Sloshing Response Research Articles

Seismic Design of a Double Deck Floating Roof Type Used for Liquid Storage Tanks

Sloshing response of a cylindrical liquid storage tank with the double deck type floating roof (DDFR) subjected to seismic excitation is considered in this paper. The aim of the paper is to clarify the significant parameters that should be considered in the seismic design of a DDFR and proposing a practical seismic design procedure for evaluating the dynamic stresses inside a DDFR. A numerical method including fluid–structure interaction and the geometry details of a DDFR tank are established. The geometric nonlinear effects on the seismic behavior of the DDFR as well as the accuracy of common analytical solution suggested in the literature are examined by the numerical model. The numerical results show that the geometric nonlinear effects can considerably reduce the seismic stress in DDFR, but have no significant effect on the liquid hydrodynamic pressure exerted on the DDFR and the roof's vertical displacement. It is also revealed that not only the general displacement of DDFR but also the local effects of liquid hydrodynamic pressure on the bottom plate should be considered for seismic design of a DDFR. Finally, a design procedure for the evaluation of dynamic stress in the DDFR due to the seismic loads is proposed and discussed.

Parametric Study of Sloshing Effects in the Primary System of an Isolated Lead-Cooled Fast Reactor

Risks related to sloshing of liquid metal coolant due to seismic excitation need to be investigated. Sloshing effects on reactor performance include first, fluid-structure interaction and second, gas entrapment in the coolant with subsequent transport of void to the core region. While the first can hypothetically lead to structural damage or coolant spill, the second increases the risk of a reactivity insertion accident and/or local dryout of the fuel. A two-dimensional computational fluid dynamics study is carried out in order to obtain insights into the modes of sloshing depending on the parameters of seismic excitation. The applicability and performance of the numerical mesh and the Eulerian volume of fluid method used to track the free surface are evaluated by modeling a simple dam break experiment. Sloshing in the cold plenum free surface region of the European Lead-cooled SYstem (ELSY) conceptual pool-type lead-cooled fast reactor (LFR) is studied. Various sinusoidal excitations are used to imitate the seismic response at the reactor level. The goal is to identify the domain of frequencies and magnitudes of the seismic response that can lead to loads threatening the structural integrity and possible core voiding due to sloshing. A map of sloshing modes has been developed to characterize the sloshing response as a function of excitation parameters. Pressure forces on vertical walls and the lid have been calculated. Finally, insight into coolant voiding has been provided.

Seismic Sloshing in a Horizontal Liquid Storage Tank

A horizontal water storage tank was analyzed for seismic shaking at the ITER Tokamak Complex in France. The objectives were to (a) estimate the seismic forces in the tank; (b) calculate the sloshing response of the tank; (c) determine if baffles are needed to control sloshing; and (d) evaluate the possibility of using a single fixed support in the longitudinal direction to allow free thermal expansion of the tank. An approximate conservative analysis predicted very high sloshing waves and seismic forces in the tank. The fluid–structure interaction in the tank showed that only about 28% of the liquid moves with the tank wall and generates seismic forces in the longitudinal direction. The remaining 72% of the liquid sloshes near the free surface and does not generate significant seismic forces. The sloshing wave is not high enough in the longitudinal direction as the fundamental sloshing mode is not excited because of its very low natural frequency. Hence, baffles are not needed to control sloshing. The seismic force is low enough for a single fixed support to resist the entire seismic force in the longitudinal direction.

Development of framework for seismic response analysis of storage tank based on fault-structure system

In this study, the framework for the seismic response analysis of oil-storage tank along fault-structure system concept has been presented; where the long period ground motion simulation and sloshing simulation based on 3D finite element method (FEM) is integrated. Three dimensional finite element model is constructed using multi-resolution structured and unstructured mesh for the ground motion prediction. For the sloshing analysis Lagrangian Finite Element Method is used. Also the effect of surface topography on the sloshing response is checked and the effect is found to be significant.

Simulation for a floating roof behavior of cylindrical storage tank due to wind load (Wind velocity effect on sloshing)

Floating roofs are used on large cylindrical storage tanks to prevent evaporation of oil. The single-deck floating roof considered herein consists of a thin circular plate, referred to as a "deck", attached to a buoyant ring with a hollow rectangular cross section referred to as a "pontoon". The deck plate is deformed to be created waves and is subjected to cyclic bending due to the wind load. Since this leads to the initiation of fatigue cracks at the welded joints, it is important to understand the wave characteristics in the deck plate. The authors have previously reported a computational fluid dynamics (CFD) analysis of a cylindrical storage tank under a wind load. The present paper describes an axisymmetric finite element analysis of the sloshing response of a single-deck floating roof on a cylindrical storage tank using the previous CFD results as the load conditions. It is assumed that the liquid is incompressible and inviscid, the roof exhibits linear elastic behavior, and the sidewalls and bottom of the tank are rigid. The effect of the wind velocity on the frequency and amplitude of vibrations in the deck plate is investigated. As a result, the relation between the amplitude of vibration and the wind velocity is shown. The predominant period of bending stress vibration of the deck plate is shorter than that of the waves.

Application of Optimization technique for Compensator design of Launcher Attitude Control

This paper deals with the compensator design of launch vehicle attitude control in atmospheric phase using optimization algorithm. Traditionally compensator design is carried out intuitively based on physical parameters of launch vehicle. It is arrived at after a long trial and error procedure to fulfil frequency domain requirements. In this paper a multi-constraint satisfaction algorithm is used to design compensator for attitude control, which takes into account the frequency and time domain requirements. The effect of actuator non-linear behavior on slosh dynamics is investigated and the analytical expression for slosh response with respect to actuator amplitude is derived. The slosh closed loop pole migration with the variation in actuator command amplitudes in root locus is discussed and the implication of acceptable actuator limit cycle amplitude on vehicle body rate is brought out.

Effects of baffles geometry on sloshing dynamics of a viscous liquid tank

Baffles are used effectively to reduce the sloshing response of liquid in the liquid storage containers. In this paper, a brief equivalent method is proposed to model the influence of different baffle geometrical effects on liquid sloshing. It has been showed that the natural frequencies and the dynamic response of the liquid in the container are drastically changed if the free liquid surface in a cylindrical container is being covered with structural parts. The advantages of a partly covered free surface plane lies in the shifting of the natural propellant frequencies above and away from the control frequency of a space vehicle, and in the decrease of the sloshing masses participating in the dynamic motion of the system. The fundamental natural frequency of a viscous and incompressible liquid has been determined for different geometrical shape and width of an annular ring baffle attached to the tank wall. The response to translational and pitching excitation has also been evaluated and showed the shifting of the resonance margins to higher values. Simulation results showed the effectiveness of this procedure. The presented approach may be applied to the various arbitrary coverage of free liquid surface and different geometry of container. Key words: Sloshing dynamics, incompressible liquid, translational/pitching excitation.

Soil interaction effects on sloshing response of the elevated tanks

The aim of this paper is to investigate how the soil-structure interaction affects sloshing response of the elevated tanks. For this purpose, the elevated tanks with two different types of supporting systems which are built on six different soil profiles are analyzed for both embedded and surface foundation cases. Thus, considering these six different profiles described in well-known earthquake codes as supporting medium, a series of transient analysis have been performed to assess the effect of both fluid sloshing and soil-structure interaction (SSI). Fluid-Elevated Tank-Soil/Foundation systems are modeled with the finite element (FE) technique. In these models fluid-structure interaction is taken into account by implementing Lagrangian fluid FE approximation into the general purpose structural analysis computer code ANSYS. A 3-D FE model with viscous boundary is used in the analyses of elevated tanks-soil/foundation interaction. Formed models are analyzed for embedment and no embedment cases. Finally results from analyses showed that the soil-structure interaction and the structural properties of supporting system for the elevated tanks affected the sloshing response of the fluid inside the vessel.

Sloshing of liquid in rigid cylindrical container with multiple rigid annular baffles: Lateral excitations

Sloshing response of liquid in a rigid cylindrical container with multiple annual rigid baffles subjected to lateral excitations has been studied. Firstly, the liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain has continuous boundary conditions of class C1. Based on the superposition principle, the analytical solutions of the liquid velocity potential corresponding to each liquid sub-domain are obtained by means of the method of separation of variables. The total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The orthogonality among the modes of liquid velocity potential is demonstrated. The dynamic response equation of liquid is established by substituting the liquid potential functions into the free surface wave equation. Finally, the surface wave height, hydrodynamic pressure distribution, resultant hydrodynamic force and moment for a container subjected to harmonic and seismic lateral excitations are discussed in detail.

Nonlinear Finite Element Analysis of Sloshing

The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.

Simulation for a Floating Roof Behavior of Cylindrical Storage Tank due to Wind Load (Sloshing Response Analysis)

Simulation for a Floating Roof Behavior of Cylindrical Storage Tank due to Wind Load (Sloshing Response Analysis)

Transient Sloshing in Partially Filled Laterally Excited Spherical Vessels

AbstractThree-dimensional transient liquid sloshing in a nondeformable spherical container filled to an arbitrary depth and subjected to an arbitrary lateral external acceleration is investigated. The problem solution is achieved by using the linear potential theory in conjunction with the Mehler-Fock transform of general order in the toroidal coordinate system, resulting in a pair of coupled integro-differential equations, which are discretized using Gauss-Laguerre quadrature formula and then solved by appropriate numerical schemes. The transient sloshing response to a real seismic event is calculated and discussed. Also, a ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of the fill depth on the time histories of the horizontal hydrodynamic forces acting on the spherical container are examined. Limiting cases are considered, and good agreements with available analytic and numerical solutions and experimental data are obtained.

THE NUMERICAL AND EMPIRICAL EVALUATION OF STRUCTURAL PERFORMANCE OF ELEVATED TANKS CONSIDERING SOIL–STRUCTURE INTERACTION EFFECTS

Water tanks are an essential lifeline whose continuing availability and serviceability immediately after earthquake events are crucial for providing undisrupted emergency services. Their seismic performance is, therefore, of paramount importance. The seismic response of an elevated liquid tank situated on a soft soil deposit was studied by means of field vibration tests and numerical simulations. The ambient and forced vibration tests were conducted to identify the soil–structure interaction (SSI) effects on the small strain dynamic behavior of the structure. A series of time domain numerical analyses were performed to evaluate the seismic performance of these structures from a performance based design point of view. The results showed that consideration of SSI increased the displacement demand significantly. Thus, the calculated maximum displacement demand for supporting frame components of the tank may be underestimated significantly when the SSI effects are neglected. In addition, the seismic induced shear forces considering SSI effects were much smaller than the seismic shear forces for the fixed based case. For some soil types, the effect of this reduction on the overall response may become more prominent than the structural ductility mechanism. This resulted in the failure mechanism being initiated by a coupled compression — bending moment effect, rather than shear failure. Finally, the sloshing response is significantly increased due to the SSI.

Nonlinear Vibrations and Chaos in Floating Roofs

Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and super harmonics in the response. The broadband structure of the frequency spectrum, the fractal structure of the Poincare maps, and the bifurcation diagram as qualitative criteria and Lyapunov exponent evolution as quantitative criterion are used to investigate the emergence of chaotic response.

Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part II: Lateral Excitation

Sloshing response of liquid in a rigid cylindrical container with a rigid annual baffle subjected to lateral excitation has been studied. The complicated liquid domain is separated into several simple sub-domains by introducing the artificial interfaces. The analytical solutions of potential function corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The total potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. On the base of the natural frequencies and modes having been obtained by the sub-domain method, the orthogonality among the sloshing modes has been demonstrated. Substituting the potential functions into the free surface wave equation establishes the dynamic response equation of liquid. Then, the generalized coordinates are solved. The sloshing surface displacement, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment are discussed for the containers subjected to harmonic and seismic lateral excitation, respectively.

Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part II: Lateral Excitation

Sloshing response of liquid in a rigid cylindrical container with a rigid annual baffle subjected to lateral excitation has been studied. The complicated liquid domain is separated into several simple sub-domains by introducing the artificial interfaces. The analytical solutions of potential function corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The total potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. On the base of the natural frequencies and modes having been obtained by the sub-domain method, the orthogonality among the sloshing modes has been demonstrated. Substituting the potential functions into the free surface wave equation establishes the dynamic response equation of liquid. Then, the generalized coordinates are solved. The sloshing surface displacement, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment are discussed for the containers subjected to harmonic and seismic lateral excitation, respectively.

812 風による円筒タンク浮屋根の挙動シミュレーション : スロッシング応答解析

The floating roofs are used in large cylindrical storage tanks to prevent evaporation of oil. The single-deck floating roof, considered herein, consists of a thin circular plate called "deck" attached to a buoyant ring of box-shaped cross section called "pontoon". The deck plates are deformed to create waves and they are subjected to cyclic bending due to wind load. This may lead to initiate fatigue cracks at the welded joints. It is important to know the characteristics of waves in the deck plate. The authors have reported the CFD analysis of a cylindrical storage tank due to uniform wind in another paper. This paper presents the axisymmetric finite element analysis for the sloshing response of the single-deck floating roofs in a cylindrical storage tank using the CFD results as the load condition. It is assumed that the liquid is incompressible and inviscid, and the roof is linear elastic while the sidewall and the bottom are rigid. The basic wave characteristics of the deck plate, such as frequency and amplitude is investigated.

Response of Liquid in Cylindrical Tank with Rigid Annual Baffle Considering Damping Effect

Sloshing response of liquid in a rigid cylindrical tank with a rigid annual baffle under horizontal sinusoidal loads was studied. The effect of the damping was considered in the analysis. Natural frequencies and modes of the system have been calculated by using the Sub-domain method. The total potential function under horizontal loads is assumed to be the sum of the tank potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. Substituting potential functions into the free surface wave conditions, the dynamic response equations including the damping effect are established. The damping ratio is calculated by Maleki method. The liquid potential are obtained by solving the dynamic response equations of the system.

Three‐dimensional sloshing: A consistent finite element approach

AbstractThis paper presents a new computational methodology based on Legendre's polynomials to predict the slosh and acoustic motion in nearly incompressible fluids in both rigid and flexible structures with free surface. Here, we have used a finite element formulation based on Lagrangian frame of reference to model the fluid motion derived using Hamiltonian equation of the fluid system. We formulated three hexahedral finite elements based on strain fields expressed in terms of extended Legendre's polynomials. Sloshing and acoustic motion of liquid is investigated using these newly formulated elements and inf–sup test is performed on these new elements to check the performance of these elements in modeling sloshing under two severe constraints, namely incompressibility and irrotationality. Comparisons of slosh and acoustic frequencies, and mode shapes with exact solutions are given. Dynamic analysis with earthquake and harmonic kind of forcing function is carried out to validate the formulated hexahedral elements to analyze the sloshing response. Numerical results obtained with these new finite elements, and with the present finite element formulation of the mathematical model agree well with the exact solution and as well as with published experimental literature. Copyright © 2010 John Wiley & Sons, Ltd.

CFD Verification of Engineering Options for Mitigating Liquid Sloshing in Topside Vessels on a Floating Production Facility

Summary This paper proposes an active-control concept that mitigates the liquid sloshing in a topside vessel by reducing the excitation source, thus extending the scope of sloshing mitigation. To verify the concept proposed, sloshing response in partially liquid-filled topside vessels was numerically investigated under various wave and vessel conditions. This study confirmed that vessel location on the top deck exhibits a weak correlation with the sloshing response. Although liquid sloshing is not very sensitive to the vessel location, it is beneficial to place the topside processing vessels as close as possible to gravity center of the floating production facilities (FPS/FPSO). It is evident that liquid sloshing in a topside vessel is closely related to the incident direction of the wave. The perpendicular incidence results in the minimum sloshing response; the parallel incidence leads to the maximum sloshing response. It is, therefore, essential to properly orient the vessel to establish perpendicular or close-to- perpendicular incidence status. It is also verified that liquid sloshing is significantly increased with length-to-diameter (L/D) ratio of a vessel. The horizontal vessels with larger L/D suffer from severe liquid sloshing. Because vertical vessels have a minimum L/D = 1.0, they always exhibit better antisloshing performance than the horizontal vessels. In addition, it is advisable to prevent a vessel from operating near the resonance-wave condition. Although the active control concept shows attractive advantages over the conventional approach, it is more feasible for layout of topside vessels on a newly built FPS/FPSO. Because most of the floating-production systems are not built from scratch such that the topside processing vessels can be placed in the optimal position and orientation but are retrofitted for a topside vessel to fit onto a limited deck space, the passive-control approach may be more applicable. Generally, a combination of the active and passive approaches should be considered to minimize liquid sloshing in a topside process vessel.