Sloshing Frequency Research Articles

Effects of Baffles on Sloshing Impact Pressure of a Chamfered Tank

In the following study, the classical Fluid-Structure Interaction (FSI) analysis of sloshing flows is given a new dimension to analyse the stability of the ship by utilization of several mitigating factors. Sloshing near the natural frequency of the tank can result in severe ullage collapse or ballast, whereas in the stable regions sloshing generally leads to cyclic stress and fatigue in thin walled tank structures. The aim is to model the generation and propagation of free surface waves in a tank having bottom baffle arrangements. Important parameters such as filling level and slosh frequency are parametrically varied to assess the impact of each of these parameters on the tank pressure. Further the geometries are studied for four phenomenon that affects the dynamic stability considerably viz. air pockets, flip through, hydraulic jump and roof impact. The comparison of simulated results show significant decline in the value of impact pressure (both maximum and average) in a chamfered tank with the use of baffles at the bottom.

Effect of baffle geometry and air pressure on transient fluid slosh in partially filled tanks

Effects of baffle geometric parameters such as curvature, opening size and shape, and inclination on the transient load shift and slosh forces within a partly filled liquid tank are investigated under longitudinal and lateral acceleration fields using computational fluid dynamic (CFD) methods. Validity of the simulations is illustrated considering steady-state responses, and fundamental slosh frequencies of cleanbore and baffled tanks. The slosh forces imposed on the baffles and end caps are evaluated for different baffle design parameters. The results suggest that the liquid cargo load shift, longitudinal and lateral forces, and pitch moment due to transient fluid slosh are strongly influenced by the baffle shape, and opening size. It is further shown that sloshing with medium to high fill levels can cause substantial increase in pressure of air trapped between the end cap and baffle, and between adjacent baffles, which contributes considerably to the resultant forces on the baffles and opposes the force due to liquid phase of the flow.

Seismic control of structures using sloped bottom tuned liquid dampers

Earlier numerous studies have been done on implementation of Tuned Liquid Damper (TLD) for structural vibration control by many researchers. As per current review there is no significant study on a sloped bottom TLD. TLD\'s are passive devices. A TLD is a tank rigidly attached to the structure and filled partially by liquid. When fundamental linear sloshing frequency is tuned to structure\'s natural frequency large sloshing amplitude is expected. In this study set of experiments are conducted on flat bottom and sloped bottom TLD at beach slope 20o, 30o and 45o, for different types of structures, mass ratio, and depth ratio to investigate the overall effectiveness of TLD and specific effect of TLD parameters on structural response. This experimental study shows that a properly designed TLD reduces structural response. It is also observed that effectiveness of TLD increases with increase in mass ratio. In this experimental study an effectiveness of sloped bottom TLD with beach slope 30o is investigated and compared with that of flat bottom TLD in reducing the structural response. It is observed from this study that efficiency of sloped bottom TLD in reducing the response of structure is more as compared to that of flat bottom TLD. It is shown that there is good agreement between numerical simulation of flat bottom and sloped bottom TLD and its experimental results. Also an attempt has been made to investigate the effectiveness of sloped bottom TLD with beach slope 20o and 45o.

In-Flight Characterization of the Cassini Spacecraft Propellant Slosh Modes

Telemetry data from three 445 N engine burns of the Cassini spacecraft are used to characterize the high- slosh characteristics of bipropellants in cylindrical tanks with spherical end domes. Comparisons between flight data and theoretical results indicate that high- clean tank slosh frequency and high- sector mode frequency could be predicted with errors of 3–5%. However, at lower tanks’ fill fractions of , when most of the propellants reside in the spherical end domes of the tanks, the prediction errors deteriorated to . Also, high- full-tank slosh mode in a tank with an eight-panel propellant management device could be modeled using an annular cylindrical tank. Again, prediction error of full-tank slosh frequency degraded with decreasing fill fractions. Based on these results, the high- sector and full-tank propellant slosh frequencies could be well predicted using simple analytical techniques before these predictions are refined by liquid slosh computer modeling tools. A set of small-amplitude oscillatory motions of the spacecraft attitude was detected during 13 science observations conducted in 2007–2008. Their frequencies matched well the low- slosh frequency predicted analytically for uncompartmented tank. The root cause and analytical prediction of the observed spacecraft oscillatory motion in low- condition is an interesting topic for future research.

Volume-Filling Effects on Sloshing Frequency in Simplified and Explicit Dynamic Finite Element Models of Tank Wagons during Braking and Turning

Volume-Filling Effects on Sloshing Frequency in Simplified and Explicit Dynamic Finite Element Models of Tank Wagons during Braking and Turning

Liquid sloshing in a circular cylindrical container containing a two-layer fluid

In this work, a semi-analytical approach is employed to investigate sloshing in an immiscible, incompressible and inviscid two-layer fluid. We evaluate natural sloshing frequencies of the two-layer fluid of different layer-wise densities $$\rho _1 < \rho _2$$ with an interface and a surface in a vertical circular cylinder. On the basis of the velocity potential formulation of the fluid motion inside the container, an infinite system of homogeneous linear equations is obtained. We demonstrate the effects of the parameters such as fluid heights and density ratio on the natural sloshing frequencies. The results are supported by relevant graphs.

A NEW GRAVITATIONAL-WAVE SIGNATURE FROM STANDING ACCRETION SHOCK INSTABILITY IN SUPERNOVAE

ABSTRACT We present results from fully relativistic three-dimensional core-collapse supernova simulations of a non-rotating star using three different nuclear equations of state (EoSs). From our simulations covering up to ∼350 ms after bounce, we show that the development of the standing accretion shock instability (SASI) differs significantly depending on the stiffness of nuclear EoS. Generally, the SASI activity occurs more vigorously in models with softer EoS. By evaluating the gravitational-wave (GW) emission, we find a new GW signature on top of the previously identified one, in which the typical GW frequency increases with time due to an accumulating accretion to the proto-neutron star (PNS). The newly observed quasi-periodic signal appears in the frequency range from ∼100 to 200 Hz and persists for ∼150 ms before neutrino-driven convection dominates over the SASI. By analyzing the cycle frequency of the SASI sloshing and spiral modes as well as the mass accretion rate to the emission region, we show that the SASI frequency is correlated with the GW frequency. This is because the SASI-induced temporary perturbed mass accretion strikes the PNS surface, leading to the quasi-periodic GW emission. Our results show that the GW signal, which could be a smoking-gun signature of the SASI, is within the detection limits of LIGO, advanced Virgo, and KAGRA for Galactic events.

Resonant sloshing in an upright annular tank

Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio $1.5\lesssim h=\bar{h}/\bar{r}_{2}$) and away from the non-dimensional inner radii $r_{1}=\bar{r}_{1}/\bar{r}_{2}=0.08546$, 0.17618, 0.27826, 0.31323, 0.31855, 0.43444, 0.46015, 0.48434, 0.68655, 0.70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank ($r_{1}=0$) are utilised for validation. Inserting an inner pole with the radii $r_{1}\approx 0.25$ and 0.35 ($1.5\lesssim h$) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears.

Liquid sloshing in partly-filled laterally-excited cylindrical tanks equipped with multi baffles

Baffles are used effectively to reduce the sloshing response of liquid in the liquid storage containers. This study is aimed at analysis of transient lateral sloshing in a partially-filled cylindrical tank with multi baffles including floating circular baffle, wall-mounted ring baffle, floating ring baffle and their combination form, and those baffles with inclination using a coupled multimodal method and scaled boundary finite element method (SBFEM). Slosh frequencies and mode shapes are initially estimated using the extending semi-analytical SBFEM by applying the linearized free surface boundary condition using the zoning method, where the liquid domain is firstly divided into several simple sub-domains so that the liquid velocity potential in each sub-domain has continuous boundary conditions of class C1. As a key point, a new type of local co-ordinate system for SBFEM with axisymmetric geometry is presented for each sub-domain. Based on the multimodal method, significant improvement in computational time is achieved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials on the two-dimensional half free-surface length. The generalized coordinates of the free-surface oscillations under a lateral excitation are then obtained from superposition of the natural slosh modes. The sloshing mass and lateral slosh force are also formulated in terms of the generalized coordinates and hydrodynamic coefficients. The validity of the model is examined through comparisons with available other solutions, and the results show that the present method has higher accuracy and efficiency with a very small number of degrees of freedom for the simulation of the complex sloshing problem partly-filled laterally-excited cylindrical tanks. It is also shown that consideration of only the first sloshing mass is adequate to represent the dynamic behavior of the liquid container quite accurately. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing masses and sloshing forces are discussed in detail.

Numerical model of sloshing in rectangular tank based on Boussinesq-type equations

The highly accurate Boussinesq-type equations in terms of velocity potential are adopted for the simulation of sloshing phenomena in a two-dimensional rectangular tank. The fully nonlinear free surface conditions are used and linearized energy dissipation term is added into the dynamic free surface condition. The total velocity potential is divided into two parts: the particular solution and the rest which is calculated by the Boussinesq-type model. Different filling levels of liquid in the tank are considered for the validation of the numerical model, including shallow water, intermediate water depth and finite water depth cases. The linear theory based on the superposition of eigen-modes corresponding to natural sloshing frequencies is introduced. Compared with results calculated by linear theory and results from literatures, the numerical model based on Boussinesq-type equations presents good performances in predicting the sloshing motions in rectangular tank with small excitation amplitude.

Stability analysis of elastic launch vehicles with fuel sloshing in planar flight using a BEM-FEM model

A numerical model is developed for investigation of coupled dynamics of fuel contained elastic launch vehicles in planar atmospheric flight. Finite element method along with the linear quasi-steady piston aerodynamic theory is used for developing an aeroelastic model. A reduced order boundary element model is used for modeling the liquid sloshing in tanks. The interaction of sloshing and aeroelasticity is studied using stability analysis of the coupled system. Results show that the slosh–aeroelastic coupling in an elastic launch vehicle occurs for low tank filling ratios and may lead to decreasing the system damping. Due to more interactions between the slosh and rigid body modes, larger damping values of the rigid body mode and lower slosh frequencies are found for an elastic vehicle compared with a rigid vehicle. It is also shown that the slosh–aeroelastic interaction is increased as the slosh inherent damping decreases.

Analytical and experimental study on natural sloshing frequencies in annular cylindrical tank with a bottom gap

This paper is concerned with the analytical derivation of natural sloshing frequencies of liquid in annular cylindrical tank and its verification by experiment. The whole liquid domain is divided into three simple sub-regions, and the region-wise linearized velocity potentials are derived by the separation of variables. Two sets of matrix equations for solving the natural sloshing frequencies are derived by enforcing the boundary conditions and the continuity conditions at the interfaces between sub-regions. In addition, the natural sloshing frequencies are measured by experiment and the numerical accuracy of the proposed analytical method is verified through the comparison between the analytical and experimental results. It is confirmed that the present analytical method provides the fundamental sloshing frequencies which are in an excellent agreement with the experiment. As well, the effects of the tank radial gap, the bottom flow gap and the liquid fill height on the fundamental sloshing frequency are parametrically investigated.

Analytically approximate natural sloshing modes and frequencies for an upright circular container with poles

Natural sloshing modes and frequencies are analytically approximated for an upright circular cylindrical tank equipped with an array of vertical poles (pipes), as happens, for example, in shafts of ocean platforms. The method leads to exact analytical solutions when they exist and demonstrates rather good accuracy in other cases. The approximate natural frequencies are compared with an existing asymptotic estimate.

EFFECT OF FREE SURFACE BOUNDARY AND WALL FLEXIBILITY IN SEISMIC DESIGN OF LIQUID STORAGE STEEL TANKS

Fluid Structure Interaction (FSI) itself is a vast and extensive discipline. It originated from studies of aero and hydro-elasticity, which are often related to aeronautics and aerospace as well as nuclear industries. In practice, within the scope of nuclear, civil, aerospace, ocean, chemical and mechanical engineering, there are many terminologies involved, ie., flow induced vibration, aero-elasticity, hydro-elasticity, fluid structure interaction and fluid solid interaction. Typical problems include structure interaction with surface and sound waves and vibrations and stabilities of cables, pipes, plates and shells. In this paper, the effect of fluid structure interaction on the modal characteristics of a cylindrical steel water tank with and without free surface effect is considered. Acoustic structure interaction using unsymmetric pressure based formulation is used to solve the coupled system using FEM and the procedure is validated using results from published literature. Two tank models (shallow and tall) are modeled using ANSYS and modal analysis was done by considering different conditions like with slosh and without slosh. The effect of fluid mass on the convective and impulsive modes of tall and shallow aspect ratio tanks is shown. Parametric study is done for different fluid levels to characterize the variation of slosh frequencies in both rigid and flexible wall conditions. Free surface is considered in fluid alone model to predict the slosh frequencies employing rigid wall boundary. Then slosh frequencies got from both rigid and flexible wall conditions are compared with design data frequency tabulated from the GSDMA Guidelines. From this we can say that the flexibility of tank wall has a greater effect on the slosh frequencies.

Analysis of liquid sloshing in LNG carrier with wedge-shaped tanks

The LNG carrier with four wedge-shaped tanks is introduced. This design aims to avoid the simultaneous occurrence of the sloshing resonance in all tanks that endangers the ship stability. A numerical strategy with the help of the boundary element method is developed to calculate the natural sloshing frequencies and corresponding modes for these wedge-shaped tanks. The effects of the inclined tank walls on the natural sloshing frequencies/modes are identified. The elevation histories of the sloshing waves in these tanks are further studied, when the carrier is excited by sway, roll, surge or pitch motions at the fundamental natural frequency of each tank. The effectivity of this new design is confirmed from the results.

Three-dimensional dynamic liquid slosh in partially-filled horizontal tanks subject to simultaneous longitudinal and lateral excitations

Three-dimensional liquid slosh in a horizontal cylindrical tank is analyzed assuming inviscid, incompressible and irrotational flows under simultaneous application of longitudinal and lateral accelerations, idealizing a braking-in-a-turn maneuver in a road tanker. The spectral problem of liquid slosh within the partially-filled tank of arbitrary cross-section and finite length is initially formulated using the higher order boundary element method (BEM). The three-dimensional Laplace equation is subsequently reduced to a two-dimensional Helmholtz equation using the separation of variables, which significantly reduces the computing demand. The computing time is further reduced by reducing the generalized eigenvalue problem to a standard one considering only the velocity potential on the half free-surface length. The resulting natural slosh frequencies and modes are implemented in a linear multimodal method to obtain generalized coordinates of the free-surface in a partly-filled circular cross-section tank. The slosh forces and moments are subsequently formulated in terms of generalized coordinates and hydrodynamic coefficients considering the damping due to liquid viscosity in the boundary layer. It is shown that the proposed BEM integrating the multimodal method yields computationally efficient solution of the three-dimensional liquid slosh within moving horizontal tanks. The validity of the model is demonstrated using reported analytical and experimental results. The range of applicability of the linear theory for predicting three-dimensional transient slosh is further discussed through comparisons with nonlinear simulation results obtained from a commercial CFD code. The results suggest that the linear theory can predict the slosh forces and moments with reasonably good accuracy when the steady-magnitudes of the lateral and longitudinal accelerations are less than 0.3 g and 0.2 g, respectively, for a tank with aspect ratio in the order of 2.4.

Sloshing-induced slamming in screen-equipped rectangular tanks in shallow-water conditions

Sloshing-induced slamming in a rectangular tank with centralized slat-screens with high solidity ratios was experimentally studied under nearly two-dimensional shallow-water conditions with large-amplitude harmonic lateral excitation. The main objective was to identify the solidity ratio that provides an optimal suppressing function on the free-surface elevation and slamming pressure on the vertical tank walls with a frequency domain containing the three lowest natural sloshing frequencies in a clean tank with a water depth-to-tank length ratio of h/l = 0.125 and a high forced sway amplitude. The experiments show that the optimal solidity ratio among four considered slat-screens is approximately 0.6-0.7 for the applied filling level and excitation amplitude in the examined forced frequency range. The results have potential applications in areas such as swash bulkhead design and liquefied-cargo tank design in ship and offshore engineering.

A coupled multimodal and boundary-element method for analysis of anti-slosh effectiveness of partial baffles in a partly-filled container

The liquid slosh within a partially-filled moving horizontal cylindrical container with different designs of longitudinal baffles is analyzed for predicting transient lateral slosh force and overturning moment, assuming inviscid, incompressible and irrotational flows. A boundary element method is initially formulated to solve the spectral problem of free liquid slosh using the zoning method involving the velocity potentials alone of the half free-surface length, which significantly increases the computational efficiency. The resulting natural slosh frequencies and modes are subsequently implemented in a linear multimodal method to obtain generalized coordinates of the free-surface under a lateral acceleration excitation. Damping due to baffles, estimated from the energy dissipated per cycle, is also implemented into the multimodal equation. The validity of the model is illustrated through comparisons with available analytical solutions. The results are presented for the tank with bottom-mounted, top-mounted and center-mounted partial baffles of different lengths. The effects of baffle design and length on the natural slosh frequencies/modes, damping ratios and hydrodynamic coefficients are further investigated. The lateral force and overturning moment due to liquid motion within the container are derived in terms of generalized coordinates and the natural slosh modes. It is shown that the multimodal method yields computationally efficient solutions of liquid slosh within moving baffled containers. The results suggest that top-mounted baffles are most effective in suppressing the fluid slosh force under more likely fill height conditions in road tankers (well above 50% of diameter), when the baffle is partly submerged in the liquid domain. The center-mounted baffle was effective under intermediate fill levels in the vicinity of 50%, while the bottom mounted baffle was effective only under very low fill heights.

Coupled analysis of nonlinear sloshing and ship motions

A coupled numerical model considering nonlinear sloshing flows and the linear ship motions has been developed based on a boundary element method. Hydrodynamic performances of a tank containing internal fluid under regular wave excitations in sway are investigated by the present time-domain simulation model and comparative model tests. The numerical model features well the hydrodynamic performance of a tank and its internal sloshing flows obtained from the experiments. In particular, the numerical simulations of the strong nonlinear sloshing flows at the natural frequency have been validated. The influence of the excitation wave height and wave frequency on ship motions and internal sloshing has been investigated. The magnitude of the internal sloshing increases nonlinearly as the wave excitation increases. It is observed that the asymmetry of the internal sloshing relative to still water surface becomes more pronounced at higher wave excitation. The internal sloshing-induced wave elevation is found to be amplitude-modulated. The frequency of the amplitude modulation envelope is determined by the difference between the incident wave frequency and the natural frequency of the internal sloshing. Furthermore, the coupling mechanism between ship motions and internal sloshing is discussed.

Effects of tank cross-section on dynamic fluid slosh loads and roll stability of a partly-filled tank truck

An analytical model of a partly-filled tank of arbitrary cross-section is developed for predicting transient lateral slosh force and overturning moment using linear slosh theory. Slosh frequencies and mode shapes are initially estimated using the variational method, which is applied to the linearized free-surface boundary condition. The resulting truncated system of linear ordinary differential equations is subsequently solved numerically to determine the fluid velocity potentials followed by hydrodynamic force and moment. The validity of the model is examined through comparisons with available analytical solutions and experimental data. The slosh force and roll moment are obtained for four different tank cross-sections, namely, circular, elliptical, modified-oval and Reuleaux-triangle. It is shown that the magnitudes of the slosh force and overturning moment are strongly dependent upon the tank cross-section. The slosh model is subsequently integrated to a roll plane model of an articulated tank-semitrailer vehicle to study the effect of dynamic liquid slosh as well as the tank cross-section on the steady-turning roll stability limit of the vehicle under constant and variable cargo load conditions. The results suggest that a tank cross-section with lower overall center of mass and lower critical slosh length yields an enhanced roll stability limit under medium- and high-fill conditions.