Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session L31: CFD: Lattice Boltzmann Methods |
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Chair: Mouhamadou Aziz Diop Room: 2018 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L31.00001: LBM study of flow-induced cavitation Giuseppe Gonnella, Goetz Kaehler, Francesco Bonelli, Antonio Lamura This work deals with the investigation of homogeneous cavitation, induced by a fast flow past a sack wall, by using the lattice Boltzmann method (LBM). Cavitation occurs, in a liquid, because of a pressure drop, which falls below a certain threshold, with the consequent formation of vapor bubbles [1]. The aim is to study the inception of cavitation by using LBM without any ``ad hoc'' cavitation model [2]. A LBM with a body force term and redefined equilibrium distribution functions is employed for describing the continuity and Navier-Stokes equations for a fluid locally satisfying the van der Waals equation of state [3]. In such a way, cavitation is directly described by the solution of the LB equation. The numerical study shows the formation of a depletion zone just under the obstacle, near its left edge, where the pressure reaches a minimum value. Cavitation occurs only when the pressure of this depletion zone reaches a value lower than the spinodal of the liquid branch, thus not confirming the Joseph's maximum tension criterion [4]. A detailed study of the flow field, of the Reynolds number effects, and of the developed cavitation regime are presented. [1] C. E. Brennen, Cavitation and Bubble Dynamics (Oxford University Press, 1995) [2] See for example M. Darbandi and H. Sadeghi, Numer. Heat Transfer A 58, 505 (2010). [3] A. Coclite, G. Gonnella, and A. Lamura, Phys. Rev. E 89, 063303 (2014). [4] G. Falcucci, E. Jannelli, S. Ubertini, and S. Succi, J. Fluid Mech. 728, 362 (2013). [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L31.00002: Numerical Simulation of Capillary Channels Growth in Heterogeneous Porous Anode in Aluminum Electrolysis Cells by Lattice Boltzmann Method Mouhamadou Diop, Moran Wang This paper presents results obtained from three-dimensional numerical simulations of multiphase reactive flows in porous anode block in aluminum cells controlling a great extent of mass, heat and chemical balance in the anode-cathode region. A lattice Boltzmann method based on thermal reactive multiphase flows, is developed to simulate the spatial and temporal distribution of fluids, the effects of gas rate and capillary instabilities in the cryolite. A new model, which involves eighteen lattice particles for the first and second derivative, is proposed to achieve accurate simulations at high fluid density ratio. The effects of the dissolution of gas and the capillary number on the flow field induced by gas bubbles evolution are investigated. It is found that capillary channels in the limit of small Stefan, the radial transport of reactant out of the capillary channel decay exponentially with the height of penetration in the porous anode. Several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L31.00003: Deformation and breakup of viscoelastic droplets in confined shear flow Mauro Sbragaglia, Anupam Gupta The deformation and breakup of Newtonian/viscoelastic droplets in systems with a Newtonian matrix are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time, the maximum extensibility of the polymers, and the degree of confinement, i.e. the ratio of droplet diameter to gap spacing. In bulk shear flow, the effects of droplet viscoelasticity on the critical capillary number for breakup are moderate in all cases studied. However, in confined conditions a different behaviour is observed: the critical capillary number of a viscoelastic droplet increases or decreases, depending on the maximum elongation of the polymers, the latter affecting the extensional viscosity of the polymeric solution. Force balance is monitored in the numerical simulations to validate the physical picture. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L31.00004: A new multi-block-LBM scheme for turbulent flow simulations Yusuke Kuwata, Kazuhiko Suga A new lattice Boltzmann multi-block scheme based on the D3Q27 multiple relaxation time method is developed for turbulent flow simulations. In the streaming step, the distribution functions in the interface of each block are transferred by considering the continuity of the macroscopic variables. The mass and momentum continuity is achieved by keeping the consistency between the equilibrium distribution functions of the finer and coarse grids, whilst the non-equilibrium part is scaled for the continuity of the stress tensor. The 3rd order Lagrangian and Helmite interpolations are applied to temporally and spatially discretized variables in the interface region of the blocks. In order to relax the numerical errors occurring at the interface, which may affect the mass and momentum conservation, new distribution functions which are defined by the combination of the two distribution functions from the finer and coarse grids are streamed. The turbulent quantities such as the Reynolds stresses, budget terms of the Reynolds stress equation and power spectrum distributions are compared with those of DNS data by the pseudo spectrum method with good agreement. Moreover, the results show seamless profiles even at the interface of the blocks. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L31.00005: Collisional Lattice Boltzmann Method for simulation of continuum through free molecular flow regimes Prakash Vedula, Abdelaziz Aliat The collisional Lattice Boltzmann Method (cLBM) involves a lattice based numerical solution of Boltzmann equation including the full collision operator (Green \& Vedula, {\it J. Stat. Mech.}, 2013). Owing to accurate representation of important symmetries of the full collision operator (beyond collision invariants) and the lack of restrictive equilibrium based assumptions, this method could be particularly useful for efficient and accurate simulation of nonequilibrium flows. In the talk, we will discuss a generalization of cLBM using arbitrary lattices for description of two-dimensional flows. We will also discuss some physical and mathematical constraints that need to be considered for selection of lattices. Based on these considerations, we will demonstrate significant improvement in accuracy of simulations of selected flows in the continuum through free molecular flow regimes (up to Knudsen number, Kn O(100)). We will compare results (including the variation of velocity profiles, wall shear stress and mass flow rate with Kn) obtained from traditional LBM and DSMC with those obtained from cLBM using non-standard lattices. Using insights from these studies, we will also present techniques for significant improvement in accuracy of conventional LBM (based on BGK collision model). [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L31.00006: A Moving Boundary Condition based on Chapman-Enskog Expansion for the Lattice Boltzmann Method Lina Xu, Laura Schaefer The lattice Boltzmann method (LBM) has been shown to be an effective numerical method to model various fluid flows, by dealing boundary conditions from the mesoscopic level with straightforward and easy-to-implement approaches, the fundamental understanding of the hydrodynamic interactions between the solid and fluid in the particulate suspensions systems can be further improved. However, most of the previous boundary conditions used for the moving complex boundaries are based on the half way bounce-back boundary condition, where the geometric integrity of the body cannot be maintained. In this presentation, a moving boundary condition based on the Chapman-Enskog expansion is proposed and applied for the moving complex surfaces, where the precise shape of the solid can be preserved. Based on the numerical experiments for modelling the particulate suspensions system, the new moving boundary condition exhibits improved numerical accuracy and stability, stronger capability to preserve the geometry integrity, and better Galilean invariance character. Moreover, this presentation provides a novel concept to construct a boundary condition for the LBM without the limitation of being based on the information from the already existing lattice nodes. [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L31.00007: An Immersed Boundary-Lattice Boltzmann Approach to the Direct Numerical Simulation of Complex Particulate Flows Baili Zhang, Ming Cheng, Zhi Shang, Jing Lou A three-dimensional momentum exchange-based immersed boundary-lattice Boltzmann method has been developed for solving fluid-particles interaction problems. This method combines the most desirable features of the lattice Boltzmann method and the immersed boundary method by using a regular Eulerian mesh for the flow domain and a Lagrangian mesh for the moving particles in the flow field. The non-slip boundary conditions for the fluid and the particles are enforced by adding a force density term into the lattice Boltzmann equation, and the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. This method preserves the advantages of lattice Boltzmann method in tracking a group of particles and, at the same time, provides an alternative approach to treat solid-fluid boundary conditions. Numerical validations show that the present method is very accurate and efficient. The code developed using this approach has been parallelized and allows the direct numerical simulation of fairly complicated phenomena such as three-dimensional particulate flow with very large numbers of particles. [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L31.00008: A multi-mesh lattice Boltzmann scheme for modeling solidification microstructure Mohammad Hashemi, Amirreza Hashemi, Mohsen Eshraghi, Sergio Felicelli A multi-mesh lattice Boltzmann (LB) scheme is developed for modelling dendritic growth during solidification of binary alloys. Different physical phenomena including: mass transport, fluid flow, and heat transfer are involved in solidification, which are solved using the lattice Boltzmann method. Considering the difference in the length scales, a separate grid is introduced for each physical model to enhance the stability and computational performance of the method. Since the solutal boundary layer is very thin, a finer mesh is required near the interface to accurately simulate the transport phenomena. To address this problem, a non-uniform mesh is considered within each model. A conservative treatment was employed between neighbouring mesh blocks to ensure the continuity of mass, energy, and momentum. The multi-mesh model developed in this work is several times faster than the conventional unigrid LB models and offers a much better stability. Considering the high computational demands of the micro-scale simulations, the model can be employed as an efficient tool for simulating microstructural evolution during solidification. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L31.00009: A conservative Dirichlet boundary treatment for the finite volume lattice Boltzmann method Leitao Chen, Laura Schaefer The finite volume lattice Boltzmann method (FVLBM) enables the model to use the exact body-fitting mesh in the flow problems that involve the complex boundaries. However, the development of proper boundary treatment for the FVLBM has been outpaced. The boundary treatments designed for the conventional lattice Boltzmann method (LBM) framework are still heavily applied to the FVLBM. The largest defect of using the old boundary treatment is that, on the Dirichlet boundaries, the macroscopic variables cannot be conserved. In another word, there exist nontrivial discrepancies between the macroscopic variables defined by the boundary conditions and those yield by the numerical solutions. The errors on the boundaries will contaminate the internal solutions and even cause instability, especially on the complex boundaries. To overcome such a shortcoming, a conservative boundary treatment for the Dirichlet hydrodynamic boundary conditions is developed for the FVLBM. Through the benchmark tests, it is shown that the macroscopic conservations on the Direchlet boundaries are up to machine accuracy and completely independent of the size of relaxation time, the type of lattice model, the level of mesh resolution, the shape of boundaries and the type of internal scheme. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L31.00010: Thermal lattice Boltzmann simulations with non-space-filling lattices Parthib Rao, Laura Schaefer Thermal lattice Boltzmann (LB) models that ensure energy conservation have been less than satisfactory, compared to the athermal LB models due to variety of reasons. However, in the last few years, there has been a renewed effort in developing kinetically-consistent, stable, and accurate thermal models based on a new theoretical interpretation of the LB method-the Gauss-Hermite (GH) expansion technique. These, so-called higher-order models have been theorized to be able to model Navier-Stokes level thermo-hydrodynamics. Pursuant to this approach, we propose to use a third-order GH expansion of the equilibrium distribution along with a non-space-filling lattice (D2Q12), to model low-speed thermal flows, where temperature evolves according to an advection-diffusion equation. Additionally, this model is also compared for accuracy and computational efficiency, with an equivalent space-filling lattice (D2Q17) and the passive-scalar model. On benchmark thermal simulations such as Rayleigh-Benard convection and thermal Couette flows, our preliminary results indicate that the D2Q12 lattice is not only as as accurate as the D2Q17 lattice, but also computationally more efficient. Therefore, the D2Q12 lattice can be used modelling flows where temperature plays the role of a passive-scalar. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L31.00011: Chapman-Enskog analyses on gray lattice Boltzmann schemes for fluid flow in porous media Chen Chen, Like Li, Renwei Mei, James Klausner Gray lattice Boltzmann (GLB) schemes have recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional reflection coefficient $\theta $, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for linear drag of the medium. These schemes are very easy to implement; but there exists uncertainty about the need for redefining macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from various GLB schemes. In this work, Chapman-Enskog analyses are performed to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in $\varepsilon $ only if $\theta =$O($\varepsilon )$ in which $\varepsilon $ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When gravitational force is considered or a body force is used to represent pressure gradient, the forcing term requires a modification factor that accounts for the effect of $\theta $. The modification factor is derived for each combination of the forcing implementation method and the GLB scheme. The theoretical findings are verified by numerical results. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L31.00012: Disc-shaped colloids interacting in a nematic liquid crystal Alena Antipova, Colin Denniston We studied the behavior of pairs of disc-shaped colloidal particles in a nematic liquid crystal using Lattice Boltzmann algorithm. Without any external forces the position of the disc with respect to the liquid crystal director minimizes the free energy of the system and no distortion of the director field is observed. When the rotating magnetic field is present, the torque on the disc with homeotropic surface anchoring should change with analogy to electrostatic energy, which implies the disc continues turning following the field. However, when the disc reaches some critical position and the director field around it is highly distorted, the disc suddenly flips to minimize the free energy. Position and motion of pairs of such discs under similar conditions can be controlled by the angular velocity of magnetic field, it's magnitude and initial configuration of the system. As a result of analysis of discs' dynamics, a new way to control self-organization of disc particles was produced. [Preview Abstract] |
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