method can be employed to predict the sloshing motion. The numerical methodology can help the engineer to predict sloshing motion of fluid.

The purpose of this paper is to derive linear modal equations describing the forced liquid sloshing in a rigid truncated (tapered) conical tank, as well as to show how to couple these modal equations with “global” dynamic equations of a complex mechanical system carrying this tank.

Derivation of the modal equations can be based on the Trefftz variational method developed by the authors in a previous paper. Describing the coupled dynamics utilizes Lukovsky' formulas for the resulting hydrodynamic force and moment due to liquid sloshing.

The so‐called Stokes‐Joukowski potentials can be found by using the Trefftz method from the authors' previous paper with the same polynomial‐type functional basis. Coupling the modal equations with the global dynamic equations becomes a relatively simple task facilitated by Lukovsky's formulas. Using the linear multimodal method can be an efficient alternative to traditional numerical and analytical tools employed for studying the coupled vibrations of a tower with a conical rigid tank on the tower top.

The derived modal equations are equipped by tables with the computed non‐dimensional hydrodynamic coefficients. Interested readers (engineers) can incorporate the modal equations into the global dynamic equations of a whole mechanical system without new computations of these coefficients.

The multimodal method can be an alternative to traditional numerical tools. Using the derived modal equations simplifies analytical studies and provides efficient calculations of the coupled dynamics of a mechanical system carrying a rigid tapered conical tank with a liquid.

Although much research work has been performed on the liquid sloshing inside simple cylindrical vessels, this paper deals with the analysis of the liquid sloshing in the annular region of more intricate coaxial circular cylinders. In this analysis, by utilizing the velocity potential theory, the transient response was formulated as a boundary value problem in the axisymmetrical vessels when the sine wave in resonance with the sloshing of the primary mode was applied.

This paper presents a new numerical model that, unlike most existing ones, can solve the whole liquid sloshing, nonlinear, moving boundary problem with free surface undergoing small to very large deformations without imposing any linearization assumptions.

The time‐dependent, unknown, irregular physical domain is mapped onto a rectangular computational domain. The explicit form of the mapping function is unknown and is determined as part of the solution. Temporal discretization is based on one‐step implicit method. Second‐order, finite‐difference approximations are used for spatial discretizations.

The performance of the algorithm has been verified through convergence tests. Comparison between numerical and experimental results has indicated that the algorithm can accurately predict the sloshing motion of the liquid undergoing large interfacial deformations.

The ability to model liquid sloshing motion under conditions leading to large interfacial deformations utilizing the model presented in this paper improves our ability to understand the problem of sloshing motion in tuned liquid dampers (TLDs), which would eventually help in constructing more effective TLDs.

The main purpose of this paper is to develop two efficient and accurate numerical analytical methods for engineering computation of natural sloshing frequencies and modes i the case of truncated circular conical tanks.

The numerical‐analytical methods are based on a Ritz Treftz variational scheme with two distinct analytical harmonic functional bases.

Comparative numerical analysis detects the limit of applicability of variational methods in terms of the semi‐apex angle and the ratio between radii of the mean free surface and the circular bottom. The limits are caused by different analytical properties of the employed functional bases. However, parallel use of two or more bases makes it possible to give an accurate approximation of the lower natural frequencies for relevant tanks. For V‐shaped tanks, dependencies of the lowest natural frequency versus the semi‐apex angle and the liquid depth are described.

The methods provide the natural sloshing frequencies for V‐shaped tanks that are valuable for designing elevated containers in seismic areas. Approximate natural modes can be used in derivations of nonlinear modal systems, which describe a resonant coupling with structural vibrations.

Although variational methods have been widely used for computing the natural sloshing frequencies, this paper presents their application for truncated conical tanks for the first time. An original point is the use of two distinct functional bases.

The purpose of this paper is to verify the ability of our in-house solver naoe-FOAM-SJTU to solve the problem of exterior fluid field coupled with interior fluid field and discover the coupling effects between exterior field (ship motion) and interior field (sloshing tanks).

The solving equation is based on Navier–Stokes equation, by comparing two turbulence models [laminar model and Reynolds-averaged Navier–Stocks (RANS)], of which RANS model are chosen to do the simulation. A unified approach is adopted to simulate exterior and interior fields simultaneously, keeping the pressure and velocity the same in external and internal fields. By adding a new function of calculating forces on different patches, the inner sloshing moments and external wave exciting moments can be output.

The in-house solver naoe-FOAM-SJTU had the ability to simulate this problem and showed well agreement with experimental results. By considering ship motion with and without sloshing, it was figured that with the existence of sloshing tank, the ship natural frequency will be changed. When the two tank fillings are the same, there will be another roll peak appeared, which is natural frequency of sloshing tanks. Considering wave height and different filling influence, the nonlinearity of sloshing in tank may give non-proportional response to ship motion.

With the ability to simulate well, the reality reference in the progress of FPSO or FLNG operation is obtained.

The value of this paper is a fully coupled CFD method which is adopted to solve the coupling effects, showing the ability to do the work well. It gives a referenced detailed information of inner and outer fluid field. Meanwhile, it carried out the impact pressure and damping force around the ship, which indicates the practical information in operations.

The purpose of this paper is to apply the Peridynamic differential operator (PDDO) to incompressible inviscid fluid flow with moving boundaries. Based on the potential flow theory, a Lagrangian formulation is used to cope with non-linear free-surface waves of sloshing water in 2D and 3D rectangular and square tanks.

In fact, PDDO recasts the local differentiation operator through a nonlocal integration scheme. This makes the method capable of determining the derivatives of a field variable, more precisely than direct differentiation, when jump discontinuities or gradient singularities come into the picture. The issue of gradient singularity can be found in tanks containing vertical/horizontal baffles.

The application of PDDO helps to obtain the velocity field with a high accuracy at each time step that leads to a suitable geometry updating for the procedure. Domain/boundary nodes are updated by using a second-order finite difference time algorithm. The method is applied to the solution of different examples including tanks with baffles. The accuracy of the method is scrutinized by comparing the numerical results with analytical, numerical and experimental results available in the literature.

Based on the investigations, PDDO can be considered a reliable and suitable approach to cope with sloshing problems in tanks. The paper paves the way to apply the method for a wider range of problems such as compressible fluid flow.