Present Lattice Boltzmann Method Research Articles

Investigation of deformation and breakup of a falling droplet using a multiple-relaxation-time lattice Boltzmann method

In this paper, a multi-relaxation-time lattice Boltzmann method for multiphase flows is employed to simulate different modes of deformation and fragmentation of an axisymmetric falling droplet under buoyancy force. To show the accuracy of the model, the Laplace law for stationary drops is conducted first. Then, drop deformation and breakup in a free fall is studied in an axially symmetric pipe. Surface tension effects as well as impacts of gas and drop viscosities are investigated for a wide range of Eötvös, Morton, and Archimedes numbers. The drag coefficient of the drop, as it falls, is measured and compared to the empirical correlations, and reasonable agreement is shown. The findings are further verified by comparing a typical bag breakup mechanism with experimental observations. It is seen that at low Eötvös numbers the drop deforms slightly and reaches a steady state. Increase of Eötvös number enhances the rate of deformation, and at a high enough Eötvös value breakup of the drop happens. While the gas viscosity is shown to have a trivial effect on the breakup of the droplet, drop viscosity is the overriding factor in the mechanism of disintegration. Consequently, various breakup modes of the falling droplet are observed just by varying the drop-based Archimedes number. By capturing different breakup mechanisms of a falling droplet such as bag breakup, shear breakup, and, particularly, multimode breakup, the present lattice Boltzmann method exhibits an excellent superiority over the sharp interface tracking schemes that fail to capture dissociation of the interface.

A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium

Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.

Lattice Boltzmann simulation for magnetic fluids in porous medium

A Lattice Boltzmann method is introduced to simulated magnetic fluids in porous medium. In the simulation, drag force and the other external forces are imported to the momentum equation. The influence of external magnetic field on thermo-sensitive magnetic fluids is expressed as a magnetic potential equation, which will be dispersed depending on the format of density and temperature. To test the reliability of the method, a validation with common fluid in porous medium is compared. Great agreement with previous results verified that the present lattice Boltzmann method is promising for simulating magnetic fluids in porous medium.

Numerical method of lattice Boltzmann simulation for flow past a rotating circular cylinder with heat transfer

Purpose – The main objective of this work is to develop a boundary treatment in lattice Boltzmann method (LBM) for curved and moving boundaries and using this treatment to study numerically the flow around a rotating isothermal circular cylinder with/without heat transfer.Design/methodology/approach – A multi‐distribution function thermal LBM model is used to simulate the flow and heat transfer around a rotating circular cylinder. To deal with the calculations on the surface of cylinder, a novel boundary treatment is developed.Findings – The results of simulation for flow and heat transfer around a rotating cylinder including the evolution with time of velocity field, and the lift and drag coefficients are compared with those of previous theoretical, experimental and numerical studies. Excellent agreements show that present LBM including boundary treatment can achieve accurate results of flow and heat transfer. In addition, the effects of the peripheral‐to‐translating‐speed ratio, Reynolds number and Pran...

Lattice-Boltzmann modeling of phonon hydrodynamics

Based on the phonon Boltzmann equation, a lattice-Boltzmann model for phonon hydrodynamics is developed. Both transverse and longitudinal polarized phonons that interact through normal and umklapp processes are considered in the model. The collision term is approximated by the relaxation time model where normal and umklapp processes tend to relax distributions of phonons to their corresponding equilibrium distribution functions-the displaced Planck distribution and the Planck distribution, respectively. A macroscopic phonon thermal wave equation (PTWE), valid for the second-sound mode, is derived through the technique of Chapman-Enskog expansion. Compared to the dual-phase-lag (DPL) -based thermal wave equation, the PTWE has an additional fourth-ordered spatial derivative term. The fundamental difference between the two models is discussed through examining a propagating thermal pulse in a single-phased medium and the transient and steady-state transport phenomena on a two-layered structure subjected to different temperatures at boundaries. Results show that transport phenomena are significantly different between the two models. The behavior exhibited by the DPL model, as thermal wave behavior goes over to diffusive behavior, tau_{T}-->tau_{q} is incompatible with any microscopic phonon propagating mode. Unlike the DPL model, in which tau_{T} only has an effect on the transient phenomena, in the PTWE model tau_{T} shows effects on phenomena at both transient and steady state. With the intrinsic compatibility to the microscopic state, discontinuous quantities, such as a jump of temperature at a boundary or at an interface, can be calculated naturally and straightforwardly with the present lattice-Boltzmann method.

Lattice Boltzmann method for solving the bioheat equation

In this work, we develop the lattice Boltzmann method (LBM) as a potential solver for the bioheat problems. The accuracy of the present LBM algorithm is validated through comparison with the analytical solution and the finite element simulation. The results show that the LBM can give a precise prediction of the temperature distribution, and it is efficient to deal with the space- and time-dependent heat source, which are often encountered in the treatment planning of tumor hyperthermia.

Lattice Boltzmann method simulation gas slip flow in long microtubes

PurposeThis paper aims to examine how using lattice Boltzmann method (LBM) aids the study of the isothermal‐gas flow with slight rarefaction in long microtubes.Design/methodology/approachA revised axisymmetric lattice Boltzmann model is proposed to simulate the flow in microtubes. The wall boundary condition combining the bounce‐back and specular‐reflection schemes is used to capture the slip velocity on the wall. Appropriate relation between the Knudsen number and relax‐time constant is defined.FindingsThe computed‐slip velocity, average velocity and non‐linear pressure distribution along the microtube are in excellent agreement with analytical solution of the weakly compressible Navier‐Stokes equations. The calculated‐friction factors are also consistent with available experimental data. For simulations of slip flow in microtube, LBM is more accurate and efficient than DSMC method.Research limitations/implicationsThe laminar flow in circular microtube is assumed to be axisymmetric. The present LBM is only applied to the simulation of slip flows (0.01 < Kn0<0.1) in microtube.Practical implicationsLattice‐BGK method is a very useful tool to investigate the micro slip flows.Originality/valueA revised axisymmetric D2Q9 lattice Boltzmann model is proposed to simulate the slip flow in axisymmetric microtubes.

SIMULATING TWO- AND THREE-DIMENSIONAL MICROFLOWS BY THE LATTICE BOLTZMANN METHOD WITH KINETIC BOUNDARY CONDITIONS

An entropic lattice Boltzmann model for gaseous slip flow in microchannels is presented. We relate the Knudsen number with the relaxation time in the lattice Boltzmann evolution equation from the gas kinetic theory. The slip velocity taking the momentum accommodation coefficient into account at the solid boundaries is obtained with kinetic boundary conditions. The two-dimensional micro-Poiseuille flow, microflow over a backward-facing step, micro-lid-driven cavity flow, and three-dimensional microflow are simulated using the present model. Numerical tests show that the results of the present lattice Boltzmann method together with the boundary scheme are in good agreement with the analytical solutions and numerical simulations by the finite volume method.

Lattice Boltzmann study on size effect with geometrical bending on phonon heat conduction in a nanoduct

Phonon heat transport based on the Boltzmann transport equation (BTE) in a free standing, bent duct with characteristic dimension down to the nanoscale is investigated through the lattice Boltzmann (LB) method. Both the thermal excited transverse and longitudinal phonons are considered. The collision term in BTE is approximated by the relaxation time approximation. Both diffusive and specular phonon scatterings at duct surfaces are considered. An analytical expression for thermal conductivity suitable for an infinitely long, straight duct with constant properties is derived. Results show that the size effect depends strongly on the Knudsen number. For large Knudsen number, heat transport is mainly dominated by the ballistics that results in strong size effect, and vice versa. For the bent duct more phonons take the passageway near the inner corner of the bending region where higher local thermal conductivity is expected. Although the specular boundary scattering introduces no change in the bulk quantities for a straight duct, it, however, brings in the geometric influence as the duct is bent. Compared to the straight duct, the bent duct has the supremacy in conducting heat as the Knudsen number is small. Conversely the straight duct presents higher conductivity when the Knudsen number is large. By the present LB method, jumps in macroscopic quantities, occurring at boundary and wall surface, can be calculated naturally and straightforwardly.

Liquid Drops on Homogeneous and Chemically Heterogeneous Surfaces: A Two-Dimensional Lattice Boltzmann Study

A boundary condition of a two-phase lattice Boltzmann (LB) method is proposed to model smooth substrates of chemically heterogeneous surfaces. The present technique is applied to the LB simulations of liquid drops on homogeneous, regularly heterogeneous, and randomly heterogeneous surfaces. It is found (i) that the LB technique can mimic not only homogeneous substrates with arbitrary wettabilities but also chemically heterogeneous substrates with arbitrary heterogeneities and wettabilities and (ii) that, in the presence of surface heterogeneities, it also can capture the contact line pinning, the contact angle hysteresis, and the effects of size and distribution of the heterogeneities on them. The results indicate that the present LB method is useful for the simulation of wetting phenomena of chemically heterogeneous surfaces.

A Lattice Boltzmann Method for a Binary Miscible Fluid Mixture and Its Application to a Heat-Transfer Problem

A lattice Boltzmann method (LBM) for an isothermal binary miscible fluid mixture is proposed. The binary miscible fluid mixture is assumed to be composed of A and B species where the fraction of B species is much smaller than that of A species. The asymptotic theory proposed by Sone [in Rarefied Gas Dynamics, edited by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), Vol. 2, p. 737] is applied to the present LBM model and the convection–diffusion equation for component B is obtained. A diffusion problem is calculated and the validity of the proposed model is shown. Also, the present method can be applied to thermal fluid systems, in which the concentration field of component B is regarded as the temperature field of component A, and a buoyancy force proportional to the temperature difference is included. Rayleigh–Bénard convection is numerically simulated. The results indicate that the present LBM is useful for the simulation of fluid flows with heat transfer as well as mass transfer.