Three-dimensional Free Surface Flows Modeled by Lattice Boltzmann Method : A Comparison with Experimental Data

Free surface fluctuations in the continuous casting mold were simulated using the three-dimensional Lattice Boltzmann method (LBM) coupled with free surface scheme. The LBM model was verified by the agreement between the calculated results and the measurements. The results indicated that free surface fluctuations at both sides of the mold were asymmetrical. Operation parameters of continuous caster played an essential role in the fluctuations of free surface. The distributions of free surface fluctuations were also quantified. The peak and trough fluctuations on both sides of the mold alternated thereon, accompanied by the stochastic formation of the vortices at the top mold. The simulation results suggest that the LBM models can offer a promising way to study free surface behaviour and related phenomena in a continuous casting mold.

In this paper we will present an algorithm to perform free surface flow simulations with the lattice Boltzmann method on adaptive grids. This reduces the required computational time by more than a factor of three for simulations with large volumes of fluid. To achieve this, the simulation of large fluid regions is performed with coarser grid resolutions. We have developed a set of rules to dynamically adapt the coarse regions to the movement of the free surface, while ensuring the consistency of all grids. Furthermore, the free surface treatment is combined with a Smagorinsky turbulence model and a technique for adaptive time steps to ensure stable simulations. The method is validated by comparing the position of the free surface with an uncoarsened simulation. It yields speedup factors of up to 3.85 for a simulation with a resolution of 4803 cells and three coarser grid levels, and thus enables efficient and stable simulations of free surface flows, e.g. for highly detailed physically based animations of fluids.

Nonlinear solutions of free surface flow under a sluice gate are studied. Upstream, the fluid is assumed to be infinitely deep, and the gate is at an angle to the horizontal axis. The flow emerges from the gate and produces a uniform flow far downstream. The problem is solved numerically by a boundary element method derived from an integral equation along the free surface. An analytical function is constructed, related to the upstream flow, so that the integral equation is solvable. As a result, a free surface flow with smooth detachment from the edge of the gate is obtained for relatively large upstream Froude numbers. As the Froude number decreases, a free surface with back flow near the edge of the gate occurs, until at a certain Froude number a stagnation point occurs. References D. D. Frangmeier, T. S. Strelkoff, Solution for gravity flow under a sluice gate, ASCE J. Engng. Mech. Div. , 94 , 1968, 153--176. B. E. Lorock, Gravity-affected flow from planer sluice gate, ASCE J. Engng. Mech. Div. , 96 , 1969, 1211--1226. Y. K. Chung, Solution of flow under sluice gates, ASCE J. Engng. Mech. Div. , 98 , 1972, 121--140. J. Asavanant, J.-M. Vanden-Broeck, Nonlinear free surface flows emerging from vessels and flows under a sluice gate, J. Austral. Math. Soc. , 38 , 1996, 63--86. doi:10.1017/S0334270000000473 J.-M. Vanden-Broeck, Numerical calculations of the free-surface flow under a sluice gate, J. Fluid Mech. , 330 , 1996, 339--347. http://journals.cambridge.org/abstract_S0022112096003849 B. J. Binder, J.-M. Vanden-Broeck, Free surface flows past surfboards and sluice gates, Eur. J. Appl. Maths. , 16 , 2005, 601--619 doi:10.1017/S0956792505006443 B. J. Binder, J.-M. Vanden-Broeck, The effect of disturbances on the flows under a sluice gate and past an inclined plate, J. Fluid Mech. , 576 , 2007, 475--490 doi:10.1017/S0022112007004806 J.-M. Vanden-Broeck, E. O. Tuck, Flow near the interaction of a free surface with a vertical wall, SIAM J. Appl. Math. , 54 , 1994, 1--33. doi:10.1137/S0036139992240838 L. H. Wiryanto, J. Widjaja, B. Supriyanto, Free-surface flow under a sluice gate from deep water, Bul. Malay. Math. Soc. , 34 , 2011, 601--609. http://www.emis.de/journals/BMMSS/vol34_3_17.html L. H. Wiryanto, E. O. Tuck, A back-turning jet formed by a uniform shallow stream hitting a vertical wall, Proc. Int. Conf. on Dif. Eqs. , Kluwer Academic Press, 1997. L. H. Wiryanto, E. O. Tuck, An open-channel flow meeting a barrier and forming one or two jets, J. Austral. Math. Soc. , 41 , 2000, 458--472. doi:10.1017/S0334270000011760 L. H. Wiryanto, Small Froude number solutions of flow caused by a line source, J. Indones. Math. Soc. , 6 , 2000, 1--6. G. C. Hocking, L. K. Forbes, A note on the flow induced by a line sink beneath a free surface, J. Austral. Math. Soc. B , 32 , 1991, 251--260. doi:10.1017/S0956792507006924 G. C. Hocking, L. K. Forbes, Subcritical free-surface flow caused by a line source in a fluid of finite depth, J. Eng. Math. , 26 , 1992, 455--466. doi:10.1007/BF00042763 L. H. Wiryanto, Zero gravity of a jet emerging from a slit, J. Indones. Math. Soc. , 12 , 2006, 89--98. L. M. Milne-Thomson, Theoretical hydrodynamics . Dover Publications, Inc., 1968, 274--281.

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

Advances of the in-house developed SWLBM framework in simulating large-scale three-dimensional violent free surface flow with intense splashing

Towards non-intrusive reduced order 3D free surface flow modelling

Motivated by the current lack of knowledge regarding phase transition in a free surface water flow, a novel and efficient numerical model for liquid-solid phase transition in a free surface flow has been developed for the Lattice Boltzmann Method (LBM). The proposed model consists of two physically sound modules for solving free surface flow and heat transport. The heat transport module features an immersed boundary method and a non-iterative enthalpy-based approach. Sub-cycling time integration, improving the numerical stability of the heat transport module, is introduced for the integration of modules. The performance and accuracy of the model are verified through a preliminary experiment involving a melting ice cube. The obtained results indicate that the phase transition of fluid in any flow regime can be easily handled by the model with reasonable accuracy.

The Lattice Boltzmann Method (LBM) which is derivative of the lattice gas automata (LGA) has recently studied as a numerical scheme for simulating fluid flows governed by the Navier-Stokes equation. The LBM is a discrete numerical method based on the Boltzmann equation. The dynamics of the LBM is divided into a propagation step and a collision step. We have proposed a model for weakly ionized plasma by introducing diffusion as a velocity to LBM. In our LBM model, ionization, recombination at the wall and ambipolar diffusion are considered. This model uses 2D9V (2 dimensions, 9 velocities) model and BGK collision operator. We have simulated various shape of discharge tubes by this model. MATLAB is suitable for matrix calculation and has a command for shifting matrix which is important in LBM. By this work, it is shown that our model simulates weakly ionized plasma well.

Open-channel flows are very common and important flows occurring in both natural and artificial watercourses such as rivers, canals and drainages, and irrigation and navigation channels. Correct prediction and simulation of the flows play a crucial role in channel design, river management and flood control. In theory, the flows can be efficiently and accurately described by the shallow-water equations in most cases. In fact, the solution to these equations has turned out to be a very successful tool to model different free-surface flows such as tides, tsunami, dam breaks, dyke breaks, bores and broken waves. Although there are many numerical methods available for solving the shallow-water equations (e.g. the finite-element method), they are often complicated and computationally demanding. Over the last decade, the lattice Boltzmann method (LBM) has been developed as a very attractive numerical method in computational fluid dynamics. The method is extremely simple and efficient with its very easy treatment of boundary conditions and natural parallel processing, and is suitable for complex flows within complicated geometries. Consequently, the LBM has been developed for shallow-water equations with or without turbulence modelling (LABSWETM and LABSWE, respectively). This paper presents both methods and their application to typical open-channel flows. The results demonstrate the power, potential, applicability and accuracy of the LBM in simulations of many open-channel flows and also indicate that the method needs to be improved for some open-channel flow problems.

In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical \ntool for simulating complex fluid flows and modeling physics and chemistry in \nfluids. Derived from the continuum Boltzmann equation used in statistical \nmechanics, the LB method has the advantage of describing non-equilibrium dynamics, \nespecially in fluid-flow applications involving interfacial dynamics and complex \nboundaries, without simplifying the physics. In addition, the parallel structure \ninherent in the LB method makes it extremely suitable for parallel computing. \nBecause of these features, the LB method affords the most comprehensive pore-scale \napproach to systematically investigate fundamental issues involving flow and \nreactive transport in porous media. In this paper, the state of the art of this \nmethod is discussed. Specifically, a multi-component LB model for simulating \nreactive transport in porous media at the pore scale is presented. In the model, a \nset of distribution functions is introduced to simulate fluid flow and solute \ntransport. The LB equation for flow recovers the correct pore-scale continuity and \nNavier-Stokes equations. The LB equations for solute transport are modified to \nrecover advection-diffusion equations for total concentrations at the pore scale. \nThe model takes into account advection, diffusion, homogeneous reactions among \nmultiple aqueous species, heterogeneous reactions between the aqueous solution and \nminerals, as well as changes in solid and pore geometry. Homogeneous reactions are \ndescribed through local equilibrium mass action relations. Mineral reactions are \ntreated kinetically through boundary conditions at the mineral surface. Simulation \nexamples presented include injection of carbon dioxide saturated brine into a \nlimestone rock with pore geometry derived from a thin section, crystal formation \nfrom a supersaturated solution without flow, and crystal formation during carbon \ndioxide sequestration in oceanic sediments.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

Purpose – Lattice Boltzmann method (LBM) is employed to explore friction factor of single-phase fluid flow through porous media and the effects of local porous structure including geometry of grains in porous media and specific surface of porous media on two-phase flow dynamic behavior, phase distribution and relative permeability. The paper aims to discuss this issue. Design/methodology/approach – The 3D single-phase LBM model and the 2D multi-component multi-phase Shan-Chen LBM model (S-C model) are developed for fluid flow through porous media. For the solid site, the bounce back scheme is used with non-slip boundary condition. Findings – The predicted friction factor for single-phase fluid flow agrees well with experimental data and the well-known correlation. Compared with porous media with square grains, the two-phase fluids in porous media with circle grains are more connected and continuous, and consequently the relative permeability is higher. As for the factor of specific porous media surface, the relative permeability of wetting fluids varies a little in two systems with different specific surface areas. In addition, the relative permeability of non-wetting fluid decreases with the increasing of specific surface of porous media due to the large flow resistance. Originality/value – Fluid-fluid interaction and fluid-solid interaction in the SC LBM model are presented, and schemes to obtain immiscible two-phase flow and different contact angles are discussed. Two-off mechanisms acting on the wetting fluids is proposed to illustrate the relative permeability of wetting fluids varies a little in two systems with different specific surface.

The problem is a free-surface flow of a fluid, emerging from a semi-infinite container. The fluid is assumed to be inviscid, incompressible and the flow to be two dimensional and irrotational. When surface tension is neglected the free surface leaves the wall of the container tangentially. We show that when surface tension is taken into account, there is, in general, a train of waves on the free surface and a discontinuity in slope where the free surface separates from the wall of the container. These new solutions include, as particular cases, previously obtained solutions for which the free surface is waveless in the far field. Although the calculations are presented for a special flow configuration, the results are general and apply to other potential free surface flows where a free-surface intersects a rigid wall.

A numerical method for solving three‐dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENSMAC, the full Navier–Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user‐friendly input data file is employed to allow almost any arbitrary three‐dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented. Copyright © 2001 John Wiley & Sons, Ltd.

Application of lattice Boltzmann method in free surface flow simulation of micro injection molding