Sloshing In Tank Research Articles

A comprehensive investigation on liquid sloshing of rectangular water tank with vertical baffles

Although numerical method is used to analyze the liquid sloshing-induced wave height and control force, it is worth noting that the effects of vertical baffle on liquid sloshing of rectangular water tanks have not been thoroughly explored. Further research in this domain would be invaluable for gaining a more profound understanding of liquid sloshing in such tanks. Therefore, the CFD method and finite volume model are employed in this paper, and the effects of vertical baffle on the liquid sloshing behaviors are comprehensively investigated, including wave height of free surface, horizontal control force, damping ratio of liquid sloshing, natural frequency, and free surface deformation. Then, the influences of excitation amplitude, water depth, number of baffles, baffle position, and baffle height are extensively explored. The accuracy of the modeling is confirmed through rigorous comparisons with existing experimental results. The number of baffles has a considerable influence on the behaviors of liquid sloshing. The effectiveness of the baffle in reducing liquid sloshing is closely tied to its position. Exceeding the baffle height beyond the water depth causes a transformation of the working mechanism and inherent properties of the rectangular water tank. The natural frequency is generally overestimated by linear potential flow theory.

Effect of the drag coefficient on the performance of vertical porous baffles in a sloshing tank

Purpose The present work involves analytical and experimental investigation of sloshing in a two-dimensional rectangular tank including the effect of porous baffles to control and/or reduce the wave motion in the sloshing tank. The purpose of this study is to assess the analytical solutions of the drag coefficient effect on porous baffles performance to track free surface motion variation in the sloshing tank by comparison with experimental shake table tests under a range of sway excitation. Design/methodology/approach The linear second-order ordinary differential equations for liquid sloshing in the rectangular tank were solved using Newmark’s beta method and obtained the analytical solutions for liquid sloshing with dual vertical porous baffles of full submergence depths in a sway-oscillated rectangular tank following the methodology similar to Warnitchai and Pinkaew (1998) and Tait (2008). Findings The porous baffles significantly reduce wave elevation in the varying filled levels of the tank compared to the baffle-free tank under the range of excitation frequencies. It is observed that the Reynolds number-dependent drag coefficient for porous baffles in the tank can significantly reduce the sloshing elevations and is found to be effective to achieve higher damping compared to the porosity-dependent drag coefficient for porous baffles in the sloshing tank. The analytical model’s response to free surface elevation variations in the sloshing tank was compared with the experiment’s test results. The analytical results matched with shake table test results with a quantitative difference near the first resonant frequency. Research limitations/implications The scope of the study is limited to porous baffles performance under range sway motion and three different filling levels in the tank. The porous baffle performance includes Reynolds number dependent drag coefficient to explore the damping effect in the sloshing tank. Originality/value The porous baffles with low-level porosities in the sloshing tank have many engineering applications where the first resonant mode of sloshing in the tank is more important. The porous baffle drag coefficient is an important parameter to study the baffle’s damping effect in sloshing tanks. Hence, obtained analytical solution for liquid sloshing in the rectangular tank with Reynolds number as well as porosity-dependent drag coefficient (model 1) and porosity-dependent drag coefficient porous baffles (model 2) performance is discussed. The model’s test results were validated using a series of shake table sloshing experiments for three fill levels in the tank with sway motion at various excitation frequencies covering the first four sloshing resonant modes.

Experimental investigation of three-dimensional free-surface and interfacial sloshing in a vertical cylindrical tank

In the present study, hundreds of experiments have been conducted on the three-dimensional free-surface and interfacial sloshing in a vertical cylindrical tank containing two immiscible liquids. The bounds of different free-surface and interfacial wave regimes are determined by maintaining fixed excitation amplitude and slowly increasing excitation frequency until another type of wave regime began to appear. In general, three types of the free-surface wave regimes are observed when the excitation frequency is in the neighborhood of the lowest natural frequency of the free surface, i.e., planar gravity wave, chaotic gravity wave, and swirling gravity wave. Similarly, when the excitation frequency is near the lowest natural frequency of the internal interface, three types of interfacial wave regimes, i.e., planar gravity wave, chaotic gravity-capillary wave, and swirling gravity-capillary wave, are generated. Besides, it is worth pointing out that when the excitation frequency is near the lowest natural frequency of the internal interface as well as very close to a third of the lowest natural frequency of the free surface, large-amplitude rotating wave motion occurs at both the free surface and the internal interface. This is due to even though the excitation frequency is far away from the natural frequency of the free surface, the secondary resonance can still become dominant and lead to large-amplitude motion of the free-surface rotating wave and subsequently influences the internal interface. This paper reveals that the sloshing behaviors of two-layer liquid in the vertical cylindrical tank are much more complicated than those of single-layer liquid.

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

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

Experimental study of sloshing characteristics in a rectangular tank with elastic baffles

A series of laboratory experiments are conducted to investigate liquid sloshing in a rectangular tank with a vertical baffle of varying elasticity under horizontal excitations. Image processing techniques are introduced to track baffle displacement, as well as to identify the free surface and the bubble. Dye visualization is employed to reveal the vortex behavior around the baffle. The air entrainment mechanism, including jet impinging, air cavity formation and deformation, and turbulent mixing, is analyzed. Moreover, the study investigates the effect of baffles with different stiffness on suppressing liquid sloshing across a wide range of excitation frequencies. The results show that the peak frequencies of the maximum free surface elevation-frequency curves correspond to the first natural frequency of fluid, the sub-resonance frequency, and the wet natural frequency of the elastic baffle. It is also found that the elastic baffle can effectively reduce liquid sloshing within a certain frequency range and balance the slamming impact both on the wall and the baffle, providing promising prospects for its practical applications.

Study on the dynamical characteristics and experimental validation for liquid sloshing in a common bulkhead tank

Study on the dynamical characteristics and experimental validation for liquid sloshing in a common bulkhead tank

Numerical Simulations of Tank Sloshing Problems Based on Moving Pseudo-Boundary Method of Fundamental Solution

The moving pseudo-boundary method of fundamental solutions (MFS) was employed to solve the Laplace equation, which describes the potential flow in a two-dimensional (2D) numerical wave tank. The MFS is known for its ease of programming and the advantage of its high precision. The solution of the boundary value can be expressed by a linear combination of the fundamental solutions. The major issue with such an implementation is the optimal distribution of source nodes in the pseudo-boundary. Traditionally, the positions of the source nodes are assumed to be fixed to keep the set of equations closed. However, in the moving boundary problem, the distribution of source nodes may influence the stability of numerical calculations. Moreover, MFS is unstable in time iterations. Hence, it is necessary to constantly revise the weighting coefficients of fundamental solutions. In this study, the source nodes were free, and their locations were determined by solving a nonlinear least-squares problem using the Levenberg–Marquardt algorithm. To solve the above least-squares problem, the MATLAB© routine lsqnonlin was adopted. Additionally, the weighting coefficients of fundamental solutions were solved as a nonlinear least-squares problem using the aforementioned method. The numerical results indicated that the numerical simulation method adopted in this paper is accurate and reliable in solving the problem of 2D tank sloshing. The main contribution of this study is to expand the application of the MFS in engineering by integrating it with the optimal configuration problem of pseudo-boundaries to solve practical engineering problems.

Numerical and experimental study on sloshing damping effects of the porous baffle

Laboratory experiments were conducted to study porous baffle effects on reducing liquid sloshing in a rectangular tank on a six-degrees-of-freedom motion simulation platform. The porous baffle that was a material layer made from spherical particles fully filled into a cage made of perforated stainless-steel plate was proposed. The free surface wave height and the impact pressure on the wall were recorded in laboratory experiments of liquid sloshing in a horizontally excited rectangular tank. These experiments were used to validate the porous media model in OpenFOAM. The OpenFOAM was then employed to simulate sloshing in a rectangular tank with a porous baffle to reveal the sloshing damping mechanism of the porous baffle by changing the external excitation frequency. The results show that the porous baffle is more effective in suppressing impact pressure at a high excitation frequency.

Viscous damping of steady-state resonant sloshing in a clean rectangular tank

A machine learning of the unknown a priori viscous damping, incorporated into the single-dominant nonlinear ‘inviscid’ modal theory by Faltinsen et al. (J. Fluid Mech., vol. 407, 2000, pp. 201–234) on resonant sloshing (the forcing frequency close to the lowest natural sloshing frequency) in a clean (no internal structures) rigid rectangular tank, is proposed. The learning procedure requires a set of measured phase lags between the harmonic horizontal tank excitation and the steady-state resonant wave response. A good consistency with experiments by Bäuerlein & Avila (J. Fluid Mech., vol. 925, 2021, A22) on the liquid-mass centre motions is shown. The latter confirms that the free-surface nonlinearity (causing an energy flow from the primary-excited to higher natural sloshing modes) and viscous damping of the higher natural sloshing modes matter, as well as that the damping rates can depend on the steady-state wave amplitude.

Experiments and analysis of dynamic characteristics of liquid sloshing in horizontal Cassini tank

In this study, the sloshing behaviors and dynamic characteristics of liquid sloshing in a horizontal Cassini tank were studied. The forces and torques generated by the liquid sloshing in non-equilibrium states were experimentally measured with force transducers which have been mounted on the experiment platform. The experiments mainly focus on the sloshing forces and torques generated by liquid sloshing in the tank. And the effects of the magnitude and frequency of the external excitations and the liquid-filling ratios on the sloshing characteristics were also studied. The experiments results show that the liquid sloshing in the Cassini tank is highly correlated with the excitation frequency where small variation in the frequency leads to complex changes in the liquid sloshing characteristics. In the cases with low liquid-filling ratio, in resonance state, the rotational sloshing is easier to be excited, however, in the stable-state the amplitudes of longitudinal sloshing force and torque are more significant than those of other sloshing conditions. The transversal sloshing force and torque are very small in both, rotational and translational nonlinear sloshing of small amplitude. In small-amplitude rotational and translational nonlinear sloshing cases, the CFD simulations were in good agreement with the experimental data. However, as the transitional compound state between different modes of vibration at various orders, the dynamic ratio of longitudinal and transversal sloshing force became large and errors occurred and became obvious in CFD simulations.

Semi-analytical method for liquid sloshing in the rigid super-elliptical tank with the ring baffle

Tanks with super-elliptical cross-sections can improve space utilization. The effect of the submerged ring baffle on liquid sloshing in the tank is studied. The semi-analytical method is developed to solve the three-dimensional (3D) sloshing problem in the baffled non-axisymmetric tank, using linear potential theory by dividing the liquid domain into sub-domains. The formal solutions are obtained analytically for the 3D non-axisymmetric sub-domains with arbitrary cross-sections, allowing for the determination of natural frequencies and modes by substituting the formal solutions into the linearized free surface condition, the boundary conditions on the baffle and tank wall and the continuity conditions at the interfaces of the interconnecting sub-domains. The dynamic response equation is derived using the mode superposition method with the damping term for swaying excitation. The obtained solution is validated by comparing it with a numerical model, demonstrating excellent accuracy and efficiency. Parametric studies are performed to determine the effect of the baffle on liquid sloshing, indicating that the baffle can considerably reduce the liquid sloshing when considering an optimal baffle position and width. This technique can be extended to investigate the sloshing reduction in vertical containers with arbitrary cross-sections.

Data-driven AI Method for the Prediction of Tank Sloshing Noise and Cabin Comfort

Data-driven AI Method for the Prediction of Tank Sloshing Noise and Cabin Comfort

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.

Coupled FPSO roll motion response and tank sloshing in a pair of two row cargo tanks

The advantages offered by Floating Production Storage and Offloading Units (FPSOs) continue to make them high in demand and widely used. Continuous loading and offloading of FPSOs means the presence of slack cargo tanks is inevitable and can impact the seakeeping performance of FPSOs. Published experimental data on this impact is limited. This paper experimentally studies liquid cargo and its effect on roll motion in a pair of two-row cargo tanks of a FPSO model in regular beam waves. The results show that the liquid cargo motion effect on floating vessels cannot be studied using solid cargo. The results also show that varying the liquid cargo loading affects floating vessels’ Response Amplitude Operators (RAOs).

Numerical simulation of wave impact and high pressure characteristics due to violent sloshing in a rectangular tank

ABSTRACT Understanding violent sloshing is of practical concern to a wide range of applications as it may compromise safety in a number of engineering applications. The present study investigates violent sloshing in a 2D tank. In particular, the evolution and influence of an air pocket and the impact pressure on tank walls are numerically studied. Since the problem involves multi-phase flows, standard dam-break problem is used for validations. The liquid depth and amplitude of excitation are systematically varied to assess the impact pressures on walls and roof of the tank. Non-linear effects are captured qualitatively and the distribution of impact pressures on the tank walls is examined. The entrainment of an air pocket by a standing wave at the tank roof is delineated. The violent sloshing wave motion causes the formation of air pockets that arise for a range of forcing amplitudes and a variety of liquid depths. Gradual decay in the impact pressure due to the generation of these air pockets is significant on overall sloshing dynamics. The maximum peak pressure predicted on the tank roof is about 10 times the static pressure, which is also about twice the peak pressure obtained on the side wall. Furthermore, the distribution of average impact-pressure profiles on the tank walls and roof is presented for different loading conditions vis-á-vis global impact characteristics of sloshing wave motion.

Investigation of the load and flow characteristics of variable mass forced sloshing

A complicated coupling system performs fuel filling operation of a ship on the sea that involves tank sloshing and filling impact. This research elaborated on the sloshing load and flow characteristics of the variable mass tank and revealed its physical process through numerical simulations to provide safety assurance for fuel filling. First, this work clarified the difference between the numerical theory of variable mass tank sloshing and that of ordinary sloshing. On this foundation, a numerical model was developed for a three-dimensional variable mass tank sloshing. In addition, the model was validated by comparing the results of the previous experiments. Second, the sloshing pressure and internal free surface of the tank were monitored by numerical simulations. At the same time, a series of sensitivity analyses were carried out against the sloshing period, filling rate, and sloshing amplitude. Finally, the baffle was added to the sloshing tank to study the influence of internal barrier structure on the sloshing flow and pressure characteristics. The following conclusions were obtained from this work: Fuel filling caused an increase in liquid mass, suppressing sloshing and increasing the tank load. Overall, the sloshing load increased with the filling rate. Moreover, the impact of internal barrier structure on sloshing is discussed in this study, and it was discovered that the sloshing effect could be efficiently suppressed by the barrier structure.

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.