Slosh Forces Research Articles

Modeling Torsional Stiffness and Damping of Liquid Slosh in Spacecraft Diaphragm Tanks

This study presents a pendulum-based empirical model of liquid slosh in spacecraft diaphragm tanks. Diaphragm torsional stiffness and effective damping are predicted within a range of lateral excitation frequency typical of launch or on-orbit operations. A pendulum-analog model with two primary slosh modes is extracted from diaphragm tank slosh data corresponding to steady-state triaxial force measurements at the support points of the tank under sinusoidal excitation. The approach leads to repeatable and accurate determination of pendulum model parameters. A gradient-based algorithm and a procedure for setting initial conditions for optimal parameter estimation are proposed to predict the liquid slosh forces and torques acting on the tank as frequency response functions of apparent mass and apparent mass moment. The pendulum models were assessed by comparing model-predicted force/torques with measurements, showing good agreement (1–5% prediction error in the time domain) under most test conditions (fill level, excitation amplitude, and frequency). An empirical model of the stiffness and damping is also proposed for the tested range of operational conditions. Because of the nonlinear nature of liquid slosh behavior in a diaphragm tank, both the stiffness and damping are local values for a given set of test conditions.

Coupling analysis of liquid sloshing and box sway motion under irregular wave actions

The coupling effect between the internal fluid sloshing and the box sway motion under irregular wave action is studied in this work. For describing external wave and internal sloshing actions, a hybrid numerical method combining linear potential flow and viscous flow is adopted. Numerical simulations show that coupling sloshing action plays an important role around sloshing natural frequencies. The significant resistant and enhanced actions can be observed at the frequencies around sloshing natural frequencies in regular waves. However, the above coupling effect approaches weak under irregular wave actions. The phase relation between the internal sloshing forces and external wave forces in regular waves cannot be found under irregular wave actions, which is the main reason for the decreased coupling sloshing effect. In all, the sway motion responses between irregular and regular wave actions show evident different behaviors from each other.

Effect of liquid sloshing in lateral and longitudinal directions on railway tank cars based on an improved equivalent model

Additional slosh forces and moments are generated owing to the movement of the liquid inside a partly filled tank car. The loads may have a great influence on the structure reliability and dynamic performance of the vehicle. An improved equivalent model of liquid sloshing is put forward to obtain the forces and moments of sloshing liquid acting on the tank during the lateral and longitudinal sloshing processes. An improved method is proposed to obtain the equivalent masses and stiffness for the improved equivalent model. The equivalent model is integrated into the multi-body dynamic model of a railway tank car with 68 degrees of freedom. Furthermore, the equivalent liquid-vehicle model is used to investigate the effects of fluid sloshing on dynamic characteristics. The influence of the filling ratio on the dynamic response of the tank car is discussed based on the forces and the corresponding moments between the tank car body and the liquid in different layers. The railway tank car is obviously influenced by the liquid sloshing during passing the curved and sloped tracks. The influence of liquid sloshing on the pitching motion of the tank is heavy if the tank is about half filled. The derailment coefficient and the wheel unloading rate are slightly influenced by the filling ratio of tank cars on curved tracks while the indices of the tank cars on sloped tracks are the greatest if the filling ratio is 40%.

Hydrodynamics Analysis on Liquid Bulk Transportation with Different Driving Cycle Conditions

Liquid bulk transport is one of the most important modes of fluid package transport, whether by sea or land. Flexitank has recently attracted the attention of shipment companies as an alternative method of fluid transportation due to the benefits of cost effectiveness, large shipping capacity, environmental friendliness, and quick loading/unloading time. However, the industry reports some cases regarding the leakage of the flexitank during transportation. While the hydrodynamic behaviour of the flexitank during transportation may influence the tank surface leakage issue. Thus, this study aims to determine the suitable filling volume capacity on flexitank by using Computational Fluid Dynamics (CFD). Hydrodynamics performance such as wall shear stress, volume fraction, dynamic pressure, and slosh force will be analyzed on different filling volume capacities and driving cycles. The filling volume capacity analyzed in this study are 5%, 10%, 15% more, or less than the reference capacity, 24000 L, based on different driving cycles: city-suburban and freeway. The results indicate that varying the fill level capacity of the tank affected the liquid sloshing behaviour and hydrodynamic performance of the tank. The highest wall shear stress (WSS) occurs at a filling volume capacity of -15 % because it is increasing the wall shear stress by 80% (city-suburban) and 35% (freeway) than the reference value. Following that, both speed profiles with a +10 % filling volume have the dynamic pressure, reducing it by 60% (city-suburban) and 47% (freeway) compared to the reference value. Thus, the filling volume of +10% is recommended to be suitable for the flexitank. Hence, this study benefits liquid bulk transportation by increasing fill level capacity and optimizing hydrodynamic performance.

Nonlinear Multimodal Model for Tuned Sloshing Dampers With Nonflat Bottoms

Abstract A third-order nonlinear multimodal model is developed for tanks with nonflat bottoms. A six-node finite element model is used to determine the mode shapes of the velocity potential and the associated natural sloshing frequencies. Using this modal information, equations of motion are developed that accommodate the nonlinear coupling among the first three sloshing modes. Damping arising from screens is incorporated into the model using the principle of virtual work. The equations of motion are ordinary differential equations that are solved using the Runge–Kutta–Gill numerical time-stepping method. The model is evaluated with an existing third-order nonlinear multimodal model for a flat-bottom tank and is found to be in excellent agreement. Demonstrative simulations are conducted for tanks with sloped-, boxed-, and ramped-bottoms. The resulting sloshing forces and wave heights at the tank end wall are calculated and presented using time series plots and frequency response plots. The excitation of higher-order sloshing modes through modal coupling results in larger wave heights, and shallower wave troughs. The sloshing forces are less impacted by the responses of higher modes. Secondary resonances are clearly visible in several frequency response plots at frequencies that correspond to the natural sloshing frequency of a higher-order mode divided by an integer. The model is applicable to tanks that are of intermediate water depth with moderate excitation amplitudes, where the response of the second- and third-order sloshing modes are less than the fundamental mode.

Computational study of sloshing in spherical tanks and the effect of using annular baffle over slosh force frequency and damping

Computational study of sloshing in spherical tanks and the effect of using annular baffle over slosh force frequency and damping

Computational study of sloshing in spherical tanks and the effect of using annular baffle over slosh force frequency and damping

Computational study of sloshing in spherical tanks and the effect of using annular baffle over slosh force frequency and damping

Numerical and experimental analysis of the effect of elastic membrane on liquid sloshing in partially filled tank vehicles

A numerical analysis for fluid-membrane interaction is conducted to investigate fluid slosh within a partially filled horizontal cylindrical tank with an elastic membrane restraining the free surface. The fluid-membrane interaction analysis is performed to investigate the effect of membrane on liquid slosh responses in terms of liquid load shifts, slosh forces, moments and slosh frequency. A series of experiments were conducted on a scaled horizontal cylindrical tank with an elastic membrane-like restraint under harmonic acceleration excitations in longitudinal or lateral direction. The validity of the numerical model is demonstrated using the laboratory-measured data. The validated model is subsequently formulated for a full scale tank and analysis are performed under excitations idealizing the straight-line braking or turning maneuvers to investigate the antislosh effectiveness of membrane. It is shown that the addition of membrane can yield substantial reduction in slosh amplitude and thus the pitch and roll moment; the slosh frequency can be substantially shifted to higher values to avoid resonance in partly filled tanks.

A linearized reduced-order model approach for sloshing to be used for aerospace design

This paper proposes Reduced-Order Models (ROMs) based on data provided by Computational Fluid Dynamics (CFD) simulations for generally flexible tanks to be embedded in a larger aerospace structure. A commercial off-the-shelf CFD code addressed to sloshing analyses is employed to generate data set to be used for the synthesis of the sloshing system ROM. The developed sloshing ROM, based on a Linearized Frequency Domain (LFD) approach, makes use of an Input/Output system identification technique from CFD transient simulations to construct an unsteady Generalized Sloshing Force (GSF) transfer function (or frequency response function) matrix. This is done in analogy with the Generalized Aerodynamic Force (GAF) matrix used to model the aircraft unsteady aerodynamics for linearized aeroelastic analyses. The obtained GSF frequency response function data are suitably fitted via a rational polynomial form in the frequency domain so achieving a state-space representation for the sloshing system. Although the formulation is applicable for any 3D tanks of arbitrary shape, a parallelepiped tank is used as benchmark in order to compare the obtained GSF frequency response matrix with that available in the literature for simple tank geometries. The prediction capability of such method is also assessed by comparing the sloshing forces provided by the ROM and those obtained via direct CFD simulations even using unsteady boundary motions different than those used for ROM identification. The obtained linearized ROM of flexible tank with sloshing fluid seems suitable for aerospace applications for perspective integrated stability and response analyses and design of the aircraft/spacecraft structures.

Coupling analysis for sway motion box with internal liquid sloshing under wave actions

This work investigates the coupling effects of internal sloshing flow on the sway motion response of rectangular box sections. The impulse-response-function method is employed for external wave action, while the viscous two-phase flow model with the volume of fluid interface capturing technique based on the OpenFOAM® package is adopted for the internal sloshing flow. A new lower critical frequency is defined to understand the coupling effects of the internal sloshing flow, which is the corresponding frequency of the minimal sway motion amplitude. The external wave and internal sloshing forces are out-of-phase at the lower critical frequency. The numerical simulations show that the lower critical frequency is equivalent to the sloshing natural frequency when the internal sloshing flow is in the non-breaking pattern. The non-breaking sloshing-induced force approaches the same magnitude as the external wave force, which leads to a zero-amplitude sway motion. When the internal sloshing exhibits the breaking phenomenon, a phase transition of the internal sloshing force can occur, which causes the lower critical frequency to be smaller than the sloshing natural frequency. The increased incident wave amplitude or decreased tank breadth can strengthen the nonlinear behavior of the sloshing coupling action. That is, the sway motion response deviates more from the linear sloshing flow results, including the smaller lower critical frequency and the larger minimal sway motion amplitude. However, with the increased breaking-sloshing-induced nonlinearity, the difference in the sway motion response between the coupling and uncoupling results reduces, which implies a lower coupling effect.

Experimental Investigation of Spherical Tank Slosh Dynamics with Water and Liquid Nitrogen

Understanding, predicting, and controlling fluid slosh dynamics is critical to safety and improving the performance of liquid propulsion systems for space missions. Computational fluid dynamics simulations can be used to predict the dynamics of slosh. Experimental and numerical studies of water slosh have been conducted; however, cryogenic slosh data relevant for validating computational fluid dynamics are lacking. This paper presents the results of slosh experiments with a spherical tank without and with a ring baffle using both water and liquid nitrogen. The experiments were designed to measure forces from continuous excitation over a relevant range of frequencies and amplitudes, natural frequency, and damping parameters. Analytical models and empirical correlations for slosh damping are constructed and compared to the experimental results. An established analytical model for slosh forces is compared to the experimental results for verification purposes. Experiments with a ring baffle installed show increased damping and attenuation of maximum slosh forces. To provide the greatest utility of these data for future rocket and spacecraft missions, the results are presented in a fully nondimensional framework.

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

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

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

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

Simulation analysis of liquid sloshing under different working conditions of hazardous materials rescue truck

The geometric model is built with SOLIDWORKS, and the VOF(Volume Of Fluid) method in the CFD(Computational Fluid Dynamics) software fluent is used to simulate the sloshing characteristics during the brake and steering of the Hazardous Materials Rescue Truck. The braking acceleration, the liquid filling ratio of the vehicle, lateral acceleration, the effect of the baffle during braking and steering are respectively studied. The results show that the steering and braking of Hazardous Materials Rescue Trucks will cause the liquid in the tank to slosh, and the liquid sloshing will cause the wall slosh force of the tank to change. The driving stability of Hazardous Materials Rescue Trucks can be effectively improved by the reduction of braking force, proper liquid-filling ratio, reduction of lateral acceleration, and increase of baffles.

Investigation of coupled dynamics of a railway tank car and liquid cargo subject to a switch-passing maneuver

The movement of the liquid cargo within a partly filled tank car is known to impose additional slosh forces and moments that may adversely affect the dynamic responses of the vehicle. This study is aimed at analyzing the liquid cargo slosh in a partly filled tank car and its effects on vehicle responses during a switch-passing maneuver. A two-dimensional analytical liquid slosh model is formulated for the analyses of the liquid load shift in the roll plane, lateral slosh force, and roll moment through summation of first four antisymmetric modes of the liquid. The analytical slosh model is integrated to a 114 degrees-of-freedom multibody dynamic model of the railway tank car comprising nonlinear wheel–rail contact and contact pairs of the suspension system. The validity of the slosh model is illustrated by comparing the responses with those reported in other studies and those obtained from a nonlinear computational fluid dynamic model. The coupled fluid–vehicle model is subsequently used to study the effects of fluid slosh during switch-passing maneuvers on different response measures, namely roll motion of the tank car, lateral and vertical wheel–rail contact forces, and derailment ratio. The significance of the liquid cargo slosh in the partially filled state is demonstrated by comparing the responses with those of the car with equivalent rigid cargo. The results show that liquid sloshing within the partly filled car can lead to higher magnitudes of car body roll angle and thereby the unloading ratio compared to the conventional rigid cargo car. Switch-passing critical speeds are further identified for different fill ratios and switch geometries. For fill ratios below 80%, the switch-passing critical speeds of the partly filled car are substantially lower compared to those of the equivalent rigid cargo car. Neglecting the contributions due to dynamic slosh force and roll moment arising from a partially filled railway tank car may thus lead to underestimation of the critical speed in switch-passing maneuvers.

Sloshing-Coupled Ship Motion Algorithm for Estimation of Slosh-Induced Pressures

The effect of coupling between sloshing and ship motions in the evaluation of slosh-induced interior pressures is studied. The coupling between sloshing loads and ship motions is modelled through a hybrid algorithm which combines a potential flow solution based on transient Green function for the external ship hydrodynamics with a viscous flow solution based on a multiphase interface capturing volume of fluid (VOF) technique for the interior sloshing motion. The coupled algorithm accounts for full nonlinear slosh forces while the external forces on the hull are determined through a blended scheme of linear radiation-diffraction with nonlinear Froude-Krylov and restoring forces. Consideration of this level of nonlinearities in ship motions is found to have non-negligible effects on the slosh-coupled responses and slosh-induced loads. A scheme is devised to evaluate the statistical measure of the pressures through long-duration simulation studies in extreme irregular waves. It is found that coupling significantly influences the tank interior pressures, and the differences in the pressures between coupled and uncoupled cases can be as much as 100% or more. To determine the RAO over the frequency range needed for the simulation studies in irregular waves, two alternative schemes are proposed, both of which require far less computational time compared to the conventional method of finding RAO at each frequency, and the merits of these are discussed.

Propellant Slosh Force and Mass Measurement

We have used electrical capacitance tomography (ECT) to instrument a demonstration tank containing kerosene and have successfully demonstrated that ECT can, in real time, (i) measure propellant mass to better than 1% of total in a range of gravity fields, (ii) image propellant distribution, and (iii) accurately track propellant centre of mass (CoM). We have shown that the ability to track CoM enables the determination of slosh forces, and we argue that this will result in disruptive changes in a propellant tank design and use in a spacecraft. Ground testing together with real-time slosh force data will allow an improved tank design to minimize and mitigate slosh forces, while at the same time keeping the tank mass to a minimum. Fully instrumented Smart Tanks will be able to provide force vector inputs to a spacecraft inertial navigation system; this in turn will (i) eliminate or reduce navigational errors, (ii) reduce wait time for uncertain slosh settling, since actual slosh forces will be known, and (iii) simplify slosh control hardware, hence reducing overall mass. ECT may be well suited to space borne liquid measurement applications. Measurements are independent of and unaffected by orientation or levels of g. The electronics and sensor arrays can be low in mass, and critically, the technique does not dissipate heat into the propellant, which makes it intrinsically safe and suitable for cryogenic liquids. Because of the limitations of operating in earth-bound gravity, it has not been possible to check the exact numerical accuracy of the slosh force acting on the vessel. We are therefore in the process of undertaking a further project to (i) build a prototype integrated “Smart Tank for Space”, (ii) undertake slosh tests in zero or microgravity, (iii) develop the system for commercial ground testing, and (iv) qualify ECT for use in space.

Numerical simulation of parametric liquid sloshing in a horizontally baffled rectangular container

Liquid sloshing is a problem of serious concern in partially filled tanks. Tank designers must ensure safe margins and develop methodologies to overcome a wide range of plausible situations related to transport, wind, earthquake loads etc. to assess the structural stability. In the present study, numerical simulations are carried out to investigate the sloshing dynamics of a partially filled rectangular container, subjected to vertical harmonic as well as seismic excitations. Unlike horizontal excitation, participation of higher modes is of prime concern in vertical (parametric) excitations. The present study numerically simulates and explores methodologies to control the slosh forces and free surface oscillations with the help of a baffle. Detailed numerical validations are carried out against other experimental and computational studies from the literature. Sloshing dynamics under imposed vertical harmonic excitations was investigated at its first and third modes. Based on a detailed study of transient wave profiles, force and pressure time histories, optimal baffle design was achieved. Optimal position of the baffle and its width are systematically obtained with reference to the quiescent free surface. The effectiveness of this baffle was tested against the well known Bhuj earthquake in India.

Coupled multimodal fluid-vehicle model for analysis of anti-slosh effectiveness of longitudinal baffles in a partially-filled tank vehicle

An efficient model is formulated for analysis of a coupled fluid slosh-vehicle dynamic system to study the effects of different baffle designs on directional dynamic performance of a partially-filled tank vehicle. A multimodal model of fluid sloshing within a baffled cylindrical tank is initially formulated using potential flow equations and linearized free-surface boundary condition considering maneuver-induced vehicle motions along the lateral, vertical and roll axes. Natural slosh modes/frequencies, hydrodynamic coefficients and Stokes-Joukowski potential associated with the multimodal model are then obtained by solving the eigenvalue problem of free fluid sloshing using a higher order boundary element 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 half free-surface length using the zoning method. The hydrodynamic force and moment obtained from the multimodal model are subsequently coupled with the TruckSim vehicle dynamic simulation platform through a MATLAB/Simulink model to obtain dynamic responses of a partially-filled tank vehicle with and without baffles under step-turn and double-lane change maneuvers. Two different designs of longitudinal baffles are considered: bottom- and top-mounted baffles. The validity and efficiency of the present boundary element method is demonstrated by comparing the results with those obtained using the boundary element method employing linear elements. The effective mass moment of inertial of the fluid in a clean-bore tank is also obtained as a function of fill ratio and compared with the reported analytical solutions for a half-full tank to further verify the model. The results suggest that directional dynamic responses of partly-filled tank vehicles can be efficiently analyzed using the coupled multimodal slosh-vehicle models with significantly lower computational effort than the methods employing computational fluid dynamic (CFD) fluid slosh models. The results further reveal that top-mounted baffles are most effective in suppressing the fluid slosh force under more likely loading conditions in road tankers.

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.