Sloshing Research Articles

Effects of longitudinal excitation on liquid hydrogen sloshing in spacecraft storage tanks under microgravity conditions

Based on the real physical model and operating environment of the spacecraft tank, the numerical model of the tank is established and the sloshing behavior of liquid hydrogen in the tank under different longitudinal excitations is studied in this work. The Realizable k- ε model is used to predict the fluid turbulence, and the mixture model is used to analyze the phase transitions and flows. The harmonic external excitation is loaded by the user-defined function (UDF). Based on the CFD sloshing model verified through comparison with experimental results, the influences of different longitudinal external excitation frequencies and amplitudes on the liquid hydrogen volume fraction in the tank are firstly analyzed. On this basis, including pressure and other physical quantities of the monitoring points and whole internal fluid domain during the sloshing simulation process are studied quantitatively. In addition, the relationship between the carrier amplitude of the sloshing curves and the external excitation amplitude is discussed. The simulation results show that in microgravity environment, compared with large amplitude excitation, high-frequency longitudinal harmonic excitation has a significant effect on the variation of physical parameters in the tank, which may become a negative factor for the safety of liquid hydrogen storage and supply systems. Meanwhile, the traditional baffle design has a limited influence on the liquid hydrogen motion under the high-frequency longitudinal excitation which may occur during the spacecraft changing load process. The results provide valuable information for the understanding of sloshing behavior and safety evaluation of the tank under longitudinal excitation.

Comparative assessment of liquid sloshing in dry and wet storage tank of floating offshore platform

In order to explore the characteristics of the single-layer liquid sloshing in offshore dry oil storage tank and the two-layer liquid sloshing in offshore wet oil storage tank, two series of experiments were carried out: one was free surface sloshing in a closed rectangular tank partially filled with colored water, and the other was interfacial sloshing in the identical tank but completely filled with white oil and colored water. The tank was mounted on a shake table and was subjected to harmonic horizontal excitation with different excitation amplitudes and a wide range of excitation frequencies, including the first seven natural modes of single-layer or two-layer liquid system. The present study find that the frequency responses of interfacial sloshing wave are analogous to those of the free surface sloshing wave, but smaller in amplitudes. The experiments also produce results that are unique to the two-layer liquid sloshing. For example, when the external excitation frequency is equal to or close to the odd mode natural frequency of two-layer liquid system, a complicated three-dimensional (3D) gravity-capillary wave might be generated at the oil-water interface. Finally, the comparisons of free surface and interfacial sloshing in the viscous damping ratio, higher sloshing modes, impact pressure amplitude and mass center displacement were conducted, which revealed the superiority of wet storage technology in structural safety and dynamic stability.

Effects of Liquid Density on the Gas-Liquid Interaction of the Ionic Liquid Compressor for Hydrogen Storage

As a new and promising compression technology for hydrogen gas, the ionic liquid compressor inherits the advantages of the ionic liquid and the hydraulic system. The liquid density is one of the key parameters influencing the fluid flow field, the sloshing of the bulk liquid, and the movement of droplets generated during the compressor operation. An appropriate selection of the liquid density is important for the compressor design, which would improve the thermodynamic performance of the compressor. However, the density of the ionic liquid varied significantly depending on the specific combination of the cation and anions. This paper proposed the methodology to select the optimal liquid density used in the ionic liquid compressor for hydrogen storage. The gas-liquid interaction in the compression chamber is analysed through numerical simulations under varied liquid density values. Results found that the increase in the liquid density promoted the detachment of the ionic liquid from the cylinder cover during the suction procedure and the contact of the bulk liquid on the compressor cover when the gas is compressed in the cylinder during the compression procedure. Both the droplet size and the dimension of the derived gas vortex decreased when the liquid density increased. The lowest mass transfer of hydrogen through the outlet was obtained at the density of 1150 kg/m3. The density of the ionic liquid from 1300 to 1450 kg/m3 is suggested to the hydrogen compressor, taking into account the transient two-phase flow characteristics, the mass transfer, and the total turbulent kinetic energy.

Equivalent Dynamic of Liquid Sloshing Coupled with Mass Transfer During On-Orbit Refueling

During an on-orbit refueling mission, the liquid fuel partially filling in the tanks will slosh and produce coupled motion with the servicer-to-client transfer, which may bring dangers to the spacecraft and even lead to attitude divergence. To effectively simulate the motion and the inertia of liquid fuel in a cylindrical tank during refueling, equivalent dynamic modeling of liquid fuel sloshing coupled with mass transfer is developed in this paper. A spring–mass–damper model with time-varying elastic and damping coefficients is implemented in the axial direction to equal the motion of the liquid mass center, while a pendulum model with time-varying pendulum length is adopted in the radial direction. An equivalent liquid elliptical cylinder is developed to approximate the inertia of dispersed liquid while sloshing. A series of computational fluid dynamics simulations are carried out to observe the liquid behaviors in the fuel tanks and to verify the proposed equivalent dynamic model. Finally, three-dimensional sloshing is theoretically and numerically analyzed.

A fast semi-analytic solution of liquid sloshing in a 2-D tank with dual elastic vertical baffles and walls

Liquid sloshing characteristics in a lateral excited two-dimensional (2-D) rectangular tank with dual elastic vertical baffles and walls have been investigated analytically. The elastic baffle or wall is regarded as an Eulerian Bernoulli beam. The complex liquid domain divides into six simple sub-domains according to the superposition principle. The formal solution of the potential function in each sub-domain is obtained using the separation of variables method. Then the formal baffle or wall deflection solution can be derived from the transverse vibration equation. The Eigen equation can be established according to the free surface, interface, and coupled vibration conditions. The coupled frequency can be obtained by solving the Eigen equation. The velocity potential under lateral excitation consists of the rigid container velocity potential and the disturbance potential. Then the coupled dynamic response equation is established using the free liquid surface equation and the coupled vibration equation. The correctness of the semi-analytic solution is verified against available data. Therefore, the numerical model of the present work can be computed quickly with semi-analytic solution and obtain the mechanism of liquid-structure interaction. Finally, the effect of baffle parameters and excitation frequency on liquid sloshing is discussed in detail.

Fault-tolerant attitude control for liquid-filled flexible spacecraft without angular velocity measurements based on disturbance observer

The problem of robust, angular velocity-free control and fault-tolerant control for liquid-filled flexible spacecraft attitude maneuver subject to unknown external disturbances is investigated. Moreover, state variables measurement uncertainty and actuator failures are explored. The liquid sloshing effect of spacecraft fuel is equivalent to a two-order spring-mass model, and the flexible attachments are equivalent to the Euler–Bernoulli beams. The external disturbance, multiple failures of the output actuator, and the coupled interference caused by liquid sloshing and vibrations of flexible attachments are distinguished as continuous and percussive disturbances. First, a fault-tolerant control method against the percussive disturbances is proposed, and the robustness performance and characteristics of this method are analyzed. Then, both continuous and percussive disturbances are considered to propose a new fault-tolerant control method based on a nonlinear disturbance observer, which is used to estimate the integrated disturbance. The Lyapunov stability theory proves that the proposed control strategy can make the state variables converge to a small neighborhood of the origin in finite time. Finally, the numerical simulation is used to verify the effectiveness and robustness of the proposed control strategy.

A Numerical Investigation of Sloshing in a 3D Prismatic Tank with Various Baffle Types, Filling Rates, Input Amplitudes and Liquid Materials

Partially filled liquid-carrying tanks have been used in many engineering applications, such as ships, vehicle fuel tanks, rockets, and drink or petroleum tankers. Liquid sloshing is an exciting phenomenon that researchers are investigating because of its complex behavior specifications. In this study, the sloshing responses of a prismatic tank with the approximate volume of an automobile fuel tank under different laterally harmonic excitation amplitudes, baffle structures, filling rates, and different types of liquid were investigated numerically. The computational fluid dynamics method (CFD) was used to solve fluid dynamics equations, and the volume of fluid method was applied to simulate two-phase flow in the tank. A validation study was performed by a literature study. Later, the effect of large and small excitation amplitudes, filling rates and fluid types on sloshing behavior were investigated and comparatively analyzed in the tank system with various baffle types.

A twin wavemaker model for liquid sloshing in a rectangular tank

Sloshing of a liquid in a rectangular container under horizontal excitations is modelled using a wave basin analogue within the framework of a potential flow theory. An initial boundary-value problem is formulated replacing fixed walls of the tank with two orthogonal twin piston-type wavemaker paddle pairs. The proposed equivalent mechanical system may be applied to a class of problems covering irrotational flow of an inviscid and incompressible fluid inside partially-filled rectangular containers exposed to translatory oscillations. An analytical solution to the problem is provided under the assumption of a small-amplitude monochromatic forcing for a classical linear wavemaker in a closed flume and two- and three-dimensional twin wavemaker problems. The model is extended to cover an arbitrary horizontal motion using a semi-analytical approach based on a difference time-marching schemes applied to linearised evolution equations in a spectral domain. This relatively simple conceptual model may be used to design a novel experimental framework for studying water wave mechanics at smaller scales relying on elongated sloshing tanks substituting typical wave flumes.

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.

Roll motion mitigation of a barge-type floating wind turbine under random excitation using a tuned liquid column damper

ABSTRACT This paper aims to numerically evaluate the performance of tuned liquid column damper (TLCD) on mitigating roll motion of a barge-type floating wind turbine system subjected to random excitation. The governing equations for modeling the interaction between the roll motion of the floating system and liquid sloshing in the TLCD were derived using a Lagrangian approach. Random excitation based on wave spectrum was generated to simulate applied moment. Then, under the constraints of barge dimension and vertical liquid column movement, Den Hartog’s method was used to obtain optimum TLCD parameters. The results show that the optimally designed TLCD can efficiently mitigate the roll motion of the floating wind turbine.

CFD Analysis on Different Filling Volume Capacity and Fluid Density for Flexitank Application

When it comes to the structural design of flexitanks used for freight transportation, liquid sloshing is a crucial subject of concern. However, with consideration of the flexitank shape, there is no specific capacity value that can be used as a guide for filling the liquid inside it. This phenomenon may cause a high-pressure impact on the flexitank, resulting in a leakage on the LLDPE package. One of the solutions to reduce the frequency of leaks occurred is to fill up the acceptable volume based on hydrodynamics performance. Therefore, the purpose of this paper is to investigate, using commercial computational fluid dynamics (CFD) software, the hydrodynamic performance of various flexitank filling volume capacities based on different liquid densities. This is evaluated by comparing the hydrodynamics study for filling capacities that are 1%, 2%, and 3% higher than the rated capacity for flexitanks that has been suggested by the Container Owner Association (COA). Due to the flexitanks thin walls, it is important to consider the impacts of fluid-structure interaction (FSI). To do this, a partitioned FSI approach is used by coupling the CFD and FEA solvers for this multi-physics issue. The main standpoint of FSI is that fluid forces are applied to structures, causing deformation. Hydrodynamic parameters such as structural deformation on flexitank, von-mises stress and von-mises strain were used to identify the suitable filling capacity for three different: water, latex, and crude palm oil, as these liquids are commonly used for flexitank. The results indicate that varying the liquid filling capacity affected the hydrodynamic performance of the flexitank. Following that, increasing the flexitank filled with water by 3% and increasing the flexitank filled with latex and CPO by 1% can lead to structural damage as it gives highest maximum value of total deformation for these capacities. Since the situation of the flexitank are in the braking condition, the highest elastic equivalent strain is occurred at the front-top of the flexitank structure.

Design and Analysis of a Sloshing Liquid Damping Device with Elastic Baffle Vibrator

Sloshing liquid damping technology is a typical passive damping technology, which has many advantages in application. To improve the sloshing intensity of liquid, it is necessary to install internal components to increase damping of liquid. Elastic materials, especially rubber materials, are widely used as internal components of the deep-water damper, which would interact well with damping liquid. In this paper, a damping device combining elastic material with sloshing liquid damper is adopted, and a new-type elastic baffle oscillator sloshing liquid damper is proposed by using the lag function of the spring device to transmit the force. The damping mechanism of the structure and the core factors affecting the damping performance are studied. The numerical simulation results show that by adjusting the stiffness of the internal spring, the phase difference between the structural displacement and the acting force of the internal spring on the structure can be changed in a large range. Under the working condition of this paper, when the elastic coefficient is 2000 N·m−1, the phase difference is close to π/2, and the amplitude of the last wave trough of the structural displacement is only 0.5% of the initial amplitude, which indicates that the damping performance is excellent.

Experimental Investigation on the Effect of Seal Presence on the Behavior of Double-Deck Floating Roofs in Cylindrical Steel Storage Tanks

Liquid storage, particularly oil and petrochemical products which are considered hazardous liquid, are an important part of the oil industry. Thin-walled vertical cylindrical steel storage tanks are widely used in recent years. Due to high sensitivity of these structures in an earthquake and other external excitations may lead to catastrophic consequences. For instance, huge economic losses, environmental damages, and casualities, many studies have been done about these structures. past studies showed that liquid storage tanks, equipped with a floating roof, are potentially vulnerable while subjected to seismic loads and earthquake has been considered as one of the most destructive natural hazards. The reason is that such tanks are made of two separated parts (shell and roof) which each may have its own responses; sometimes causing resonance phenomenon and so that, roof movements, roof-fluid interaction, roof-shell interaction, and also the way they are attached should still be investigated. Experimental tests of floating roof’s vertical fluctuation was performed in a full-scale reservoir tank and assessing of the results demonstrated that presence of a seal between floating roof and shell plate can significantly increase damping ratio in liquid sloshing and also suppress the roof`s vertical displacements. In other words, seal can control a floating roof and make it stop moving vertically over few cycles.

Influence of Liquid Sloshing in the Vertical Limbs of Tuned Liquid Column Dampers on Structural Response Reduction

Influence of Liquid Sloshing in the Vertical Limbs of Tuned Liquid Column Dampers on Structural Response Reduction

Advanced GNC-oriented modeling and simulation of Vertical Landing vehicles with fuel slosh dynamics

This paper introduces a flexible framework to enable high-fidelity simulations of the fuel slosh dynamics for verification of the Guidance, Navigation and Control (GNC) algorithms. The sloshing phenomenon must be tackled during the control system design phase and the GNC software run and validated within appropriate simulation frameworks. Equivalent mechanical models can well approximate sloshing under specific assumptions, allowing the derivation of the multibody vehicle’s equations of motion; however, while suitable for analysis and control synthesis purposes, this approach presents several limitations for implementation as a simulation model. In this work, the multibody plant embedding slosh dynamics is modeled by means of the DLR’s Vertical Landing Vehicles Library (VLVLib) written using the object-oriented Modelica modeling language. The advantages of using Modelica are explored throughout the paper. Given that control synthesis, analyses and simulation campaigns are usually performed in the Matlab/Simulink environment, a core point of the proposed solution is to achieve a good synergy within the latter and the Modelica plant model with the least readaptation burden for the developer. The strategies to achieve a full integration and verification tool chain are illustrated. The potential of this approach is demonstrated via two different test cases: a lunar landing scenario of the ALINA spacecraft developed by PTS, and CALLISTO reusable rocket demonstrator.

Observer-based boundary feedback control for attitude tracking of rigid bodies with partially liquid-filled cavities

In the attitude tracking control tasks of rigid bodies with partially filled cavities, liquid sloshing is a crucial characteristic that hinders effective controller design and accuracy improvement. To overcome this problem, we propose a novel boundary feedback control (BFC) scheme based on the PDE-ODE cascade governing the rigid body attitude and internal liquid dynamics. We further develop an innovative PDE-based observer to cope with requirements on the infinite number of unmeasurable boundary states. Thus, using only attitude data, the discussed boundary controller can stabilize the attitude tracking error and the infinite-dimensional internal dynamics. The asymptotic stability of the closed-loop observer-based controller is established via the Lyapunov direct method. Finally, to show its efficacy, the proposed methodology is applied to the attitude tracking problem of a typical liquid-propellant satellite. In summary, the novelty is twofold: (i) due to dealing with the original involved PDE-ODE cascade, the formulated control strategy is more accurate than the relevant studies that have used liquid rigidity and potential ideal flow assumptions; (ii) the observer design approach is much broader than existing ones for nonlinear parabolic-type PDEs.

Friction pendulum-strengthened tuned liquid damper (FPTLD) for earthquake resilience of isolated structures

Conventional base isolation has been commonly used to protect structures against destructive earthquakes. However, base-isolated structures can be vulnerable to ground motions, including resonant frequency components, which cause significant displacement of the isolation floor and a weakened isolating effect. To address this issue, this study develops a friction pendulum-strengthened tuned liquid damper (FPTLD) as a hybrid isolating system that comprises a friction pendulum subsystem mounted at the bottom of a liquid tank with sloshing liquid inside. Its configuration and theoretical analysis model are established, based on which the experimental test of the tuned liquid subsystem and finite element simulation of the complete FPTLD are conducted for validation. The nonlinear stochastic response analysis is performed for an FPTLD-equipped isolated structure within a probabilistic framework. Correspondingly, the dual-modal and lightweight-based control benefits of the FPTLD over conventional and TLD-equipped isolation systems are clarified by an extensive parametric analysis. Based on the simultaneous control of the isolation floor and the superstructure, a multiperformance-based design framework is presented for the FPTLD, and an easy-to-use design formula is obtained by fitting its numerical design results. To illustrate the effectiveness of the developed device and the design method, the FPTLD is used in a typical base-isolated building subjected to various seismic excitations. The obtained results show that the optimized FPTLD with adjustable tuning degrees—liquid sloshing and friction pendulums—is highly effective in simultaneously enhancing the multiple seismic performances of the superstructure and the isolation floor. In particular, compared with conventional and tuned liquid damper-equipped isolation systems, the FPTLD facilitates sufficient utilization of the entire liquid for efficient energy absorption by implementing friction pendulums, reducing the deformation demand of an isolation floor. Benefitting from the friction pendulums with a constant isolating period, the FPTLD demonstrates a robust multiperformance mitigation effect against the variation in the liquid height. It thereby presents a practical solution to the retrofitting or new construction of a base-isolated structure using a nonspecific designed liquid tank or landscape.

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.

Study of the Sloshing Dynamics in Partially Filled Rectangular Tanks with Submerged Baffles Using VOF and LES Turbulence Methods for Different Impact Angles

This research studies how the angle and dimensions of a single baffle affect the dynamics of a fluid in a closed rectangular tank under an accelerated harmonic vibration in resonance. A half-filled non-deformable rectangular tank with a single centered submerged baffle has been simulated using ANSYS® FLUENT. The study aims to characterize the effect of changing the baffle’s angle; hence, 10 simulations have been performed: without a baffle, 90°, 30°, 60°, 120° and 150°, either maintaining the baffle’s length or the projected height constant. The computational fluid dynamics (CFD) method using volume of fluid (VOF) and large eddy simulation (LES) are used to predict the movement of the fluid in two dimensions, which have been benchmarked against experimental data with excellent agreement. The motion is sinusoidal in the +X direction, with a frequency of oscillation equal to its first vibration mode. The parameters studied have been the free surface elevation, values at three different points and maximum; the center of gravity’s position, velocity, and acceleration; and the forces against the tank’s walls. It has been found that the 90° angle has the most significant damping effect, stabilizing the free-surface elevation, reducing the center of gravity dispersion, and leveling the impacting forces. Smaller angles also tame the sloshing and stabilize it.

Adaptive predefined-time control for liquid-filled flexible spacecraft attitude stabilization during orbit maneuver

A predefined-time attitude stabilization for complex structure spacecraft with liquid sloshing and flexible vibration is investigated under input saturation during orbital maneuver. First, the attitude dynamics model of liquid-filled flexible spacecraft is constructed. Meanwhile, the influence of solar panel vibration and liquid sloshing is treated as a disturbance in the controller design. Next, an adaptive predefined-time control scheme is proposed by applying sliding mode control theory. A predefined-time convergent sliding surface and reaching law are designed to ensure the predefined-time fast convergence rate. Furthermore, a novel adaptive algorithm is developed to handle the disturbances from liquid sloshing and flexible vibration, ensuring that the system converges to a small neighborhood of the equilibrium. Additionally, a new auxiliary system is constructed to deal with the effects of input saturation. At last, one simulation case is performed to verify the feasibility and advantages of the proposed algorithm.