CFD Simulations of Non-Linear Sloshing in a Rotating Rectangular Tank Using the Level Set Method

2016 ◽  
Author(s):  
Erlend Liavåg Grotle ◽  
Hans Bihs ◽  
Eilif Pedersen ◽  
Vilmar Æsøy
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Time Evolution ◽  
Level Set Method ◽  
Level Set ◽  
Turbulence Energy ◽  
Limiting Factor ◽  
Surface Time ◽  
Non Linear ◽  
Multiple Grids

In this paper, numerical simulations of non-linear sloshing in rectangular tanks are presented. Model implementations in the open source software REEF3D are tested and results compared with experimental data. Three different conditions are compared with experiments in 2D. First, the free surface time-evolution is compared for both linear and non-linear sloshing. In the last case, video images from the SPHERIC project are compared with simulations images of the free surface. A condition with lateral wave impacts in sloshing, with a frequency closer to the natural frequency of the first mode, can be found in this case. The non-linear sloshing, case 2, is also simulated in 3D. The numerical model is solving the RANS equations with the k-ω turbulence model. The level set method is used to capture the interface. Higher order discretization schemes are implemented to handle time-evolution and convective fluxes. A ghost cell method is used to account for solid boundaries and multiple grids for parallel computations. It is found that the limiting factor for the eddy-viscosity has significant influence in case 2 and 3. As the sloshing becomes more violent, the increased strain at the gas-liquid interface overproduces turbulence energy with unrealistically high damping of the motion. 3D simulations are only performed in case 2, which shows slightly better comparison than with 2D. Due to non-linearities and small damping, the time to reach steady-state may take several cycles, but no information is given in the paper [1]. The last case shows promising results for the global motion. As expected, the break up of the liquid surface makes it difficult to resolve each phase. But overall, the numerical model predicts the sloshing motion reasonably well.

Computational Fluid Dynamics Simulations of Nonlinear Sloshing in a Rotating Rectangular Tank Using the Level Set Method

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Erlend Liavåg Grotle ◽  
Hans Bihs ◽  
Vilmar Æsøy ◽  
Eilif Pedersen
Keyword(s):  
Numerical Model ◽  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Turbulence Energy ◽  
Limiting Factor ◽  
Nonlinear Sloshing ◽  
Interface Location ◽  
Dynamics Simulations

In this paper, numerical simulations of nonlinear sloshing in rectangular tanks are presented. Model implementations in the open source software reef3d are tested, and the results are compared with experimental data from three different conditions. The interface location is compared for both linear and nonlinear sloshing. The nonlinear sloshing is simulated in both two-dimensional (2D) and three-dimensional (3D). Video images from the SPHERIC project are compared with simulations for the interface. A condition with lateral wave impacts in sloshing, with a frequency close to the natural frequency of the first mode, can be found in this case. The numerical model is solving the Reynolds-averaged Navier–Stokes (RANS) equations with the k–ω turbulence model. The level set method is used to capture the interface. Higher order discretization schemes are implemented to handle time-evolution and convective fluxes. A ghost cell method is used to account for solid boundaries and parallel computations. It is found that the limiting factor for the eddy-viscosity has significant influence in the nonlinear sloshing cases. As the sloshing becomes more violent, the increased strain at the gas–liquid interface overproduces turbulence energy with unrealistically high damping of the motion. Three-dimensional simulations show slightly better comparison than 2D. Due to nonlinearities and small damping, the time to reach steady-state may take several cycles. The last case shows promising results for the global motion. As expected, the breakup of the liquid surface makes it difficult to resolve each phase. But overall, the numerical model predicts the sloshing motion reasonably well.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

scholarly journals Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

2014 ◽  
Vol 6 (2) ◽  
pp. 1523-1554 ◽  
Author(s):  
B. Hillebrand ◽  
C. Thieulot ◽  
T. Geenen ◽  
A. P. van den Berg ◽  
W. Spakman
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Material Flow ◽  
Flow Modeling ◽  
Material Interfaces ◽  
Level Set Function ◽  
Geophysical Processes ◽  
Rayleigh Taylor Instability ◽  
Set Function

Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface and on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as a Rayleigh–Taylor instability, post glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

Simulation of Wave-Body Interaction Using a Single-Phase Level Set Function in the SWENSE Method

2013 ◽  
Author(s):  
Gabriel Reliquet ◽  
Aurélien Drouet ◽  
Pierre-Emmanuel Guillerm ◽  
Erwan Jacquin ◽  
Lionel Gentaz ◽  
...  
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Single Phase ◽  
Stokes Equations ◽  
Flow Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Level Set Function ◽  
Set Function

The purpose of this paper is to present combination of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations – [1]) method — an original method to treat fully nonlinear wave-body interactions — and a free surface RANSE (Reynolds Averaged Navier-Stokes Equations) solver using a single-phase Level Set method to capture the interface. The idea is to be able to simulate wave-body interactions under viscous flow theory with strong deformations of the interface (wave breaking in the vicinity of the body, green water on ship decks…), while keeping the advantages of the SWENSE scheme. The SWENSE approach is based on a physical decomposition by combining incident waves described by a nonlinear spectral scheme based on potential flow theory and an adapted Navier-Stokes solver where only the diffracted part of the flow is solved, incident flow parameters seen as forcing terms. In the single-phase Level Set method [2, 3], the air phase is neglected. Thus, only the liquid phase is solved considering a fluid with uniform properties. The location of the free surface is determined by a Level Set function initialised as the signed distance. The accuracy of simulation depends essentially on the pressure scheme used to impose free surface dynamic boundary condition. Comparisons of numerical results with experimental and numerical data for US navy combatant DTMB 5415 in calm water and in head waves are presented.

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