Waves Simulation in an Excited Cylindrical Tank Using σ-Transformation

2010 ◽  
Author(s):  
M. Eswaran ◽  
Ujjwal K. Saha
Keyword(s):  
Free Surface ◽  
Excitation Frequency ◽  
Time History ◽  
Breaking Waves ◽  
Liquid Sloshing ◽  
Practical Significance ◽  
Road Transportation ◽  
Viscous Effects ◽  
Liquid Free Surface ◽  
Small Depth

Free surface motions of the liquid in partially filled tanks under gravity are of practical significance particularly in marine and road transportation applications. For this reason, liquid sloshing has always been a research subject attracting great concern during the last several decades. Numerical experiments of sloshing wave motion are undertaken in a 2-D tank which is moved horizontally. Results of liquid sloshing induced by sinusoidal base excitations are presented for small to steep non-breaking waves. The numerical model is valid for any water depth except for small depth when viscous effects would become important. Solutions are limited to steep non-overturning waves. In this paper, the semi-circular domain with time-varying fluid surface was mapped onto a rectangular domain by the σ-transformation. Based on the inviscid flow equations, a fully non-linear finite difference model has been developed. The simulations are limited to a half-filled container. The liquid free surface elevation and wave phase-plane diagram have been plotted for different tank excitation frequency. It has been observed that while increasing the tank frequency, the liquid wave height in the tank changes according to the system natural frequency. Finally, the proposed computational scheme has been applied to a real engineering problem to capture the irregular behavior of liquid free surface inside the tank. For this, acceleration-time history of EW and NS components of the EL-Centro earthquake, California has been studied and analyzed.

Low Steeping Waves Simulation in a Vertical Excited Container Using σ Transformation

2009 ◽  
Author(s):  
M. Eswaran ◽  
U. K. Saha
Keyword(s):  
Free Surface ◽  
Structural Integrity ◽  
Breaking Waves ◽  
Rectangular Domain ◽  
Practical Significance ◽  
Computational Domain ◽  
Road Transportation ◽  
Central Difference ◽  
Flow Equations ◽  
Vertical Excitation

A fluid partially occupying a moving tank undergoes wave motions (sloshing). These motions generate severe hydrodynamic loads that can be dangerous for structural integrity and stability of rockets, satellites, LNG ships, trucks and even stationary petroleum containers. Free surface motions of the liquid in partially filled tanks under gravity are of practical significance particularly in marine and road transportation applications. For this reason, liquid sloshing has always been a research subject attracting great concern during the last several decades. In this paper, a fully non-linear finite difference model has been developed based on the inviscid flow equations, and a simple mapping function was used to remove the time-dependence of the free surface in the fluid domain. The time-varying fluid surface can be mapped onto a rectangular domain by the σ-transformation. This method is a simple way to simulate non-breaking waves quickly and accurately especially that has a low steepness. The fluid motion is solved in a unit square mesh in the transformed flow domain (i.e., computational domain). The fourth order central difference scheme and the Gauss–Seidel point successive over-relaxation iterative procedure are used to capture the free surface wave profiles and the free surface elevation plots of the fluid domain. Difference between the peaks and troughs of waves are discussed for the case of vertical excitation of first three natural frequency of the tank. Phase-plane diagrams are drawn to show the non-linearity of the motion of time dependent free surface. The results agree well with the previously published results.

Random Excitation of a Structure Interacting With Liquid Sloshing Dynamics

2002 ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim
Keyword(s):  
Free Surface ◽  
Natural Frequency ◽  
Internal Resonance ◽  
Gaussian White Noise ◽  
Liquid Sloshing ◽  
Elastic Structure ◽  
Center Frequency ◽  
System Response ◽  
Liquid Free Surface ◽  
Sloshing Dynamics

The nonlinear random interaction of an elastic structure with liquid sloshing dynamics in a cylindrical tank is investigated in the neighborhood of 1:2 internal resonance. Such internal resonance takes place when the natural frequency of the elastic structure is close to twice the natural frequency of the antisymmetric sloshing mode (1,1). The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. The analytical model involves three sloshing modes; (1,1), (0,1) and (2,1). The system response statistics and stability boundaries are numerically estimated using Monte Carlo simulation. The influence of the excitation center frequency, its bandwidth, and the liquid level on the system responses is studied. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. As the liquid depth decreases, the region of nonlinear interaction shrinks which is associated with a shift of the peak of the structure mean square response toward the left side of the frequency axis.

Modal Analysis of Transient Liquid Sloshing in Partially-Filled Tanks

2014 ◽  
Vol 526 ◽  
pp. 127-132 ◽  
Author(s):  
Xue Lian Zheng ◽  
Xian Sheng Li ◽  
Yuan Yuan Ren ◽  
Zhu Qing Cheng
Keyword(s):  
Fourier Transform ◽  
Free Surface ◽  
Time Domain ◽  
Periodic Oscillation ◽  
Liquid Sloshing ◽  
First Order ◽  
Liquid Free Surface ◽  
Fluent Simulation ◽  
Fill Level ◽  
The Time Domain

To investigate the dynamic characteristics of liquid sloshing in partially-filled tanks, FLUENT simulation for liquid sloshing in cylinder tanks with the 40% liquid fill level and subject to lateral accelerations of 0.1 g-0.4 g were carried out. By the observation of transient sloshing force and the liquid free surface, it was found that the liquid sloshing is a periodic oscillation. Fourier transform was utilized to transform the sloshing forces in the time domain to the signals in the frequency domain. By spectrum analysis, it was found that the first-order oscillation that has the biggest amplitude is the most important one for liquid sloshing. For further command on liquid sloshing, modal shapes for the first sixth modal were acquired by ANSYS. It is drawn that the odd modals have anti-symmetrical shapes and the first-order oscillation makes the biggest contribution on liquid sloshing, the even modals have symmetrical shapes and could not contribute to liquid sloshing.

Experimental and Numerical Study on Liquid Sloshing Dynamics with Single Vertical Porous Baffle in a Sway Excited Ship Tank

2020 ◽  
Author(s):  
Sahaj k v ◽  
Nasar Thuvanismail
Keyword(s):  
Free Surface ◽  
Boundary Element ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Boundary Element Methods ◽  
Liquid Sloshing ◽  
Shake Table ◽  
Natural Period ◽  
Rectangular Tank ◽  
Porous Screen

<p>Liquid motion in partially filled tanks may cause large structural loads if the period of tank motion is close to the natural period of fluid inside the tank. This phenomenon is called sloshing. Sloshing means any motion of a free liquid surface inside a container. The effect of severe sloshing motion on global seagoing vessels is an important factor in safety design of such containers. In order to examine the sloshing effects, a shake table experiments were conducted for different water fill depth of aspect ratio 0.163, 0.325 and 0.488. The parametric studies were carried out to show the liquid sloshing effects in terms of slosh frequencies, maximum free surface elevation and hydrodynamic forces acting on the tank wall. Sloshing oscillation for the excitation frequency f<sub>1</sub>, f<sub>2</sub>, f<sub>3</sub>, f<sub>4 </sub>and f<sub>5</sub> are observed and analysed. The excitation frequencies is varied between 0.4566 Hz to 1.9757 Hz and constant amplitudes of 7.5mm was adopted. The movement of fluid in a rectangular tank has been studied using experimental approach and different baffle configurations were adopted for analysing the sloshing oscillation, natural frequencies and variation in wave deflection. The adopted porosities in the present study is 15% – 25 %. Porous screen is placed inside the tank at L/2 location and study is extended for single porous screen for better wave energy absorption. Capacitance wave probes have been placed at tank ends to record the free surface water elevation. Load cells are used to measure the sloshing force inside the tank. Linear variable displacement transducers is used to measure the displacement of shake table. In the present study single porous screen under the action of wave were analysed to understand the wave control performance due to porosity parameters. A boundary element model is developed to calculate problems of wave interaction with a porous screen structure. The numerical results from the present boundary element methods (BEM) are compared with series of experiments conducted in a rectangular tank with various baffle porosities and submerged depths.</p><p> </p>

FLOW VISUALIZATION AT THE LIQUID FREE SURFACE

1993 ◽  
Vol 1 (3) ◽  
pp. 181-188
Author(s):  
M. D. Cazacu
Keyword(s):  
Free Surface ◽  
Flow Visualization ◽  
Liquid Free Surface

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Numerical Analysis of the Tapping Atomic Force Microscopy on a Viscoelastic Sample

2014 ◽  
Author(s):  
Ben Carmichael ◽  
Gary Frey ◽  
S. Nima Mahmoodi
Keyword(s):  
Numerical Analysis ◽  
Time History ◽  
Equation Of Motion ◽  
Viscous Effects ◽  
Force Microscopy ◽  
Forcing Function ◽  
Atomic Force ◽  
Cantilevered Beam ◽  
Soft Samples ◽  
The Galerkin Method

Mechanical characterization of thin samples is now routine due to the prominence of the Atomic Force Microscope. Advances in amplitude modulation techniques have allowed for accurate measurement of a sample’s elastic properties by interpreting the changes in the vibration of a cantilevered beam in intermittent contact. However, the nonlinearities associated with contact complicate attempts to find an accurate time-history for the beam. Furthermore, the inclusion of viscous effects, common to soft samples, puts an explicit solution even farther from reach. A numerical method is proposed that analyzes the time-history and frequency response of a microcantilever beam with a viscoelastic end-condition. The mathematics can be simplified by incorporating the viscoelastic end-condition into the equation of motion directly by modeling it as a distributed load. A forcing function can then be derived from the Standard Linear Solid model of viscoelasticity and implemented in the non-conservative work term of Hamilton’s principle. The Galerkin method can separate the resulting nonlinear equation of motion into time and space components. Performing a numerical analysis of the time factor equation provide the beam’s response over time. The results demonstrate the distinctive effects of viscoelasticity and periodic contact on the beam’s motion and provide the framework for the determination of viscous properties using dynamic techniques.

scholarly journals Dynamic Behavior of Liquid Free Surface in a Cylindrical Container Subject to Vertical Vibration

1984 ◽  
Vol 27 (227) ◽  
pp. 923-930 ◽  
Author(s):  
Hiroyuki HASHIMOTO ◽  
Seiichi SUDO
Keyword(s):  
Free Surface ◽  
Dynamic Behavior ◽  
Vertical Vibration ◽  
Cylindrical Container ◽  
Liquid Free Surface

Profilometry of a liquid-free surface with large slope variations

1997 ◽  
Vol 36 (13) ◽  
pp. 2905
Author(s):  
Luis P. Thomas ◽  
Roberto Gratton ◽  
Beatriz M. Marino
Keyword(s):  
Free Surface ◽  
Liquid Free Surface

Advanced CFD Simulations of free-surface flows around modern sailing yachts using a newly developed openFOAM solver

2016 ◽  
Author(s):  
Janek Meyer ◽  
Hannes Renzsch ◽  
Kai Graf ◽  
Thomas Slawig
Keyword(s):  
Free Surface ◽  
Large Scale ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Body Motion ◽  
Computational Time ◽  
Efficient Computation ◽  
Surface Flows ◽  
Scale Free ◽  
Wide Range

While plain vanilla OpenFOAM has strong capabilities with regards to quite a few typical CFD-tasks, some problems actually require additional bespoke solvers and numerics for efficient computation of high-quality results. One of the fields requiring these additions is the computation of large-scale free-surface flows as found e.g. in naval architecture. This holds especially for the flow around typical modern yacht hulls, often planing, sometimes with surface-piercing appendages. Particular challenges include, but are not limited to, breaking waves, sharpness of interface, numerical ventilation (aka streaking) and a wide range of flow phenomenon scales. A new OF-based application including newly implemented discretization schemes, gradient computation and rigid body motion computation is described. In the following the new code will be validated against published experimental data; the effect on accuracy, computational time and solver stability will be shown by comparison to standard OF-solvers (interFoam / interDyMFoam) and Star CCM+. The code’s capabilities to simulate complex “real-world” flows are shown on a well-known racing yacht design.

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