Simulation Of Free Surface Flows Research Articles

Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM

The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) [1] for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.

Three‐dimensional free surface flow simulation of segregating dense suspensions

AbstractThis paper presents a 3D numerical solution algorithm for the simulation of free surface flows of dense suspensions including particle migration phenomena. Segregation of the solid phase in processes such as powder injection molding and molding of semi‐solid materials affects the rheology of the mixture and therefore the filling pattern. Segregation affects also the final properties and characteristics of such molded parts as a non‐uniform particles distribution leads to non‐uniform shrinkage, warpage and non‐uniform mechanical properties. In this paper, particle migration is modeled using the diffusion flux model of Phillips et al. (Phys. Fluids A 1992; 4:30–40) and is extended to address 3D mold filling problems. The solution algorithm is validated against flow problems for which experimental and numerical data are available: circular Couette flow, piston‐driven flow and sudden contraction–expansion flow. The particle migration model is then used to simulate mold filling problems in which the piston movement in the sleeve is known to induce particle migration before the material enters the cavity. An arbitrary Lagrangian–Eulerian (ALE) formulation is developed and combined to a level‐set front capturing method to simulate the piston movement and the evolution of the free surface in molding simulations. The ALE formulation is first compared with an Eulerian solution for the case of the piston‐driven flow problem. The approach is then applied to injection molding problems to study the evolution of particle distributions during molding and in the final molded parts. Copyright © 2008 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.

Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monge-Ampère equation

The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge-Ampère equation. The results of numerical experiments will illustrate the capabilities of these methods.

Parasitic current generation in Combined Level Set and Volume of Fluid immiscible fluid simulations

The Continuum Surface Force technique is a popular tool used to implement surface tension forces in Eulerian based Computational Fluid Dynamics codes. Under this technique, inaccuracies present in calculating the surface tension force can manifest themselves as `parasitic' currents. We detail a new Combined Level Set and Volume of Fluid implementation of the Continuum Surface Force method. We then develop a correlation for the magnitude of parasitic currents that are generated under this new method, as a function of both the numerical and physical parameters employed in a simulation. A set of numerical experiments validate this correlation and show that, importantly, the magnitude of currents produced by the method decreases as the computational cell size reduced. References J. U. Brackbill, D. B. Kothe, and C. Zemach. A continuum method for modelling surface tension. Journal of Computational Physics, 100:335--354, 1992. Dalton J. E. Harvie, M. R. Davidson, and Murray Rudman. An analysis of parasitic current generation in volume of fluid simulations. Appl. Math Mod., 30(10):1056--1066, 2006. doi:10.1016/j.apm.2005.08.015 D. B. Kothe and R. C. Mjolsness. RIPPLE: A new model for incompressible flows with free surfaces. American Institue of Aeronautics and Astronautics, 30 (11):2694--2700, 1992. Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stephane Zaleski, and Gianluigi Zanetti. Modelling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics, 113:134--147, 1994. Murray Rudman. A volume-tracking method for incompressible multifluid flows with large density variations. International Journal for Numerical Methods in Fluids, 28:357--378, 1998. Ruben Scardovelli and Stepahe Zaleski. direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 31:567--603, 1999. J. A. Sethian and Peter Smereka. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics, 35:341--372, 2003. doi:10.1146/annurev.fluid.35.101101.161105 Mark Sussman. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics, 187:110--136, 2003. doi:10.1016/S0021-9991(03)00087-1 Mark Sussman and Elbridge Gerry Puckett. A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 162:301--337, 2000. doi:10.1006/jcph.2000.6537 Mark Sussman, Peter Smereka, and Stanley Osher. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114:146--159, 1994. S. P. van der Pijl, A. Segal, C. Vuik, and P. Wesseling. A mass-conserving level-set method for modelling of multi-phase flows. International Journal for Numerical Methods in Fluids, 47:339--361, 2005. doi:10.1002/fld.817

603 CIP-LSM法を用いた自由表面流解析の非構造格子系への拡張(OS2.CIP法とその関連手法(1),オーガナイズドセッション)

603 CIP-LSM法を用いた自由表面流解析の非構造格子系への拡張(OS2.CIP法とその関連手法(1),オーガナイズドセッション)

Free surface flow modelling on dynamically refined hexahedral meshes

An efficient method for modelling incompressible free surf ace flows is presented. The method unites the projection method for solving the Navier-Stokes equations and the particle level set method for free surface evolution. The method uses adaptively refined hexahedral meshes built on an enhanced octree data structure. Free surface flow simulation has increasingly attracted att ention of the scientific community. It has applications in diverse disciplines, suc h as geophysics, petroleum engineering, biology, etc. The method discussed in this paper is designed for appli- cations in computer graphics. It targets modelling, animating, and controlling vis- cous liquids in a 3D environment. The objectives of practical computer animation impose several partly controver- sial requirements on simulation. It should be efficient enou gh to run various scenar- ios for acceptable time. However, it should retain enough detail to give a realistic behaviour and the possibility of flow control. Direct numeri cal simulation provides the desirable realism, since it is based on accurate simulat ion of physical processes. However, it is computationally expensive and based on the assumption that after set- ting an initial state the fluid is left to flow freely. This appr oach reduces capabilities to control the flow locally and globally. A feasible compromi se between complex- ity, realistic behaviour, and flow control is provided by a co mputational technology which has been developed in the last decade by many researchers (1, 8, 14, 15, 18). In this paper we present our version of the numerical method forming such tech- nology. We do not address the issues of flow control here. We ju st note that this technology opens several possibilities to control the fluid flow (5). The general idea of the method is to use fractional steps in order to unite the projection method for solving the Navier-Stokes equations and the particle level set method for free surface evolution. The computational efficiency of the method is based on two points. First, the pressure projection method is one of the most efficient solvers for the unsteady Navier-Stokes equations (22). Second, the particle level set method is one of the most convenient and efficient approaches in simulation of free surface evolution (18). The framework of fractional steps allows us to combine both approaches and gives additional control over liquid motion.

Numerical solution of 3D free surface flows using implicit methods

AbstractThis work presents an implicit technique for simulating three‐dimensional unsteady low Reynolds number free surface flows of non‐Newtonian fluids. It is based on the Marker‐and‐Cell technique and it employs finite differences on a staggered grid. Validation results and the numerical simulation of complex free surface flows are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.

Numerical simulations of 3D free surface flows by a multilayer Saint‐Venant model

AbstractWe present a multilayer Saint‐Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of a Navier–Stokes system approximation deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint‐Venant‐type systems. The idea is to obtain an accurate description of the vertical profile of the horizontal velocity while preserving the robustness and the computational efficiency of the usual Saint‐Venant system.For each time‐dependent layer, a Saint‐Venant‐type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth.We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier–Stokes solver of the Telemac‐3D code developed by Electricité de France. Copyright © 2007 John Wiley & Sons, Ltd.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic–elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

Sea water desalination by reverse osmosis: the true needs for energy

Almost half the exploitation costs of sea water reverse osmosis plant is affected to the electricity costs. Therefore, it's crucial to control those, and firstly to evaluate it. Each case should be treated independently, since the need in electricity depends on different factors: sea water characteristics, values taken for RO sizing parameters, electromechanical components efficiency . and, last but not least, choice of the system for hydraulic energy recovery of the concentrate. Energy recovery devices are an important part of any sea water reverse osmosis system, and any future decrease in specific energy consumption is dependent upon the further development and improvement in the performance of such devices. Recent technological innovations, such as energy recovery turbine, are required to reduce and improve the energy consumption. One of the simplest methods to operate a sea water RO unit is to run the pump at constant speed, to obtain the required membrane feed pressure through a feed throttle valve, and to recover the remaining brine energy via a Pelton turbine. Increasing hydraulic performances of Pelton turbines requires the optimisation of all components, taking into account their coupling. Until now the development of Pelton turbines has relied almost entirely on experimental and empirical knowledge and has not benefited from numerical flow simulation. This is mainly due to the fact that until now CFD simulations of free surface flows have not been fully validated and were impractical in an industrial environment, mainly due to the large computing time and resources that are needed. The numerical codes are still under development and, as with all CFD methods, have to be evaluated and validated before they can be used as standard tools in design. The highly successful use of CFD in Francis and Kaplan turbines has brought benefits of improved performance, more rapid and less risky design processes, large reduction in the need for empirical methods and reduced need for model and prototype tests. It is natural that these modern sophisticated design tools should now be adapted for use in Pelton turbines.

Modification of Surface Capturing Method Using WENO Scheme

The present study restructured a surface capturing method using the optimized WENO scheme for numerical simulations of free surface flows in order to decrease influences of numerical diffusion upon interfaces. Main modifications are as follows. The weight function in the optimized WENO scheme was modified in consideration of interface gradient. A compression parameter in the artificial compression method was modified to avoid over-compression in smooth regions and reduction of numerical accuracy. The method correcting the numerical flux on cell faces was restructured in order to suppress occurrence of non-physical volume fractions. The present surface capturing method was applied to two convective problems. Numerical diffusions are very low around discontinuous regions, and the present method can capture interfaces more sharply than the previous one proposed by the authors. The present method has good conservation property at the time of interface transport as well as the previous surface tracking methods and surface capturing methods. There-fore, the calculation accuracy was greatly improved.

APPLICABILITY OF MPS METHOD TO BREAKING AND POST-BREAKING OF SOLITARY WAVES

As a meshfree particlemethod, the MPS (Moving Particle Semi-implicit) method is an efficient numerical tool for simulating flowswith complicated behavior of water surface, such aswave breaking. In this paper, the MPS method hasbeen applied to solve the Navier-Stokes equation for simulating the breaking and post-breaking of solitary waves on a uniform slope. The high precision of MPS method in the simulation of violent free surface flows, likethebreaking waves, isconfirmed through both quantitative and qualitative comparisons to other numerical results by the BEM or the VOF and experimental data. The process of splashup which ishard to be simulated by conventionalgrid-based methods is alsowell reproduced by the MPS method.

1002 フリーラグランジュ法による粘性自由表面流れの数値解析(OS10.メッシュフリー/粒子法とその関連技術(1))

Free-Lagrange method has been combined with the free-mesh FEM and applied to the numerical simulation of viscous free surface flows. The nodes distributed over the fluid region are regarded as fluid particles and moved in a Lagrangian manner every time step. In this paper, we report a new numerical technique for calculating the interaction between the fluid and rigid walls. The proposed method has been applied to the broken-dam problem in a bounded region in which flowing liquid strikes a rigid vertical wall and run up along it. Encouraging numerical results have been obtained.

Numerical Simulation of Liquid Metal Free-surface Flows in the Presence of a Uniform Static Magnetic Field

Three-dimensional numerical simulations with a new-developed modeling of two-phase flow have been carried out for free-surface flows of an electric conducting fluid in the presence of a uniform static magnetic field. In this study, several examples such as collapsing liquid column, oscillating droplet in a non-gravitational field and falling droplet in a gravitational field are presented. The driving mechanisms of the flow in these problems are the gravity and the surface tension. The numerical results reveal that the induced electromagnetic force acts to dampen the electric conducting fluid flow efficiently when a uniform vertical magnetic field is applied while it acts to enforce a tendency of two-dimensional flow when a uniform horizontal magnetic field is applied.

A time-splitting method on a nonstaggered grid in curvilinear coordinates for implicit simulation of non-hydrostatic free-surface flows

The numerical solution of flows with a freely moving boundary is of great importance in practical application such as ship hydrodynamics. Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady and steady free-surface flows on a nonstaggered grid in curvilinear coordinates, using a non-hydrostatic pressure distribution. In this model, Reynolds equation and the kinematic free-surface boundary condition are solved simultaneously, so that the water-surface elevation can be integrated into the solution and solved for, together with the velocity and pressure field. In computational space, the Cartesian velocity components and the pressure are defined at the center of a control volume, while the volume fluxes are defined at the midpoint on their corresponding cell faces. Detailed numerical results are presented for the wave generation above an obstacle and resonant motion standing wave. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.Key words: free-surface simulation, nonstaggered grid, time-splitting method, unsteady flow, turbulent flow.

Three-Dimensional Simulation of Free-Surface Flows Using Polyhedral Finite Volumes

The issue of mesh quality has become a topic of increasing interest among scientists and professionals working in the field of computational fluid dynamics, as it has a major impact on model performance. Here we introduce a mesh generation method that is based on a Voronoi decomposition of the flow domain, resulting in polygonal regions in 2D and polyhedral cells in 3D. The discretised Reynolds equations for arbitrary cells are derived using a fmite volume approach and the required boundary conditions are discussed. Both the grid generation process and a solver for the turbulent flow equations have been implemented in the simulation model RSim-3D. The model has been applied to several test cases and the results have been satisfactory. Polyhedral cells have the potential to delivering more accurate results under certain flow conditions than hexahedral cell types.

On the application of the single-phase level set method to naval hydrodynamic flows

The application of the single-phase level set approach to the numerical simulations of three-dimensional free surface flows around complex geometries, at both non-breaking and breaking regimes is presented. In this approach only the liquid phase is simulated and the level set function is used as tracking device to locate the free surface position. The extrapolation of the solution in the dummy points in the gaseous phase is such that second-order accuracy is maintained also in the points adjacent to the free surface; the time evolution of the level set function and the re-initialization step have been merged so to get a function which is a distance function everywhere, and satisfies, at the same time, the kinematic condition on the free surface. The implementation of this technique into a general purpose Reynolds averaged Navier–Stokes (RANS) equations solver developed at INSEAN [Di Mascio A, Broglia R, Favini B. A Second Order Godunov-type Scheme for Naval Hydrodynamics. Kluwer Academic/Plenum Publishers; 2001, p. 253–61], is described in details; capabilities of the algorithm in dealing with non-breaking and breaking flows in the naval hydrodynamic context will be demonstrated by using a submerged hydrofoil and two different ship hulls in straight course as test cases. Comparisons with both experimental data and numerical surface fitting computations are presented; convergence properties of the algorithm, as well as validation and verification assessment will be also discussed.

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

The smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows. The basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH. In particular, a drop of an Oldroyd-B fluid impacting a rigid plate is simulated. Results for a Newtonian fluid are also presented for comparison. It is found that the original SPH method, which has been successfully applied to the simulation of transient viscoelastic flows in bounded domains (such as the start-up flow between parallel plates), is unable to simulate the viscoelastic free surface flow considered here because of the so-called tensile instability. This instability leads to unrealistic fracture and particle clustering in fluid stretching and may eventually result in complete blowup of the simulation. Recent works have shown that in simulations of elastic solids the tensile instability can be removed by an artificial stress. Here we show that the same idea also works for viscoelastic fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. Numerical results obtained are in good agreement with those simulated by a finite difference technique.

Numerical simulation of liquid/gas phase flow during mold filling

A numerical model for simulation of liquid/gas phase flow during mold filling is presented. The incompressible Navier–Stokes equations are discretized on a fixed Cartesian mesh with finite difference method. The fractional-step scheme is employed for enforcing incompressibility constraint. The free surface effects are calculated using the volume of fluid method based on the piecewise-linear interface reconstruction and split Lagrangian advection of volume fraction field. Adding limited compressibility to the gas phase led to improvement in convergence rate of Poisson equation solver (about 2-fold). This new concept permits simulation of two-phase incompressible free surface flow during mold filling, without using outflow boundary condition. Numerical results are presented for several test cases, which demonstrate validity, capability and performance of the proposed method in contrast with the traditional (fully incompressible) approach.