Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger(SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop.These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Smoothed-Particle Hydrodynamics Simulation of Ship Motion and Tank Sloshing under the Effect of Regular Waves

Predicting the response of liquefied natural gas(LNG)contained in vessels subjected to external waves is extremely important to ensure the safety of the transportation process.In this study,the coupled behavior due to ship motion and liquid tank sloshing has been simulated by the Smoothed-Particle Hydrodynamics(SPH)method.Firstly,the sloshing flow in a rectangular tank was simulated and the related loads were analyzed to verify and validate the accuracy of the present SPH solver.Then,a three-dimensional simplified LNG carrier model,including two prismatic liquid tanks and a wave tank,was introduced.Different conditions were examined corresponding to different wave lengths,wave heights,wave heading angles,and tank loading rates.Finally,the effects of liquid tank loading rate on LNG ship motions and sloshing loading were analyzed,thereby showing that the SPH method can effectively provide useful indications for the design of liquid cargo ships.

The Effects of Fluid Sloshing on Different Baffle Configurations in Storage Tanks Transported on Trucks during an Emergency Braking

Different Baffle designs usable in cylindrical and elliptical storage tanks carried by trucks often used for transporting inflammable liquid materials in Cameroon are investigated to evaluate their safest fluid sloshing damping response during emergency braking where the magnitude of sloshing waves are the greatest. The uncontrolled fluid sloshing creates thrust on the walls of the tanks usually felt externally on the truck carrying the tank and capable of hindering driver’s effort to maintain steer ability and improve on safety during critical braking moments. The study first passes through COMSOL, to expose the safest margin of each Baffle type at instantaneous fluid pressure wave propagation initiated at a single phase to reflect sloshing in the storage tank during an emergency braking by the truck carrying the tank. The vivid results can be seen in the domain of Acoustic Iso-surface Pressure response;but also acoustic Pressure and Sound pressure response are seen automatically. Secondly, through an experimental finding in which fluid is forced to pass through each Baffle and the resistance to fluid flow is a measured as it’s the Baffle’s damping ability. Either, the fluid is lost through the Baffle and by determination of the surface load exerted on each Baffle due to the reaction of the residual fluid acting on the surface of each Baffle after some of it is Lost, the individual sloshing damping abilities are exposed. By comparing the Experimental outcome with the computational response obtained, an ideal Baffle design is proposed for cylindrical and elliptical tanks and considered to respond to abrupt braking more effciently. The application of the Baffle designs with an average multiple holes rather than the usual face centered proved to be more effcient in fluid sloshing as they provide a more uniformly distributed damping pressure during fluid sloshing in the tank thereby reducing the magnitude of forward thrust that can be created by the conventional Baffle type during emergency braking hence contributing to improving safety. Mindful of the human, material and environmental damages that an accident involving mobile petroleum storage tanks can course, this study is therefore of great significance for design optimization by petroleum storage tank manufacturing companies in Cameroon.

A BOUNDARY ELEMENT METHOD FOR SMALL-AMPLITUDE VISCOUS FLUID SLOSHING IN COUPLE WITH STRUCTURAL VIBRATION

A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.

Nonlinear semi-analytical modeling of liquid sloshing in rectangular container with horizontal baffles

A nonlinear semi-analytical scheme is proposed for investigating the finiteamplitude nonlinear sloshing in a horizontally baffled rectangular liquid container under the seismic excitation.The sub-domain method is developed to analytically derive the modal behaviors of the baffled linear sloshing.The viscosity dissipation effects from the interior liquid and boundary layers are considered.With the introduction of the generalized time-dependent coordinates,the surface wave elevation and velocity potential are represented by a series of linear modal eigenfunctions.The infinite-dimensional modal system of the nonlinear sloshing is formulated based on the Bateman-Luke variational principle,which is further reduced to the finite-dimensional modal system by using the NarimanovMoiseev asymptotic ordering.The base force and overturning moment induced by the nonlinear sloshing are derived as the functions of the generalized time-dependent coordinates.The present results match well with the available analytical,numerical,and experimental results.The paper examines the surface wave elevation,base force,and overturning moment versus the baffle parameters and excitation amplitude in detail.

Review on the Progress and Issues in Liquid Tank Sloshing of Ships

With the development of large liquid cargo ships,liquid tank sloshing has gradually become a hot research topic in the area of shipping and ocean Engineering.Liquid tank sloshing,characterized by strong nonlinearity and randomness,not only affects the stability of the ship but also generates a huge impact force on the wall of the tank.To further investigate liquid tank sloshing,a comprehensive review is given on the research process of the most focused subjects of liquid sloshing.Summarizing the existing research will help to identify issues in the current field and provide useful references.The methods for investigating sloshing,the research progress and the situations worldwide are discussed.The advantages and defects of experiments and numerical simulations are also explored.The problems which need to be explored in the future are subsequently proposed.

Structural Analogy for Dynamic Analysis of Liquid Sloshing

The analogy between the wave equation of liquid and the Navier equations of structural elasticity is examined in detail. By introducing appropriate parameters, the structural counterpart of the liquid sloshing model can be easily built. Therefore, the dynamic analysis of liquid sloshing can be reduced to that of structural elasticity, and the existing FEM structural analysis computer programs can be applied to liquid sloshing analysis without any modification. The present method also reveals the internal relationship between liquid sloshing and structural vibration. The effectiveness and reliability of the method is illustrated by the numerical example.

ALE FINITE ELEMENT ANALYSIS OF NONLINEAR SLOSHING PROBLEMS BASED ON F LUID VELOCITY POTENTIAL

Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.

HYBRID APPROACH FOR ESTIMATING COUPLING EFFECT BETWEEN PROPELLANT SLOSHING DYNAMIC AND SPACECRAFT GNC

An approach based on equivalent mechanics theory and computational fluid dynamics （CFD） technology is proposed to estimate dynamical influence of propellant sloshing on the spacecraft. A mechanical model is estab- lished by using CFD technique and packed as a ＂sloshing＂ block used in spacecraft guidance navigation and control （GNC） simulation loop. The block takes motion characteristics of the spacecraft as inputs and outputs of pertur- bative force and torques induced by propellant sloshing, thus it is more convenient for analyzing coupling effect between propellant sloshing dynamic and spacecraft GNC than using CFD packages. An example demonstrates the accuracy and the superiority of the approach. Then, the deducing process is applied to practical cases, and simulation results validate that the proposed approach is efficient for identifying the problems induced by sloshing and evaluating effectiveness of several typical designs of sloshing suppression.

Effects of Perforated Baffle on Reducing Sloshing in Rectangular Tank:Experimental and Numerical Study

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional （3D） rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

Investigation of the Effects of Baffles on the Shallow Water Sloshing in A Rectangular Tank Using A 2D Turbulent ISPH Method

Liquid sloshing is a common phenomenon in the liquid tanks transportation. Liquid waves lead to fluctuating forces on the tank wall. Uncontrolled fluctuations lead to large forces and momentums. Baffles can control these fluctuations. A numerical method, which has been widely used to model this phenomenon, is Smoothed Particle Hydrodynamics(SPH). The Lagrangian nature of this method makes it suitable for simulating free surface flows. In the present study, an accurate Incompressible Smoothed Particle Hydrodynamics(ISPH) method is developed and improved using the kernel gradient correction tensors, particle shifting algorithms, k–ε turbulence model, and free surface particle detectors. Comparisons with the experimental data approve the ability of the present algorithm for simulating shallow water sloshing. The main aim of this study is to investigate the effects of the vertical baffle on the damping of liquid sloshing. Results show that baffles number has a major role in sloshing fluctuation damping.

A SPH simulation on large-amplitude sloshing for fluids in a two-dimensional tank

Smoothed particle hydrodynamics（SPH） is a mesh-free adaptive Lagrangian particle method with attractive features for dealing with the free surface flow.This paper applies the SPH method to simulate the large-amplitude lateral sloshing both with and without a floating body,and the vertical parametrically-excited sloshing in a two-dimensional tank.The numerical results show that the SPH approach has an obvious advantage over conventional mesh-based methods in handling nonlinear sloshing problems such as violent fluid-solid interaction,and flow separation and wave-breaking on the free fluid surface.The SPH method provides a new alternative and an effective way to solve these special strong nonlinear sloshing problems.

Damping computation of liquid sloshing with small amplitude in rigid container using FEM

An FEM （Finite Element Method） based damping estimation method of liquid sloshing with small amplitude in rigid container is proposed. Damping of the sloshing is affected by many factors and some of them are very complicated. Therefore, this paper aims to provide an estimation range, instead of computing the exact value of damping. This method will consider the dissipation at wall, in the interior, and at the contaminated free surface. Owing to the complexity of viscous damping at the free surface, damping of two extreme conditions are computed to estimate the range of actual damping. An iterative algorithm is designed to solve a special general eigenvalue problem. Comparing the computation results with experimental results, it is found that most of the experimental results are within the range of the numerical estimation. Therefore, the method is effective in estimating the range of the damping of liquid sloshing with small amplitude in rigid container.

Numerical simulations of sloshing and suppressing sloshing using the optimization technology method

Sloshing is a common phenomenon in nature and industry, and it is important in many fields, such as marine engineering and aerospace engineering. To reduce the sloshing load on the side walls, the topology optimization and optimal control methods are used to design the shape of the board, which is fixed in the middle of the tank. The results show that the new board shape, which is designed via topology optimization, can significantly reduce the sloshing load on the side wall.

Experimental Study on Sloshing Characteristics in the Elastic Tank Based on Morlet Wavelet Transform

Hydroelastic effect of sloshing is studied through an experimental investigation. Different excitation frequencies are considered with low-fill-depth and large amplitude. Morlet wavelet transform is introduced to analyze the free surface elevations and sloshing pressures. It focuses on variations and distributions of the wavelet energy in elastic tanks. The evolutions of theoretical and experimental wavelet spectra are discussed and the corresponding Fourier spectrums are compared. Afterwards, average values of the wavelet spectra are extracted to do a quantitative study at various points. From the wavelet analysis, sloshing energies are mainly distributed around the external excitation frequency and expanded to high frequencies under violent condition. In resonance, experimental wavelet energy of the elevation in elastic tanks is obviously less than that in the rigid one; for sloshing pressures, the elastic wavelet energy close to the rigid one and conspicuous impulse is observed. It recommends engineers to concern the primary natural frequency and impulsive peak pressures.

Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

An Approximation to Energy Dissipation in Time Domain Simulation of Sloshing Waves Based on Linear Potential Theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory. The boundary value problem is solved by the NURBS （non-uniform rational B-spline） higher-order panel method, in which a time-domain Green function is employed. The energy dissipation is modeled by changing the boundary condition on solid boundaries. Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion. Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other. It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.

Experimental Study on A Sloshing Mitigation Concept Using Floating Layers of Solid Foam Elements

A sloshing mitigation concept taking advantage of floating layers of solid foam elements is proposed in the present study. Physical experiments are carried out in a liquid tank to investigate the hydrodynamic mechanism of this concept. Effects of the foam-layer thickness, excitation amplitude, and excitation frequency on the sloshing properties are analyzed in detail. It is found that the floating layers of solid foam elements do not evidently affect the fundamental natural sloshing frequency of the liquid tank evidently among the considered cases. At the resonant condition, the maximum wave height and dynamic pressure are greatly reduced as the foam-layer thickness increases. Higher-order pressure components on the tank side gradually vanish with the increase of the foam-layer thickness. Cases with different excitation amplitudes are also analyzed. The phenomenon is observed when the wave breaking in the tank can be suppressed by solid foam elements.

Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems

A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory.

Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method

A meshless numerical simulation method, the moving-particle semi-implicit method （MPS） is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method （ICCG）, the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.