Lattice Boltzmann

Chen S and Doolen G D 1998 Lattice Boltzmann method for fluid flows Ann. Rev. Fluid Meoh. 30 329-64... 

Theissen O, Gompper G and Kroll D M 1998 Lattice-Boltzmann model of amphiphilic systems Euro. Phys. Lett. 42 419... 

Langevin simulations of time-dependent Ginzburg-Landau models have also been performed to study other dynamical aspects of amphiphilic systems [223,224]. An attractive alternative approach is that of the Lattice-Boltzmann models, which take proper account of the hydrodynamics of the system. They have been used recently to study quenches from a disordered phase in a lamellar phase [225,226]. 

Another numerical study of free-surface flow patterns in narrow channels was conducted by Yang et al. [185]. They considered the flow of bubbles of different size driven by body forces, for example the rising of bubbles in a narrow capillary due to buoyancy. The lattice Boltzmann method [186] was used as a numerical scheme... 

M. D. Mantle, A. J. Sederman, L. F. Gladden 2001, (Single- and two-phase flow in fixed-bed reactors MRI flow visualisation and lattice-Boltzmann simulations), Chem. Eng. Sci. 56, 523. 

B. Manz, L. F. Gladden, P. B. Warren 1999, (Flow and dispersion in porous media Lattice-Boltzmann and NMR studies), AIChE J. 45, 1845. 

S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon Press, New York, 2001. 

J. M. Yeomans, Mesoscale simulations lattice Boltzmann and particle algorithms, PhysicaA 369, 159 (2006). 

Note that the lubrication effect due to particle collisions in liquid is significant. The liquid layer dynamics pertaining to the lubrication effect was examined by Zenit and Hunt (1999). Zhang et al. (1999) used a Lattice-Boltzmann (LB) simulation to account for a close-range particle collision effect and developed a correction factor for the drag force for close-range collisions, or the lubrication effect. Such a term has been incorporated in a 2-D simulation based on the VOF method (Li et al., 1999). Equation (36) does not consider the lubrication effect. Clearly, this is a crude assumption. However, in the three-phase flow simulation, this study is intended to simulate only the dilute solids suspension condition (ep = 0.42-3.4%) with the bubble flow time of less than 1 s starting when bubbles are introduced to the solids suspension at a prescribed ep. 

A. From Lattice-Gas to Lattice-Boltzmann 1. Lattice-Gas Models... 

In the paper by Hill et al. (2001b), values for A2 are only given for a finite number of gas fractions1 however, A2 is nearly the same as A0 (Koch and Hill, 2001). Note that in Section II.D we suggest a different expression for /i, also on the basis of lattice Boltzmann simulations. 

Beetstra, R., van der Hoef, M. A., and Kuipers, J. A. M. Drag force from lattice Boltzmann simulations of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres, Manuscript submitted to AIChE J. (2006). 

The emphasis in this chapter is on the fruitful application of Large Eddy Simulations for reproducing the local and transient flow conditions in which these processes are carried out and on which their performance depends. In addition, examples are given of using Direct Numerical Simulations of flow and transport phenomena in small periodic boxes with the view to find out about relevant details of the local processes. Finally, substantial attention is paid throughout this chapter to the attractiveness and success of exploiting lattice-Boltzmann techniques for the more advanced CFD approaches. 

Numerical scheme Finite volume (FLUENT) Lattice-Boltzmann... 

Lattice-Boltzmann is an inherently time-dependent approach. Using LB for steady flows, however, and letting the flow develop in time from some starting condition toward a steady-state is not a very good idea, since the LB time steps need to be small (compared to, e.g., FV time steps) in order to meet the incompressibility constraint. 

Lattice-Boltzmann exhibits some inherent properties that favor the speed of the simulations, and therefore make the method a serious candidate and... 

Derksen, J. J., Kooman, J. L., and Van den Akker, H. E. A., Parallel flow simulations by means of a lattice-Boltzmann scheme , In B. Hertzberger, P. Sloot (Eds.), High-Performance Computing and Networking , Lecture Notes in Computer Science 1225, 524-530 (1997). 

Rohde, M., Extending the Lattice-Boltzmann method—novel techniques for local grid refinement and boundary conditions , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (2004). 

Contributions to pressure drop have also been studied by lattice Boltzmann simulations. Zeiser et al. (2002) postulated that dissipation of energy was due to shear forces and deformational strain. The latter mechanism is usually missed by capillary-based models of pressure drop, such as the Ergun equation, but may be significant in packed beds at low Re. For a bed of spheres with N — 3, they found that the dissipation caused by deformation was about 50% of that... 

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