Sloshing Motion Research Articles

Suzaku Observations of the Cold Front in A3667: A Nonequilibrium Ionization State of the Intracluster Medium

Abstract We present a systematic study of the thermodynamic properties of the intracluster medium (ICM), including the plasma conditions in the ICM, in the merging galaxy cluster A3667 using Suzaku. We analyze the X-ray spectra of the ICM between the northwestern and the southeastern radio relics across a prominent cold front in A3667 to search for the ICM in a nonequilibrium ionization (NEI) state. We find that the ICM inside the cold front exhibits an NEI state with an ionization parameter of (2.2 ± 0.4) × 1011 s cm−3 at the 90% confidence level, which is lower than that expected from a collisional ionization equilibrium state of the ICM (i.e., n e t > 1012 s cm−3). The timescale calculated from the ionization parameter of the ICM inside the cold front is 3.9 − 0.8 + 0.7 Myr , which is much shorter than the thermal equilibration timescale. A weak transonic sloshing motion might explain the possibility that the ICM inside the cold front of A3667 is in the NEI state. In addition, the NEI state of the ICM in A3667 seems to be associated with the elongated radio halo bridging the region between the northwestern radio relic and the prominent cold front in A3667 across the cluster center.

Nonlinear linear dynamics and numerical analysis of a sloshing tank

Sloshing motion in liquids refers to the phenomenon of oscillation or agitation that occurs when a liquid is subjected to movement or disturbance. This can happen in containers, tanks, ships, or any other object that contains liquid and is subject to movement, such as acceleration, deceleration, turning or tilting. These oscillations can be caused by several factors, such as sudden changes in speed, changes in the direction of movement, winds, waves, or even internal movements of the liquid due to its own inertia. Sloshing can have significant effects in different contexts, such as naval engineering, liquid cargo transportation, storage tank projects, among others. Therefore, the study of sloshing is important to ensure the safety and stability of structures that contain moving liquids, as the forces resulting from these oscillations can affect structural integrity and even lead to accidents if they are not properly considered and controlled. Mathematical models and computer simulations are often used to predict and mitigate the effects of sloshing in different applications. Thus, this work investigates a mathematical model that describes a tank coupled to an electric motor, and therefore we determine the parameter space of the Lyapunov Exponent, basins of attraction, bifurcation diagrams and phase maps. These numerical analyzes are important to determine the range of parameters that diagnose chaos in the system.

Investigation of liquid sloshing characteristics in tanks using an OpenFOAM solver with arbitrary excitation

A multiphase flow solver with mesh motion is typically used for simulations of liquid sloshing in containers, such as those in spacecraft, aircraft, and ships. The mode of the mesh motion should be predefined by functions, which is difficult for a sustained and arbitrary motion. In the present work, a general solver without mesh motion for liquid sloshing in tanks is proposed, based on the interFoam solver in OpenFOAM, by tracking the free surface using the volume of fluid method. An arbitrary excitation loading algorithm is implemented for automatically loading the three-dimensional arbitrary acceleration data. Moreover, the energy equation with phase change is also newly implemented in this solver so that the heat and mass transfer can be evaluated for cryogenic fuels during sloshing. In this way, arbitrary external excitations can be directly imported for any arbitrary sloshing case, and the characteristics of liquid sloshing and oscillation forces can be directly simulated without mesh motion. The solver is validated using different cases, and the influence of sloshing on the mass transfer rate and the effect of the baffle on the liquid sloshing characteristics are investigated. The results indicate that the solver can be easily applied to engineering problems involving liquid sloshing.

Rapid sloshing-free transport of liquids in arbitrarily shaped containers

We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneuvers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulum model to represent the sloshing dynamics and suggest a novel parameter identification scheme suitable for arbitrary container shapes and any number of sloshing modes. By computing natural modes and fluid reaction forces and torques for imposed harmonic container motions via a finite element model, we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We also provide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameter estimates. The proposed feedforward control method uses a virtual tray pendulum on which we place the container (in the form of its equivalent pendulum model). Designing the virtual tray such that the fluid’s dominant sloshing mode cannot be excited by horizontally moving the tray pendulum pivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property of the resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in higher modes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed method is demonstrated through extensive simulations and experimental results using a Martini cocktail glass, whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept.

Numerical and Experimental Studies of Shallow‐Water Sloshing Motions in a Prismatic Tank

Shallow‐water sloshing behavior within a prismatic tank has been analyzed utilizing a model of Boussinesq‐type equations. The Boussinesq‐type equations are calculated by the five‐points finite difference method and extrapolating boundary technique are adopted for simulating the runup phenomena around the inclined bottom. The numerical grid points are divided into the wet region which are evaluated by the Boussinesq‐type equations and the dry region which are obtained from extrapolating boundary technique. The experimental studies of sloshing motions in the prismatic tank were carried out based on the six degrees of freedom motion platform. And the free surface profiles on the inclined bottom were compared between the numerical and experimental results. In the vicinity of the lowest natural frequency, the numerical model presents very good performance on nonbreaking sloshing motions. Based on the numerical Boussinesq‐type model, the frequency response of sloshing motion in prismatic tanks with different inclined bottoms is compared and the transformation from hard-spring effect to soft-spring effect can be found. With the angle of inclined bottom decreased the main wave pattern in the prismatic tank change from nonlinear traveling waves to standing waves.

Sloshing reduction in microgravity: Thermocapillary-based control and passive baffles

In this work, we numerically analyze different thermocapillary-based strategies for active control of sloshing in microgravity. The fluid system considered is an open rectangular container holding a L×H=30 × 15 mm2 volume of liquid. A classical controller is implemented to reduce the natural sloshing motion of the system, which is characterized by its decay time τd. The controller produces an output signal ΔT that is applied anti-symmetrically at the lateral walls of the container, driving thermocapillary flow. Its performance is characterized via the functional P=(1−λ) τ̂+λ κ̂, which allows for a trade-off between the damping of unwanted sloshing modes and the cost of implementing the control, with normalized decay time τ̂ and cost κ̂, and modulated by λ∈[0, 1]. We optimize P for discrete values of λ and determine the optimal performance envelope. The results show that thermocapillary controllers are generally able to reduce τd by a 50% factor, with reasonable cost and controller output. A novel strategy combining thermocapillary controllers and passive baffles is further proposed and assessed. On their own, passive baffles can reduce the natural decay time of sloshing by an 80% factor at zero cost. In addition, they significantly alleviate the thermal requirements associated with the control, while providing additional improvements in τd. Finally, the aforementioned strategies are tested against a reboosting maneuver of the International Space Station, showing their potential for sloshing reduction in microgravity.

Understanding electrohydrodynamic (EHD) performance of corona discharge via particle image velocimetry (PIV)

Electrohydrodynamic (EHD) pumping through corona discharge has found many interesting applications, as it does not require any mechanical moving parts. However, understanding the EHD performance of the corona discharge is crucial for a controllable manipulation of the fluids. This study investigates the pumping performance of an in-house built corona discharge setup for inducing circular motions in the fluids. Silicone oils of different kinematic viscosities are used as the EHD fluid. The EHD performance/fluid characteristics are studied experimentally using particle image velocimetry (PIV) under different DC corona voltages and their results are verified using the continuity equation. Additionally, an analytical model is derived using the Navier–Stokes equations. A clear scaling effect of the corona voltage is seen for the EHD fluid. The EHD fluid exhibits higher velocities at high corona voltages with low perturbation frequency (< 3 Hz) which is attributed to a sloshing motion in the fluid. This naturally occurring sloshing (out-of-plane) motion can be utilized when mixing is desired in the fluid. The results of this study can be used for contact-less and controllable manipulation of dielectric fluids (i.e., silicone oils) for potential applications in emulsion formation and separation.Graphical abstract

Statistical analysis of sloshing-induced dissipative energy across a range of Froude numbers

Fuel sloshing-induced damping is currently being studied extensively within the EU-funded SLOWD project as a means of passively reducing dynamic loads in aircraft wings. It is of interest to be able to determine which parameters have the greatest influence on the added damping from the sloshing motion. An uncertainty in the measured sloshing force has been observed when multiple consecutive and identical oscillation cycles are considered in sinusoidal excitation experiments, leading to variations in the measured energy dissipation. This current work considers liquid undergoing vertical sloshing motions for different fill level and excitation conditions (frequency and amplitude) leading to energy dissipation via several possible physical mechanisms. The sloshing dissipation is measured experimentally across a large number of excitation cycles and for each excitation amplitude, expressed in the form of Froude (Fr) numbers. Depending on the Fr number, distinct sloshing mechanisms dominate the dissipative effects and induce a particular variance across the identical cycles analysed. The sloshing-induced energy dissipation variation is quantified and correlated with different mechanisms depending on Fr number, helping to explain various non-stationary effects that are observed even in well-controlled experimental conditions. As well as improving the insights into the inherent dispersion nature of the studied phenomena, this research also establishes experimental characteristics suitable for future model validation and calibration.

Experimental measurement and numerical validation of sloshing effects on resistance increase in head waves

Most sea trials of large merchant ships are carried out with the filling ballast water in cargo, and the trial environment may involve mild waves as well. It causes the ship to undergo a coupling effect between external wave excitation and internal sloshing motion, and an understanding of such coupling is important to analyze the components of the total resistance measured in sea trials. In this study, a blunt modified Wigley equipped with two inner tanks is selected to observe its hydrodynamic responses under head waves, using both experimental measurement and numerical computations. Ship is considered to have a forward motion at the Froude number of 0.2, and three filling conditions varying from low filling to high filling have been arranged for two inner tanks. For validation, numerical computation is performed based on the three-dimensional Rankine panel method with the linearized boundary value problems. Both seakeeping and internal sloshing flow are analyzed using the linear potential theory. The validation presents a sufficient agreement between experimental measurement and numerical results with or without the sloshing effect, and both two methods have shown that the sloshing coupling effect is generally insignificant for present ship model. However, when the wave encounter frequency becomes very close to the tank natural frequency, the medium filling tanks generate a strong coupling effect which can restrain ship motion responses as well as added resistance.

Numerical analyses of liquid slosh by Finite volume and Lattice Boltzmann methods

Liquid slosh phenomenon has been widely observed in aerospace and aeronautic engineering. In this paper, Finite volume method (FVM) and Lattice Boltzmann method (LBM) are proposed to perform the quick evaluation of liquid slosh behaviour under different container designs. The effectiveness of the numerical models is validated by the existing experimental data. The validated models are then used to study the fuel slosh behaviour with different baffle ring designs. By inserting the baffle to divide the liquid region into multiple sections, the slosh motion of the liquid is suppressed. At the same time, the effectiveness and time efficiency of LBM model have been demonstrated by a parallel comparison with the results from the FVM model. It is found that the computational time cost of LBM model is only around 7.0% of the time cost for FVM model without compromise of the numerical accuracy. This supports the future utilisation of LBM model in quick design evaluation of slosh-like problem.

Dynamic response analysis of submerged floating tunnel - canyon water system under earthquakes

Submerged Floating Tunnel (SFT) is one new type of infrastructure, representing a challenge in structural engineering, both on the theoretical and operational fields. Several research work focused on this innovative structure, especially on effects of dynamic loadings such as earthquakes and sea waves. So far, the dynamic response of SFT under vertical seismic ground motion input and secondary hydrodynamic pressure has been studied deeply using theoretical and numerical methods. However, the dynamic response characteristics of SFT-Canyon water system under surging caused by the canyon horizontal sloshing motion remain unclear. In this paper, a new mathematical model for analyzing the dynamic response characteristics of SFT-Canyon water system caused by horizontal sloshing motion was proposed, which considered the transmission effect of canyon water to the original horizontal seismic wave input. Firstly, the canyon was simplified as a rectangular water tank and hydrodynamic potential flow theory was used to study the dynamic input to SFT through canyon water. After that, based on the theory of structural dynamics, SFT was simplified as an elastic support beam, and the action of horizontal seismic input was considered as the load transmitted through the fluid in the canyon to study the response of SFT transmitted through water. Finally, we used verified MATLAB coding to achieve Duhamel integration to solve the mathematical model of the system dynamic response under the action of sine wave and seismic wave respectively. Besides, the factors affecting the maximum vertical displacement response of SFT under hydrodynamic pressure caused by horizontal seismic input to the canyon were discussed.

Effect of Bottom Geometry on the Natural Sloshing Motion of Water inside Tanks: An Experimental Analysis

The present work aims at understanding and modelling some key aspects of the sloshing phenomenon, related to the motion of water inside a container and its effects on the substructure. In particular, the attention is focused on the effects of bottom shapes (flat, sloped and circular) and water depth ratio on the natural sloshing frequencies and damping properties of the inner fluid. To this aim, a series of experimental tests has been carried out on tanks characterised by different bottom shapes installed over a sliding table equipped with a shear load cell for the measurement of the dynamic base shear force. The results are useful for optimising the geometric characteristics of the tank and the fluid mass in order to obtain enhanced energy dissipation performances by exploiting fluid–structure interaction effects.

Influence of aspect ratio and fill: Level on the thermal de-stratification in an upright cylindrical tank subjected to lateral sloshing motion

Influence of aspect ratio and fill: Level on the thermal de-stratification in an upright cylindrical tank subjected to lateral sloshing motion

H∞ Control Design for a Rigid-Flexible Spacecraft under a Fuel Slosh Influence

The spacecraft Attitude Control System (ACS) performance and robustness depend on the interactioneffects between the fuel slosh motion, the panel's flexible motion, and the spacecraft rigid motion, mainly duringtranslational and/or rotational maneuvers. In regards to satellite pointing accuracy flexibility and fuel, slosh is thetwo most important effects that should be considered in the satellite ACS design since their interactions can damage the ACS performance and robustness. Once, the lowest vibration frequencies, normally of the sloshing modeare about six times less than of the ACS bandwidth. Therefore, there is a strong possibility that this mode can destabilize the ACS pointing accuracy. This phenomenon is called spillover because the control effort spills over outside the control bandwidth. As a result, the designer needs to explore the limits between the conflicting requirements of performance, that is, increase of the bandwidth without introduction noise in the ACS keeping the systemrobustness to parameters variation. In this paper, one applies the H infinity control method which can deal withthese two design requirements (performance and robustness) considering the controller error pointing that may belimited by the minimum time necessary to suppress disturbances that affect the satellite attitude acquisition. Theequations of motions are obtained considering the Lagrange method for small flexible deformations and a mechanical model of liquid sloshing which allows modeling and investigating the longitudinal dynamic characteristics of apartially filled liquid tank during a pitch maneuver, satisfying performance and robustness requirements.

Coupling Effects of Sloshing and Barge Motion in Variable Bathymetry

Abstract Two partially filled tanks fixed on rectangular barge floating in variable bathymetry is studied based on the linearized potential theory in the frequency domain. The internal sloshing motion is simulated by linearized superposition of natural sloshing modes. The motion of barge is solved by matching eigenfunctions expansion in the external fluid domain. The computational model is verified by experimental results. Coupling sway and roll motions of floating body with different filling levels are compared. The effects of both inclined bottom with different slopes and hump-shaped bottom with different heights are analyzed. Viewing from the results, coupling sway and roll motions of floating body are significantly affected by the shapes of bottoms.

Analytical Study on the Effect of a Horizontal Perforated Plate on Sloshing Motion in a Rectangular Tank

Abstract Tank sloshing in a liquid cargo ship will cause instability or even overturning of its carrier if the external wave frequency is close to the natural frequency of the tank. The inherent damping of a tank without inner structures has been found to be insufficient for suppressing violent sloshing motion. A variety of damping plates have been designed to increase the inherent damping of the tank. Of them, a horizontal perforated plate (HPP) has been proved to be effective for dissipating energy in a swaying tank through experiments. In this study, the sloshing problem in a tank with an HPP under swaying and rolling excitation is analytically studied based on the potential theory. The quadratic pressure loss boundary at the perforated plate is adopted, and the matched eigenfunction expansion method (MEEM) with iterative calculations is used to develop the analytical model. Based on the different porosities and submerged depths of the plate, both the free surface elevations and the hydrodynamic coefficients are carefully examined. The results give a better understanding in the effect of the inner HPP on the sloshing motion in the ship tank.

Coupled Behavior of Sloshing and Ship Motion of an LNG Carrier with Prismatic Chamfered Tanks

Coupled Behavior of Sloshing and Ship Motion of an LNG Carrier with Prismatic Chamfered Tanks

Numerical study on structural response of anti-sloshing baffles of different configurations in a sloshing tank considering hydroelasticity

With the enlargement of liquid containers, unexpected deformation and damage of the containers might happen. As a commonly used way to suppress intense sloshing, anti-sloshing baffles usually sustain liquid loads with a large wetted area. Therefore, it is necessary to investigate the structural response of the anti-sloshing baffles taking hydroelasticity into account to guarantee the structural safety. This paper presents a numerical study on the structural response of horizontal and vertical baffles of different configurations in a sloshing tank considering hydroelasticity. Two validations on the effectiveness of the numerical methods and convergence tests are conducted. Influences of baffle height and length of the horizontal and vertical baffles on the structural response are examined through a series of simulations, from which amplitudes, frequencies of different vibration components and energy ratio of the wetted natural vibration caused by hydroelasticity are obtained and analyzed. Additionally, possible structural resonances of the horizontal and vertical baffles caused by the periodic sloshing motion and hydroelastic effects are shown, indicating the necessity of considering hydroelasticity. Meaningful conclusions are drawn on the characteristics of structural response, the effects of baffle configuration and the occurrence of structural resonance of the baffle from a structural safety point of view.

Numerical simulation of partially filled liquid containers with special type bottom geometry under earthquake excitation

Numerical simulation of liquid in partially filled tank of flat bottom and bottom box shape is investigated in the present paper. Previously, dynamic response of flat bottom tank has been carried out numerously, but the dynamic response of bottom box tank remains unclear. Therefor a parametric study on bottom box shape tank is carried out to understand the dynamic response of contained liquid under both harmonic excitation and real earthquake excitation. The efficacy of the present numerical model is verified by comparing the results with the published results. Galerkin’s finite element method is used to derive the modal equations of motion for sloshing. The slosh wave displacement, hydrodynamic pressure distribution and the base shear, are quantified for the bottom box shape tank. According to the dynamic analysis results larger size of bottom box significantly reduces the effective mass of liquid which keeps the container on safer side than the flat bottom container.

Numerical investigation of interfacial dynamics for the melt pool of Ti-6Al-4V powders under a selective laser

The complex evolution of a melt pool of Ti-6Al-4V powder particles under a moving selective laser was studied numerically. A laser power of 175 W and scanning speeds of 850, 1250, and 1650 mm/s were used. An effective laser source term with a time-varying maximum intensity was applied to a representative cross section to simplify the three-dimensional problem into a two-dimensional computational domain. The numerical results were validated using experimental observations. The effects of surface tension, Marangoni, and recoil forces on the interfacial morphology were investigated numerically.For a scanning speed of 1250 mm/s, the Marangoni effect initially begins to pull the interfacial melting flow from the laser focus region to the lateral powder. Meanwhile, the accumulated laser energy leads to evaporation, producing a corresponding recoil force. The transport phenomena caused by the Marangoni effect and the inward recoil force contribute to the local suppression of the melt pool. The Marangoni flow conveys the laser energy to the lateral powder, which significantly enhances the wetting phenomenon. In the next stage, the surface tension force gradually becomes dominant, eliminating the local suppression and concave curvature. The interfacial curvatures in this stage overshoot when they change signs. This tendency results in a periodic sloshing motion and oscillation of the melt pool.This study provides a thorough understanding of the wetting and morphology of the melt pool from a microscopic viewpoint, which could result in detailed design guidelines.