Improved Lattice Boltzmann Model Research Articles

An improved lattice Boltzmann model for fluid–fluid–solid flows with high viscosity ratio

In this paper, we present an improved lattice Boltzmann model for fluid–fluid–solid (FFS) flows with a high viscosity ratio. The bounce-back particle model is combined with the Shan–Chen (SC) multicomponent model. We extend the bounce-back scheme based on velocity interpolation and a fresh-node initialization approach with second-order accuracy to moving particles within the framework of the multicomponent model. An improved virtual solid density model for wetting boundary conditions is employed to implement contact angles on curved boundaries. We examine the factors that lead to the violation of mass conservation, and an easy redistributing method is developed to fix the mass leakage issue. The combined multiphase particle model is able to simulate FFS flows with a high viscosity ratio of up to 1000 while preserving the total mass of the two fluids. The performance of the approach is tested by a variety of numerical experiments. The dynamic behaviors of moving contact lines on the curved boundary are validated by a droplet wetting on a solid particle. The model is then applied to simulate dynamic FFS problems, such as particle wetting at the fluid interface and particle motion through a fluid–fluid interface. According to the simulation results, the present model is capable of capturing the total force exerted on a particle by the fluid and the interface. However, the SC-type fluid–solid interaction force does not equal the capillary force in the present model. Finally, the self-assembly process of two floating particles on a liquid–liquid interface is investigated.

Improved phase-field-based lattice Boltzmann method for thermocapillary flow.

In this paper, we present an improved phase-field-based lattice Boltzmann (LB) method for thermocapillary flows with large density, viscosity, and thermal conductivity ratios. The present method uses three LB models to solve the conservative Allen-Cahn equation, the incompressible Navier-Stokes equations, and the temperature equation. To overcome the difficulty caused by the convection term in solving the convection-diffusion equationfor the temperature field, we first rewrite the temperature equationas a diffuse equationwhere the convection term is regarded as the source term and then construct an improved LB model for the diffusion equation. The macroscopic governing equationscan be recovered correctly from the present LB method; moreover, the present LB method is much simpler and more efficient. In order to test the accuracy of this LB method, several numerical examples are considered, including the planar thermal Poiseuille flow of two immiscible fluids, the two-phase thermocapillary flow in a nonuniformly heated channel, and the thermocapillary Marangoni flow of a deformable bubble. It is found that the numerical results obtained from the present LB method are consistent with the theoretical prediction and available numerical data, which indicates that the present LB method is an effective approach for the thermocapillary flows.

An Improved Lattice Boltzmann Model for Convection Melting in the Existence of an Inhomogeneous Magnetic Field

An Improved Lattice Boltzmann Model for Convection Melting in the Existence of an Inhomogeneous Magnetic Field

Coking Prediction in Catalytic Glucose Conversion to Levulinic Acid Using Improved Lattice Boltzmann Model

Considering process efficiency, flow and coking are important aspects in biomass and its derivatives for catalytic conversion to value-added products. However, these investigations are scarcely inv...

A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder

In this paper, an improved lattice Boltzmann model that incorporates the effect of heat capacity is adopted to simulate the conjugate natural convection in a square enclosure with a circular cylinder, and the square cavity considered is bounded by four finite thickness and conductive walls. Influences of Rayleigh number, wall thermophysical properties, and wall thickness on streamlines, isotherms and Nusselt number are analyzed. It is found that the heat transfer rate obtained for different wall thicknesses is usually smaller than that for the zero wall thickness, while this difference is not apparent for a larger thermal conductivity ration. Additionally, the study also shown that the increase of the outer wall thickness tends to decrease the heat transfer rate. The effects of the geometric parameter, including aspect ratio and vertical cylinder location, on heat transfer are also studied.

An improved lattice Boltzmann model for high gas and liquid density ratio in composite grids

Lattice Boltzmann method is one of the widely used in multiphase fluid flow. However, the two main disadvantages of this method are the instability of numerical calculations due to the large density ratio of two phases and impossibility of the temperature distribution to be fed back into the velocity distribution function when the temperature is simulated. Based on the combination prescribed by Inamuro, the large density ratio two-phase flow model and thermal model makes the density ratio of the model simulation to be increased to 2778:1 by optimizing the interface distribution function of two-phase which improves the accuracy of differential format. The phase transition term is added as source term into the distribution function controlling two phase order parameters to describe the temperature effect on the gas-liquid phase transition. The latent heat generated from the phase change is also added as a source term into the temperature distribution function which simulates the movement of the flow under the common coupling of density, velocity, pressure and temperature. The density and the temperature distribution of single bubble are simulated. Comparison of the simulation results with experimental results indicates a good agreement pointing out the effectiveness of the improved model.

Numerical simulation of bubble growth on and departure from the heated surface by an improved lattice Boltzmann model

Abstract Based on the phase change model developed by lattice Boltzmann method (LBM), an improved source term which is responsible for phase change is proposed. The computation of the latent heat is taken into consideration to avoid the error and instability caused by the equation of state (EOS). Periodic bubble growth and departure from a heated surface during the boiling process is investigated based on the newly developed lattice Boltzmann model. Effects of gravity, contact angel and superheat on bubble departure diameter and release period under constant wall temperature conditions are illustrated. The three-phase contact line movements of the vapor bubble and the wall heat flux are also described. The results reflect the dynamic features and the influencing mechanism of bubble in boiling period, and this research lays the foundation of further studies on thermal-hydraulics and safety analysis by LBM.

Phase field lattice Boltzmann model for two-phase flow coupled with additional interfacial force

The phase field model has become increasingly popular due to its underlying physics for describing two-phase interface dynamics. In this case, several lattice Boltzmann multiphase models have been constructed from the perspective of the phase field theory. All these models are composed of two distribution functions: one is used to solve the interface tracking equation and the other is adopted to solve the Navier-Stokes equations. It has been reported that to match the target equation, an additional interfacial force should be included in these models, but the scale of this force is found to be contradictory with the theoretical analysis. To solve this problem, in this paper an improved lattice Boltzmann model based on the Cahn-Hilliard phase-field theory is proposed for simulating two-phase flows. By introducing a novel and simple force distribution function, the improved model solves the problem that the scale of an additional interfacial force is not consistent with the theoretical one. The Chapman-Enskog analysis shows that the present model can accurately recover the Cahn-Hilliard equation for interface capturing and the incompressible Navier-Stokes equations, and the calculation of macroscopic velocity is also more efficient. A series of classic two-phase flow examples, including static drop test, droplets emerge, spinodal decomposition and Rayleigh-Taylor instability is simulated numerically. It is found that the numerical solutions agree well with the analytical solutions or the existing results, which verifies the accuracy and feasibility of the proposed model. In addition, the Rayleigh-Taylor instability with the imposed random perturbation is also simulated, where the influence of the Reynolds number on the evolution of the phase interface is analyzed. It is found that for the case of the high Reynolds number, a row of “mushroom” shape appears at the fluid interface in the early stages of evolution. At the later stages of evolution, the fluid interface presents a very complex chaotic topology. Unlike the case of the high Reynolds number, the fluid interface becomes relatively smooth at low Reynolds numbers, and no chaotic topology is observed at any of the later stages of evolution.

Simulation of liquid–vapour phase transitions and multiphase flows by an improved lattice Boltzmann model

An improved lattice Boltzmann (LB) model with a new scheme for the interparticle interaction force term is proposed in this paper. Based on the improved LB model, the equation-free method is implemented for simulating liquid–vapour phase change and multiphase flows. The details of phase separation are presented by numerical simulation results in terms of coexistence curves and spurious currents. Compared with existing models, the proposed model can give more accurate results in a wider temperature range with the spurious currents reduced and less time consumed. Characteristics of phase separation can be quickly and accurately reflected by the proposed method. Then, the contact angle of the solid surface is numerically investigated based on the proposed model. The proposed model is valid for steady flow with near zero velocity; unsteady cases will be investigated in further studies. This work will be helpful for our long-term aim of multi-scale modelling of convective boiling.

An extended thermal Lattice Boltzmann model for transition flow

In the last two decades, mathematical models based on the Lattice Boltzmann method have been developed in an effort to accurately capture flow characteristics in rarefied conditions, including thermal effects. In order to improve their performance to characterize fluid conditions for the entire transition flow regime, a new wall-distance function has been developed based on existing Molecular Dynamics data and implemented to a D2Q13 Lattice Boltzmann model. The ability of the improved Lattice Boltzmann model to capture thermal effects on fluid conditions due to heat conduction and convection is demonstrated by simulating rarefied Fourier flow and Couette flow within micro/nano-channels, respectively, and validated against Direct Simulation Monte Carlo data as well as data based on the linearized Boltzmann equation. The results show that the proposed Lattice Boltzmann model is capable of simulating conditions, including thermal effects, in rarefied flow for the entire Knudsen number range representing slip, transition, and the low end of molecular flow regimes.

Simulation of two-phase flows of a droplet impacting on a liquid film with an improved lattice Boltzmann model

Based on the lattice Boltzmann method (LBM), an improved pseudo-potential model, combined with a method of adding force term, is used to simulate the two-phase flows caused by a liquid droplet impacting on a liquid film. In this model, the different phases are treated as one fluid, and the interfaces between the vapor and liquid phases can be obtained by density value of the fluid. This variant of the LBM allows one to obtain the densities of vapor and liquid with high accuracy. The model is validated by an example of phase separation. The early stage of the impact of droplet on liquid film is simulated, and the results are qualitatively consistent with physical phenomena.

Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows

An improved model for simulation of phase transitions and single-component multiphase flows by lattice Boltzmann method is proposed and developed in this paper. It is shown that both the scheme for the interparticle interaction force term and the method of incorporating the force term are important for obtaining accurate and stable numerical results for simulations of single-component multiphase flows. A new scheme for the force term is proposed and simulation results of several non-ideal equation of state suggest that the proposed scheme can greatly improve the coexistence curves. Among several methods of incorporating the force term, the exact difference method is shown to have better accuracy and stability. Furthermore, it avoids the unphysical phenomenon of relaxation time dependence. Compared with existing models, the proposed model, consisting of the new force term scheme together with the exact different method to incorporate the force term, can give more accurate and stable numerical results in a wider temperature range with the spurious currents greatly reduced. Droplet motion and coalescence processes on surfaces with wettability gradients are numerically investigated based on the newly proposed model. The velocity field and mechanism of droplet motion are illustrated in details.

AN IMPROVED THERMAL LATTICE BOLTZMANN MODEL FOR FLOWS WITHOUT VISCOUS HEAT DISSIPATION AND COMPRESSION WORK

An improved lattice Boltzmann model is proposed for thermal flows in which the viscous heat dissipation and compression work by the pressure can be neglected. In the improved model, the whole complicated gradient term in the internal energy density distribution function model is correctly discarded by modifying the velocity moments' condition. The corresponding macroscopic energy equation is exactly derived through Chapman–Enskog expansion. In particular, based on the improved thermal model, a double-distribution-function lattice BGK model is developed for two-dimensional Boussinesq flow, which is a typical flow with negligible viscous heat dissipation and compression work. A two-dimensional plane flow and the natural convection of air in a square cavity with various Rayleigh numbers are simulated by using the double-distribution-function lattice BGK model. It is found that there is excellent agreement between the present results with the analytical or benchmark solutions.

An Improved Lattice Boltzmann Model for Immiscible Fluids

An Improved Lattice Boltzmann Model for Immiscible Fluids

An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale

In this paper, we improve the lattice Boltzmann pore‐scale model for multicomponent reactive transport in porous media developed in a previous study. Instead of applying a thermal boundary condition to solute transport, we rigorously derive the distribution function boundary condition for the total solute concentration. This is achieved first by correcting an expression of the particle distribution function in terms of the corresponding concentration and its gradient and then by deriving and using the relation that the nonequilibrium portion of the distribution function in opposite directions takes on opposite signs. We implement the new boundary condition in both the two‐dimensional nine‐speed (D2Q9) and four‐speed (D2Q4) lattices. Simulations of reactive transport in various chemical and geometrical systems using different models are carried out, and results are compared to analytic expressions or two‐dimensional FLOTRAN simulations. It is found that with this new boundary condition, the solute mass is strictly conserved by heterogeneous reactions, as was not the case using the thermal boundary condition. It is also found that compared with the D2Q9 model, the D2Q4 model has comparable accuracy and better computational efficiency.

Two-dimensional lattice Boltzmann model for compressible flows with high Mach number

In this paper we present an improved lattice Boltzmann model for compressible Navier–Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67 (2003) 036306], (ii) a modified Lax–Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.

LATTICE BOLTZMANN APPROACH TO HIGH-SPEED COMPRESSIBLE FLOWS

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara15 and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios (1000:1) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

Multi-component lattice Boltzmann equation for mesoscale blood flow

We present an improved lattice Boltzmann model of multi-component flow which permits practical, hydrodynamic modelling of multiple immiscible fluids. The model is robust and significantly reduces the interface anisotropy and micro-currents, which are artefacts observed in many schemes. Our new scheme is used on a particular regime of blood flow: that of the veinule mesoscale, where it is necessary to resolve significant numbers of deformable, interacting cells, which we model as incompressible liquid drops. We demonstrate the model's ability to recover the complex flow phenomena typical of the veinule scale.

Lattice Boltzmann model with nearly constant density.

An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.

Improved lattice Boltzmann model for incompressible two-dimensional steady flows.

An improved lattice Boltzmann model with single time relaxation has been proposed for incompressible two-dimensional (2D) steady flows. In the improved model, the steady-state incompressible Navier-Stokes equations can be recovered in exact form and the density of the fluid becomes an irrelevant invariant, satisfying the requirement of incompressibility. Exact analytical solutions to the distribution functions of the 2D triangular and square lattice Boltzmann models have been obtained for steady plane Poiseuille flow based on the present scheme. Boundary conditions that can be used to recover exactly such analytical solutions in numerical simulations are proposed.