Slosh Loads Research Articles

Numerical studies on effects of slosh coupling on ship motions and derived slosh loads

This work presents development of a ship motion algorithm coupled with slosh loads and studies the effect of the coupling on both slosh loads and ship motions for different conditions. A hybrid approach by combining a potential flow based solution scheme for the external fluid flow and a viscous flow solver for the internal sloshing flow is adopted for the computation. The potential flow solution for the ship motion problem is achieved by using boundary element method (BEM) based on transient Green's function technique, while the viscous flow solution for the sloshing problem is achieved using finite volume method (FVM) based on viscous multiphase interface capturing volume of fluid (VoF) technique. Validation of the developed method is made against experiments and numerical computations available in literature. The severity of the coupling effect for various filling conditions is studied, and it is observed that coupling is more severe at low filling conditions resulting in a significant damping of roll RAO near the resonance and a shift in the peak. Damping in the roll response in turn results in a low sloshing loads. For a few filling conditions, however, the coupling effect produces higher roll response leading to higher slosh loads. Consideration of non-linearities in ship motions associated with Froude–Krylov and restoring forces, and the effect of sway-roll coupling in the ship motions on sloshing are studied and found that these aspects of ship motions can have non-negligible influence on the slosh loads. Long duration simulation studies reveal that there can be significant differences in the computed tank wall pressures between the coupled and uncoupled cases.

Novel Nonlinear Fuel Slosh Surrogate Reduced-Order Model for Aircraft Loads Prediction

Characterization of nonlinear slosh loads in aircraft remains a challenging problem. This work benchmarks a frozen fuel mass model against computational fluid dynamics data across a complete flight envelope. Thereafter, a novel surrogate reduced-order model aimed at improving on frozen fuel mass predictions is proposed. For a given tank geometry, the surrogate reduced-order model employs computational fluid dynamics simulations from which limit state slosh loads may be computed. These are calculated as a function of the mode of excitation (vertical or lateral), fill level, excitation frequency, and excitation amplitude. The resulting response surface is then described via a kriging interpolation-based surrogate reduced-order model. The surrogate is combined with a novel metric for the amplification factor (the ratio of the actual load to that induced by a frozen fuel mass) to predict the transient slosh-induced force due to arbitrary gust-type excitations. The latter is characterized as a priori in terms of acceleration amplitude and frequency via Fourier decomposition. It is demonstrated that the proposed surrogate reduced-order model improves the accuracy in predicting lateral slosh-induced loads by an average of 150% as compared to a frozen fuel mass model for a range of excitations, while being conservative.

FIELD TESTING AND VALIDATION OF DIRECTIONAL DYNAMICS MODEL OF A TANK TRUCK

A two–axle vehicle, equipped with a semi–transparent cylindrical tank, is fabricated and instrumented to determine the dynamics of sloshing cargo and its effects on directional response of the vehicle. The directional dynamics of a partially filled tank truck is investigated via computer simulation of a three–dimensional vehicle model incorporating a quasi–dynamic roll plane model of the tank. Field tests are performed for typical lane change and turning manoeuvres, and the corresponding directional response data are compared to the computer simulation results to validate the analytical model. The study concludes that the results obtained from the analytical vehicle model, incorporating quasi–dynamic fluid analysis, correlate well with the field measured data for different fill levels, vehicle speeds, and directional manoeuvres. Motion of the fluid–free surface and the corresponding lateral load transfer, attained via computer simulation, are further compared to those established from the field measured data to conclude that a quasi–dynamic analytical model can accurately predict the fluid slosh loads.

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.

Fluid-Structure Interaction Modelling of Internal Structures in a Sloshing Tank Subjected to Resonance

In this paper we develop a three-dimensional, fully coupled, partitioned-based fluid-structure interaction (FSI) model for liquid sloshing analysis in partially filled containers. Different tank geometries are considered in the present study focusing on both the rigid and flexible baffles and their influence on slosh loads at the tank walls. For the purpose of validation, we develop a stand-alone CFD model and compare the results with the previously existing numerical model and experimental data from the literature. Once such a validation is complete, we incorporate a rigid baffle like obstruction to study the effect of the baffle on sloshing using the stand alone CFD model. The numerical simulations predict that the influence of baffle like obstructions can help in mitigating the tank resonance. Using the standalone CFD model as a base, we develop a FSI model by incorporating the elastic-plastic material properties on the baffle to study the effect of a flexible baffle inside a sloshing tank. A comparative study between the force response of the rigid and flexible baffles during various slosh loads is examined by varying the amplitude of the tank excitation for the same fill level and frequency. The FSI model reveals details on slosh forces experienced by the baffle that are dampened owing to its flexibility. In addition to predicting the forces on the baffle, the FSI model also helps to predict the corresponding nodal displacements and stress states of the baffle under various slosh loads.

A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank

The liquid sloshing in a moving partially filled rectangular tank with a vertical baffle is investigated. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the nonlinear behavior of liquid sloshing. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of finite difference approximations with the moving coordinate system. The ratio of baffle height to the initial liquid depth has been changed in the range of 0≤ h B / h≤1.2. The critical baffle height to reach the roof of the tank and the baffle height beyond the liquid does not get over the baffle anymore have been investigated. The vortex originated by the flow separation from the baffle tip became weaker with increasing the baffle height. In order to assess the accuracy of the method used, some results with baffle height are compared with the experimental results. Comparisons show good agreement for slosh loads in the cases investigated. The free surface elevation and the time variations of pressures have been also presented.

Sloshing in a three-dimensional rectangular tank: Numerical simulation and experimental validation

Pressure variations and three-dimensional effects on liquid sloshing loads in a moving partially filled rectangular tank have been carried out numerically and experimentally. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the non-linear behavior and damping characteristics of liquid sloshing. A moving coordinate system is used to include the non-linearity and avoid the complex boundary conditions of moving walls. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of the finite difference approximations. In order to mitigate a series of discrete impacts, the signal computed is averaged over several time steps. In order to assess the accuracy of the method used, computations are compared with the experimental results. Several configurations of both baffled and unbaffled tanks are studied. Comparisons show good agreement for both impact and non- impact type slosh loads in the cases investigated.

Modeling and Simulation of Vehicles Carrying Liquid Cargo

A method for modeling and simulation of the dynamics ofvehicles subject to liquid slosh loads is presented. The vehiclecomponents are modeled as a multibody system, the sloshing liquiddynamics is determined from solving the instationary, incompressibleNavier–Stokes equations under consideration of free surfaces. Toanalyze the overall system dynamics, the concept of modular simulationis applied decomposing the dynamic system into subsystems. The rigidbody and fluid subsystems are modeled by separate software codes whichare coupled by the transfer of in- and output variables duringsimulation runtime.

Dynamics of Liquid Sloshing in Horizontal Cylindrical Road Containers

A study of the liquid behaviour in horizontal cylindrical road containers undergoing a steady turning manoeuvre is presented and discussed. The steady state solutions are derived analytically from the hydrostatic equations. The transient solutions are obtained by numerical integration of the Navier-Stokes, continuity and free-surface equations. The non-dimensional governing equations are solved in primitive variables by using a modified marker-and-cell technique which involves the interpolation-reflection type boundary conditions developed for this investigation. The mathematical model of the liquid motion includes all essential non-linear effects and allows the damped natural frequencies of liquid vibrations to be obtained as well as the magnitudes of the liquid slosh loads. This study also enables the coupled directional dynamics of the ‘vehicle-liquid tank’ system undergoing different road manoeuvres to be investigated by integrating the non-linear fluid slosh model and an appropriate vehicle model simultaneously.

Impact of Dynamic Fluid Slosh Loads on the Directional Response of Tank Vehicles

SUMMARY A comprehensive directional dynamics model of a tractor-tank trailer is developed by integrating a non-linear dynamic fluid slosh model to the three-dimensional vehicle dynamics model. The nonlinear fluid slosh equations are solved in an Eulerian mesh to determine dynamic fluid slosh loads caused by the dynamic motion of the vehicle. The dynamic fluid slosh forces and moments are coupled with the vehicle dynamics model to study the directional response characteristics of tank vehicles. The directional response characteristics of partially filled tank vehicles employing dynamic slosh model are compared to those employing quasi-dynamic vehicle model, for steady as well as transient directional maneuvers. Simulation results reveal that during a steady steer maneuver, the dynamic fluid slosh loads introduce oscillatory directional response about a steady-state value calculated from the quasi-dynamic vehicle model. The directional response characteristics obtained using the quasi-dynamic and dynamic fluid slosh models during transient steer inputs show good correlation. Based on this study, it can be concluded that the quasi-dynamic model can predict the directional response characteristics of tank vehicles quite close to that evaluated using the comprehensive fluid slosh model.