Computational Evaluation of Stability in Slosh Dynamics of Tank Vehicles Using Zero Moment Point

2019 ◽  
Author(s):  
M. Usman ◽  
M. Sajid
Keyword(s):  
Free Surface ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Computational Effort ◽  
Surface Boundary ◽  
Zero Moment Point ◽  
Liquid Domain ◽  
Computational Evaluation ◽  
Zero Moment ◽  
Tank Vehicles

Abstract Sloshing characterized by inertial waves has an adverse effect on the directional dynamics and safety of partially filled tank vehicles, limiting their stability and controllability during steering, accelerating or braking maneuvers. A mathematical description of the transient fluid slosh in a horizontal cylindrical tank should consider the simultaneous lateral, vertical and roll excitations assuming potential flows and a linearized free-surface boundary condition. While the determination of vehicle stability would require coupling this model to a dynamic roll plane model of a tank vehicle resulting in a computationally expensive analysis. Considering the need for a simpler method to predict roll stability for partially filled tank vehicles, we explore the Zero Moment Point of a liquid domain as a novel solution to this challenge. Numerical investigations are carried out in a three-dimensional partially filled tanks while tracking the movement of the liquid-air interface by employing the volume of fluid method in OpenFOAM. The center of Mass and Zero Moment Point were calculated from the computational results using analytical expressions. The movement of free surface is found to be in good agreement with available literature. The center of mass of the liquid domain was traced as a practical means to quantify the slosh in the tanker. The analyses are performed for different fluid fill heights at varying speeds. The results suggest that the roll stability of tank vehicles can be efficiently analyzed using the zero moment point with significantly lower computational effort.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength panels on the exact submerged body surface, the boundary integral equations are solved numerically at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceed until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared with the experiments for both linear computations and body-exact computations.

scholarly journals Investigation of Zero Moment Point in a Partially Filled Liquid Vessel Subjected to Roll Motion

2020 ◽  
Vol 10 (11) ◽  
pp. 3992
Author(s):  
Muhammad Usman ◽  
Muhammad Sajid ◽  
Emad Uddin ◽  
Yasar Ayaz
Keyword(s):  
Autonomous Vehicles ◽  
Center Of Mass ◽  
Flow Analysis ◽  
Liquid Interface ◽  
Liquid Region ◽  
Time Step ◽  
Two Phase ◽  
Zero Moment Point ◽  
Zero Moment ◽  
Air Liquid Interface

Liquid-handling robots are designed to dispense sub-microliter quantities of fluids for applications including laboratory tests. When larger amounts of liquids are involved, sloshing must be considered as a parameter affecting stability, which is of significance for autonomous vehicles. The measurement and quantification of slosh in enclosed volumes poses a challenge to researchers who have traditionally resorted to tracking the air–liquid interface for two-phase flow analysis. There is a need for a simpler method to predict rollover in these applications. In this work, a novel solution to address this problem is proposed in the form of the Zero Moment Point (ZMP) of a dynamic liquid region. Computational experiments of a partially filled, two-dimensional liquid vessel were carried out using the Volume of Fluid (VOF) method in a finite volume based open-source computational fluid dynamics solver. The movement of the air–liquid interface was tracked, while the Center of Mass and the resulting Zero Moment Point were determined from the numerical simulations at each time step. The computational model was validated by comparing the wall pressure and movement of the liquid-free surface to experimentally obtained values. It was concluded that for a dynamic liquid domain, the Zero Moment Point can be instrumental in determining the stability of partially filled containers subjected to sloshing.

Five Years of Numerical Naval Ship Hydrodynamics at DTNSRDC

1981 ◽  
Vol 25 (04) ◽  
pp. 219-235
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Numerical Methods ◽  
Initial Period ◽  
Three Dimensional ◽  
Hydrodynamic Performance ◽  
Ship Motions ◽  
Surface Boundary ◽  
Local Flow ◽  
Ship Hydrodynamics ◽  
Naval Ship

In 1974 the Numerical Naval Ship Hydrodynamics Program was established at the David W. Taylor Naval Ship Research and Development Center. The objective of the program is to develop new numerical methods which can be used to evaluate those hydrodynamic performance characteristics which cannot be satisfactorily predicted by traditional methods. In this paper, the accomplishments during the first five-year period (1974–1979) are discussed. During this initial period, the effort was devoted entirely to naval ship free-surface problems. Several successful methods have been developed for solving fully three-dimensional ship-motions, ship-wave-resistance and local-flow problems using linearized free-surface boundary conditions. Numerical methods have also been developed for unsteady and steady two-dimensional problems where the exact free-surface conditions are satisfied. These new numerical methods are more accurate than the conventional computational methods and they can be used to analyze several naval free-surface problems which previously could only be investigated experimentally. It is concluded that the Numerical Naval Ship Hydrodynamics Program should include consideration of all areas in naval ship hydrodynamics where it is believed that the application of advanced numerical techniques and computers can result in better solution techniques.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

Numerical Study of Forward-Speed Ship Motion and Added Resistance

2017 ◽  
Author(s):  
D. C. Hong ◽  
T. B. Ha ◽  
K. H. Song
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Results ◽  
Surface Boundary ◽  
Forward Speed ◽  
Added Resistance ◽  
Following Seas

The added resistance of a ship was calculated using Maruo’s formula [1] involving the three-dimensional Kochin function obtained using the source and normal doublet distribution over the wetted surface of the ship. The density of the doublet distribution was obtained as the solution of the three-dimensional frequency-domain forward-speed Green integral equation containing the exact line integral along the waterline. Numerical results of the Wigley ship models II and III in head seas, obtained by making use of the inner-collocation 9-node second-order boundary element method have been compared with the experimental results reported by Journée [2]. The forward-speed hydrodynamic coefficients of the Wigley models have shown no irregular-frequencylike behavior. The steady disturbance potential due to the constant forward speed of the ship has also been calculated using the Green integral equation associated with the steady forward-speed free-surface Green function since the so-called mj-terms [3] appearing in the body boundary conditions contain the first and second derivatives of the steady potential over the wetted surface of the ship. However, the free-surface boundary condition was kept linear in the present study. The added resistances of the Wigley II and III models in head seas obtained using Maruo’s formula showing acceptable comparison with experimental results, have been presented. The added resistances in following seas obtained using Maruo’s formula have also been presented.

scholarly journals Numerical Study of Violent Impact Flow Using a CIP-Based Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qiao-ling Ji ◽  
Xi-zeng Zhao ◽  
Sheng Dong
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Large Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Small Scale ◽  
Surface Boundary ◽  
Two Phase ◽  
Constrained Interpolation

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

scholarly journals Numerical model of energy dissipation and shallow-water sloshing motions in tank under different coupled excitations

2021 ◽  
Author(s):  
Yan Su
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Numerical Model ◽  
Shallow Water ◽  
Three Dimensional ◽  
Wave Crest ◽  
Surface Boundary ◽  
Transient Wave ◽  
Irregular Free Surface ◽  
Free Surface Oscillations

AbstractShallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.

scholarly journals LARGE-WAVE SIMULATION OF TURBULENT FLOW INDUCED BY WAVE PROPAGATION AND BREAKING OVER CONSTANT SLOPE BED

2012 ◽  
Vol 1 (33) ◽  
pp. 65
Author(s):  
Gerasimos Kolokythas ◽  
Aggelos Dimakopoulos ◽  
Athanassios Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Wave Breaking ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Large Wave ◽  
Wave Simulation ◽  
Constant Slope ◽  
Good Agreement

In the present study, the three-dimensional, incompressible, turbulent, free-surface flow, developing by the propagation of nonlinear breaking waves over a rigid bed of constant slope, is numerically simulated. The main objective is to investigate the process of spilling wave breaking and the characteristics of the developing undertow current employing the large-wave simulation (LWS) method. According to LWS methodology, large velocity and free-surface scales are fully resolved, and subgrid scales are treated by an eddy viscosity model, similar to large-eddy simulation (LES) methodology. The simulations are based on the numerical solution of the unsteady, three-dimensional, Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow boundary conditions. The case of incoming second-order Stokes waves, normal to the shore, with wavelength to inflow depth ratio λ/dΙ = 6.6, wave steepness H/λ = 0.025, bed slope tanβ = 1/35 and Reynolds number (based on inflow water depth) Red = 250,000 is investigated. The predictions of the LWS model for the incipient wave breaking parameters - breaking depth and height - are in very good agreement with published experimental measurements. Profiles of the time-averaged horizontal velocity in the surf zone are also in good agreement with the corresponding measured ones, verifying the ability of the model to capture adequately the undertow current.

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