Large-amplitude Sloshing Research Articles

Experimental investigation of liquid-tank interaction effects on full containment LNG storage tanks through shaking table tests

Liquefied natural gas (LNG) storage tanks play a crucial role as primary storage facilities in modern gas supply systems. This study investigates the seismic response of full containment LNG storage tanks through shaking table tests. A 1/14 scale model structure is meticulously constructed and subjected to testing. The test comprises two distinct phases: an empty tank phase and a water-filled tank phase. The primary emphasis of this paper is the exploration of the effects of liquid–tank interaction. A novel no-contact binocular video synchronization measurement system is developed by utilizing high-speed cameras to accurately measure the liquid sloshing height. The seismic responses of both the liquid and the tank, including acceleration and hydrodynamic pressure, are meticulously measured and analyzed. Findings reveal that the filling fluid has a significant effect on the tank, particularly the steel inner tank. The liquid sloshing phenomenon influences the hydrodynamic pressures, with the magnitude of influence decreasing as the liquid depth increases. In addition, a comparison is conducted between the experimental liquid sloshing height and hydrodynamic pressure results and those obtained from liquid linear forced sloshing theory. Liquid linear forced sloshing theory fails to accurately predict liquid sloshing height for large-amplitude sloshing but provides a rough estimate of hydrodynamic pressure distribution on the tank wall. Two simplified mechanical models for liquid sloshing are proposed and compared with the experimental results. The outcomes demonstrate that the Housner method exhibits relatively large errors, while the simplified mechanical models based on liquid linear forced sloshing theory accurately describe cases with small-amplitude liquid sloshing.

Numerical Study on Thermodynamic Coupling Characteristics of Fluid Sloshing in a Liquid Hydrogen Tank for Heavy-Duty Trucks

The large-amplitude sloshing behavior of liquid hydrogen in a tank for heavy-duty trucks may have adverse effects on the safety and stability of driving. With successful application of liquid hydrogen in the field of new energy vehicles, the coupled thermodynamic performance during liquid hydrogen large-amplitude sloshing becomes more attractive. In this paper, a three-dimensional numerical model is established to simulate the thermodynamic coupling characteristics during liquid hydrogen sloshing in a horizontal tank for heavy-duty trucks. The calculation results obtained by the developed model are in good agreement with experimental data for liquid hydrogen. Based on the established 3D model, the large-amplitude sloshing behavior of liquid hydrogen under extreme acceleration, as well as the effects of acceleration magnitude and duration on liquid hydrogen sloshing, is numerically determined. The simulation results show that under the influence of liquid hydrogen large-amplitude sloshing, the convective heat transfer of fluid in the tank is greatly strengthened, resulting in a decrease in the vapor temperature and an increase in the liquid temperature. In particular, the vapor condensation caused by the sloshing promotes a rapid reduction of pressure in the tank. When the acceleration magnitude is 5 g with a duration of 200 ms, the maximum reduction of ullage pressure is 1550 Pa, and the maximum growth of the force on the right wall is 3.89 kN. Moreover, the acceleration magnitude and duration have a remarkable influence on liquid hydrogen sloshing. With the increase in acceleration magnitude or duration, there is a larger sloshing amplitude for the liquid hydrogen. When the duration of acceleration is 200 ms, compared with the situation at the acceleration magnitude of 5 g, the maximum reductions of ullage pressure decrease by 9.46% and 55.02%, and the maximum growth of forces on the right wall decrease by 80.57% and 99.53%, respectively, at 2 g and 0.5 g. Additionally, when the acceleration magnitude is 5 g, in contrast with the situation at a duration of acceleration of 200 ms, the maximum-ullage-pressure drops decrease by 8.17% and 21.62%, and the maximum increase in forces on the right wall decrease by 71.80% and 88.63%, at 100 ms and 50 ms, respectively. These results can provide a reference to the safety design of horizontal liquid hydrogen tanks for heavy-duty trucks.

Wave-based attitude control of in-orbit spacecraft with large-amplitude slosh

This paper aims to reach high-quality attitude control and large-amplitude slosh suppression when a typical liquid-filled spacecraft executes three-axial large-angle maneuvers, by applying a wave-based attitude controller (WBAC). First, the sloshing dynamics is modeled by using a spherical pendulum, whose motion is expressed by splitting its coordinates. Thus, the large-amplitude lateral sloshing and the rotary sloshing as well as the over-all rigid motion of a liquid with respect to the tank in spacecraft can be approximately described. Second, the dynamics equations of system in terms of hybrid coordinate for the liquid-filled spacecraft are derived via the Lagrangian formulation. Third, an improved WBAC for three-axial large-angle maneuvers of in-orbit liquid-filled spacecraft is designed by adding a derivative control law and a gravity-gradient-torque compensation law to a wave-based control law. Simulations of three-axial large-angle maneuver demonstrate good performance of the WBAC in shortening completion time of attitude maneuvering, suppressing the jitter in the angular velocity of spacecraft, and accelerating the large-amplitude slosh suppression, simultaneously. The results indicate the potential applications of the proposed WBAC in the large-angle attitude maneuvering of liquid-filled spacecraft when there exists large-amplitude liquid slosh.

Improved Moving Pulsating Ball Equivalent Model for Large-Amplitude Liquid Slosh

In the process of spacecraft launching, maneuvering, rendezvous, and docking, the liquid fuel may slosh violently due to the action of inertia force and gravity, and the additional sloshing force will have an important impact on the spacecraft. To meet the requirement of high-fidelity real-time simulation of an on-board computer, in this paper, an equivalent dynamic model for large-amplitude liquid sloshing is studied and validated. First, the moving pulsating ball model (MPBM) of liquid large-amplitude sloshing motion is extended to the gravity environment, and the gravity is added to the dynamic equation of the pulsating ball to derive the normal force of the MPBM. At the same time, the equivalent model of the liquid that does not participate in sloshing is introduced, which makes the calculation of the center of mass of the liquid more accurate. The validity of the improved MPBM (IMPBM) in cases of small-amplitude sloshing, large amplitude sloshing and zero momentum maneuvers is verified by three examples. Finally, an experimental platform is designed and built to verify the numerical simulation results. It is shown that the IMPBM can well reflect the reactive force for liquid sloshing in both spherical and nonspherical tanks.

Composite equivalent mechanical models for large-amplitude liquid sloshing in axisymmetrical tanks

Equivalent mechanical models are widely used to describe the dynamics of liquid sloshing in aerospace engineering, but the traditional equivalent mechanical models based on linear theory have poor applicability and accuracy in large-amplitude sloshing. The composite equivalent modeling method suitable for large-amplitude sloshing in normal and low-gravity is proposed in this paper. By considering the change of liquid equilibrium position in sloshing, the large-amplitude motion of the liquid relative to the tank is decomposed into bulk motion following the equivalent gravity and additional small-amplitude sloshing, thus greatly expands the application scope of the linear equivalent mechanical model. Taking the axisymmetrical tanks as examples, the liquid dynamic equilibrium position following the equivalent gravity under large-amplitude sloshing is determined, and the composite equivalent mechanical model in the form of a spherical pendulum is established. For spherical tanks, all liquid is assumed to be involved in bulk motion and the model parameters are found constant during sloshing. For non-spherical tanks such as cylindrical and Cassini tanks, liquid near the tank wall is assumed motionless relative to the tank, and the time-dependent model parameters are approximated by linear interpolation based on equivalent gravity and inclination of the liquid surface. Based on the spherical pendulum model, the dynamic equation of the equivalent system is derived, thus the slosh forces, moments and positions of the liquid center of mass under large translational and rotational excitations are calculated in 3D axisymmetrical tanks. To verify the validity of the modeling method and the accuracy of the composite model, the results of the composite equivalent mechanical model, the traditional equivalent mechanical model as well as the computational fluid dynamics (CFD) software are compared and analyzed. As shown by the results, the composite equivalent mechanical model proposed can accurately predict the dynamic responses of large-amplitude liquid sloshing in axisymmetrical tanks.

Absolute nodal coordinate finite element approach to the two-dimensional liquid sloshing problems

Two-dimensional large-amplitude liquid sloshing in the rectangular rigid container is numerically simulated through absolute nodal coordinate finite element method, which can describe the large deformation of continuum by using a small number of elements. The incompressible constraint of Newtonian fluid is imposed by the penalty function method. Furthermore, the motion of rigid container is described by absolute nodal coordinate reference node and the liquid kinetic equations are derived in the total Lagrangian formulation, which can easily be combined with the solid nonlinear finite element and the multi-body system algorithms. The free sliding and non-penetrating boundary constraint equations for rectangular tank are derived. To ensure the stability and the conservation of the solution in long time simulations, the system dynamic equations are solved by Bathe integral scheme. Three numerical examples are used to verify the effectiveness of the proposed method, including the free spreading of a square liquid column and the large amplitude sloshing of liquid under rotational and horizontal excitations. A good consistency is obtained by comparing the calculated results with experimental and other numerical results reported in the literature.

Large Motion Dynamics of In-Orbit Flexible Spacecraft with Large-Amplitude Propellant Slosh

A general methodology for the dynamics of spacecraft with rigid–liquid–flexible body coupling is established by using Kane’s equations, whereby the combined sloshing in multiple tanks and the dynamic stiffening of flexible solar panels are both accommodated. First, the kinematic evolution equation of attitude motion is expressed in terms of quaternions. Second, the liquid sloshing dynamics in the tanks are made by including the constraint-surface model. Third, the stiffening effect of the flexible solar panels is incorporated into the dynamics formulation by adopting the hypothesis of geometrically nonlinear deformation rather than that of Kirchhoff–Love plate. Kane’s method is chosen for its efficiency in deriving the coupled dynamics model of a spacecraft undergoing large overall motion. Simulation examples are given to validate the reliability of this dynamics model in predicting the total slosh force and the total slosh torque under complicated excitations, to manifest the superiority of the methodology based on the geometrically nonlinear deformation over the conventional theory based on the assumption of the Kirchhoff–Love plate, and to analyze the rigid–liquid–flexible coupling effects of the spacecraft during the in-orbit three-axis stabilized maneuver. It is found that there is a violent disturbance to the attitude motion in the form of beat vibration due to the nonlinear coupling effects among the large-amplitude sloshing in multiple tanks, the vibration of geometrically nonlinear deformation of flexible solar panels, and the control system.

Experimental and Numerical Studies on Sloshing Dynamics of PCS Water Tank of Nuclear Island Building

Water tank is one important component of passive containment cooling system (PCS) of nuclear island building. The sloshing frequency of water is much less than structure frequency and large-amplitude sloshing occurs easily when subjected to seismic loadings. Therefore, the sloshing dynamics and fluid-structure interaction (FSI) effect of water tank should be considered when the dynamic response of nuclear island building is analyzed. A 1/16 scaled model was designed and the shaking table test was done, in which the hydrodynamic pressure time histories and attenuation data of wave height were recorded. Then the sloshing frequencies and 1st sloshing damping ratio were recognized. Moreover, modal analysis and time history analysis of numerical model were done by ADINA software. By comparing the sloshing frequencies and hydrodynamic pressures, it is proved that the test method is reasonable and the formulation of potential-based fluid elements (PBFE) can be used to simulate FSI effect of nuclear island building.

Attitude tracking control of flexible spacecraft with large amplitude slosh

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed. A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics, liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.

Dynamic Response of Base-Isolated Concrete Rectangular Liquid-Storage Structure Under Large Amplitude Sloshing

AbstractConsidering concrete nonlinearity, the wave height limit between small and large amplitude sloshing is defined based on the Bernoulli equation. Based on Navier-Stokes equations, the mathematical model of large amplitude sloshing is established for a Concrete Rectangle Liquid-Storage Structure (CRLSS). The results show that the seismic response of a CRLSS increases with the increase of seismic intensity. Under different seismic fortification intensities, the change in trend of wave height, wallboard displacement, and stress are the same, but the amplitudes arc not. The areas of stress concentration appear mainly at the connections between the wallboards, and the connections between the wallboard and the bottom.

Nonlinear model and attitude dynamics of flexible spacecraft with large amplitude slosh

This paper is focused on the nonlinearly modelling and attitude dynamics of spacecraft coupled with large amplitude liquid sloshing dynamics and flexible appendage vibration. The large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process. A modification is introduced in the capillary force computation in order to more precisely estimate the settling location of liquid in microgravity or zero-g environment. The flexible appendage is modelled as a three dimensional Bernoulli-Euler beam and the assumed modal method is employed to derive the nonlinear mechanical model for the overall coupled system of liquid filled spacecraft with appendage. The attitude maneuver is implemented by the momentum transfer technique, and a feedback controller is designed. The simulation results show that the liquid sloshing can always result in nutation behavior, but the effect of flexible deformation of appendage depends on the amplitude and direction of attitude maneuver performed by spacecraft. Moreover, it is found that the liquid sloshing and the vibration of flexible appendage are coupled with each other, and the coupling becomes more significant with more rapid motion of spacecraft. This study reveals that the appendage's flexibility has influence on the liquid's location and settling time in microgravity. The presented nonlinear system model can provide an important reference for the overall design of the modern spacecraft composed of rigid platform, liquid filled tank and flexible appendage.

Equivalent mechanical model of large-amplitude liquid sloshing under time-dependent lateral excitations in low-gravity conditions

Subjected to external lateral excitations, large-amplitude sloshing may take place in propellant tanks, especially for spacecraft in low-gravity conditions, such as landers in the process of hover and obstacle avoidance during lunar soft landing. Due to lateral force of the order of gravity in magnitude, the amplitude of liquid sloshing becomes too big for the traditional equivalent model to be accurate. Therefore, a new equivalent mechanical model, denominated the “composite model”, that can address large-amplitude lateral sloshing in partially filled spherical tanks is established in this paper, with both translational and rotational excitations considered. The hypothesis of liquid equilibrium position following equivalent gravity is first proposed. By decomposing the large-amplitude motion of a liquid into bulk motion following the equivalent gravity and additional small-amplitude sloshing, a better simulation of large-amplitude liquid sloshing is presented. The effectiveness and accuracy of the model are verified by comparing the slosh forces and moments to results of the traditional model and CFD software.

Attitude Dynamics and Control of Liquid Filled Spacecraft with Large Amplitude Fuel Slosh

AbstractThis paper focuses on the attitude dynamics and control of liquid filled spacecraft, and the large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process, specifically for the occurrence of large amplitude slosh. This model is improved by incorporating a static capillary force and an effective mass factor. The improvements on this model are validated with previously published experiment results. The spacecraft attitude maneuver is implemented by the momentum transfer technique, and the feedback control strategy is designed based on Lyapunov theory. The effects of liquid viscosity, tank location and desired steady time on sloshing torque and control torque are investigated. The attitude control strategy applied in this paper is proved to be applicable for the coupled liquid filled spacecraft system. The obtained conclusions are useful to aid in liquid filled spacecraft overall design.

Attitude Dynamics and Control of Spacecraft with Multiple Liquid Propellant Tanks

AbstractThis paper focuses on the dynamics and control of spacecraft with multiple liquid propellant tanks. The liquid slosh dynamics are included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the liquid reorientation process, especially for large-amplitude slosh. This model is improved by incorporating a static capillary force and an effective mass factor. The improvements are validated with previously published experiment results. The spacecraft attitude maneuver is implemented by the momentum transfer technique. The designed feedback control strategy is demonstrated to be efficient and robust for the coupled liquid-filled spacecraft system. For the two-tank system, two eccentric cases of concern are an asymmetric tank arrangement and an unbalanced propellant mass distribution in the two tanks. The effects of the two eccentric cases on sloshing torque and control torque are investigated. Some conclusions o...

Large-Amplitude Sloshing Analysis and Equivalent Mechanical Modeling in Spherical Tanks of Spacecraft

Liquid sloshing of a large amplitude is prone to take place under excitation, especially when the gravitational intensity becomes small. A composite equivalent mechanical model is established to efficiently and accurately predict the slosh forces and moments exerted on a spherical propellant tank in a spacecraft. The modeling is based on an assumption of the dynamic equilibrium position of the liquid, which changes with time-dependent tank motion. Equivalent gravity is defined to describe the dynamic equilibrium position and act as a restoring force during sloshing. Sloshing of the liquid is assumed to take place around the dynamic equilibrium position. The validity of the modeling method is verified through numerical examples. Good stability and the ability to accurately predict the dynamic response under the violent sloshing of the composite model are revealed.

Constraint surface model for large amplitude sloshing of the spacecraft with multiple tanks

The large amplitude sloshing problem of a spacecraft with multiple tanks is studied by using a three-dimensional constraint surface model. The mechanical model portrays the liquid as a point mass moving inside the constraint surface, which is the locus of liquid center of mass locations prescribed by slowly rotating the tank in one-g field. Sloshing forces of liquid in propellant tank are calculated with different actuated accelerations and different filling ratios. The simulation results are in good agreement with the computational fluid dynamics simulation results, which confirm the accuracy of the three-dimensional constraint surface model for solving large amplitude sloshing problems. The coupled problem between liquid sloshing and spacecraft body motion is also calculated using the mechanical model, and the comparison between simulation results and the in-orbit experimental results of the Sloshsat FLEVO satellite is discussed.

Sloshing in a rectangular tank based on SPH simulation

A ship would generate significant sloshing when subjected to underwater explosion loads; the sloshing will reduce the ship's stability and even cause the ship to capsize when coupled with internal liquid sloshing. It is of great significance to research on the characteristics of the sloshing loads in a tank to improve the ship's stability and security. The liquid sloshing in a tank is a complex process characterized with nonlinearity and strong randomness, and large amplitude sloshing is a great challenge for both theoretical models and numerical algorithms. Yet as a meshfree method, Smoothed particle hydrodynamics (SPH) has great advantages of solving such large deformation problems because of the nature of self-adaptiveness and Lagrangian. This paper focuses on the SPH core issues, such as the accuracy and the stability of the kernel function and boundary treatments. Firstly, the accuracy and computational stability of four common SPH kernel functions are simply investigated by two simple cases, and a more appropriate kernel function is selected. Secondly, the dummy particles and a novel boundary treatment considering the boundary motion are applied. Furthermore, the laws of impact pressure of the two-dimensional tank under forced rolling with different excitation frequencies and excitation angles are studied. Then, the influences of a baffle for the liquid sloshing in a two-dimensional tank under forced surging are analyzed, and the action mechanisms of the baffle are summarized. Finally, the coupled motion of swaying and surging for a three-dimensional tank is studied, which aims to lay a foundation for further study on the influence of sloshing loads on real ship motions.

The Numerical Simulation of 2D Sloshing Tank

In this study, a two-dimensional numerical method based on the volume of fluid method is used to solve for water sloshing. The 2D equations of fluid motion are derived in a moving coordinate system. For modeling impact pressure induced by large amplitude sloshing, an emphasis is given to the numerical treatment of the free surface, which is sensitive to the simulation. Liquid sloshing inside a rectangular tank is simulated. The time histories of the free surface shape and the dynamic pressure inside the tank are obtained. The results are compared with an experimental data. These comparisons show that this method can be used to simulate the sloshing induced impact loads. Then series of violent sloshing phenomenon is given and compared.

Solution of moving-boundary problems by the spectral element method

This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid–structure interaction. This model uses a moving-grid technique to solve the Navier–Stokes equations expressed in the arbitrary Lagrangian–Eulerian kinematics. The discretization in space is based on the spectral element method. The coupling of the fluid equations and the moving-grid equations is essentially done through the conditions on the moving boundaries. Two- and three-dimensional simulations are presented: translation and rotation of a cylinder in a fluid, and large-amplitude sloshing in a rectangular tank. The accuracy and robustness of the present numerical model is studied and discussed.

Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment

The dynamic problem of three-dimensional liquid sloshing is numerically studied in this paper. The arbitrary Lagrange-Euler (ALE) kinematic description is introduced into the control equations system. The discrete numerical equations of finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by our differential geometry method derived. The normal vector on free surface is calculated by using accurate formula presented in this paper. The numerical computations are performed and the comparison not only between numerical results and analytical results but also between numerical results and experimental results validated the effectiveness of the method. Finally, large amplitude sloshing of three-dimensional liquid in low-gravity environment is simulated and some important nonlinear characteristics are obtained. From the numerical results, it is concluded that the character of nonlinear sloshing of the liquid under low-gravity environment is much different from that of the liquid sloshing under normal gravity environment.