Present Lattice Boltzmann Method Research Articles

Lattice Boltzmann method for coupled radiation-conduction heat transfer in participating medium with graded-index

Graded-index materials are effective to control thermo-optical systems, due to its special physical characteristics. And quantitatively calculation for energy transfer process is valuable for the research of graded-index materials. Thus, reliable numerical method is required. Lattice Boltzmann method (LBM) is a mesoscopic numerical method with unique advantages on coupling muti-physical field. Here, we provide a LBM to couple radiation and conduction within graded-index medium under a unified framework. Through several 1-D cases, the great consistence between present LBM and references indicates that LBM has excellent availability and accuracy. Furthermore, LBM is expanded to coupled 2-D problem. The present LBM is expected to simulate coupled radiation-conduction heat transfer in participating medium with graded-index effectively.

Non-orthogonal multiple-relaxation-time lattice Boltzmann method for vorticity-streamfunction formulation

In this work, we propose a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) for the two-dimensional (2D) incompressible Navier-Stokes equations in vorticity-stream function formulation. In this method, the vorticity and the streamfunction equations are calculated by two separate LB equations, which are constructed by using the non-orthogonal transformation matrix. Most importantly, to eliminate the residual term that may appear in the recovered vorticity equation, the convection term is handled as a source term in the LB equation rather than being directly recovered by the evolution equation. In addition, due to the convection term in our method is computed with a local scheme, it retains the parallel feature of the standard LBM. We then test the accuracy and the stability of the present LBM by considering various benchmark examples. The results show that the present method has a second-order convergence rate in space. Our numerical results indicate that the present LBM is a good candidate for solving streamfunction-vorticity formulation.

A conservative phase‐field lattice Boltzmann method for incompressible two‐phase flows

AbstractIn this work, a conservative phase‐field lattice Boltzmann method (LBM) is proposed for incompressible two‐phase flows. In this method, two LB models are adopted to solve the nonlocal Allen–Cahn equation (ACE) and the Navier–Stokes equations, respectively. Unlike the previous models for the nonlocal ACE with a space‐time‐dependent Lagrange multiplier, a simple multiple‐relaxation time LB model is designed for the conservative and nonlocal ACE with a curvature‐dependent Lagrange multiplier, which can eliminate the problem of inherent coarsening process. Through the Chapman–Enskog analysis, the present LB model can correctly recover the ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LBM is validated by two tests, that is, the horizontal translation of two circular interfaces and a bubble rising under gravity, and the results show that the present LBM has a superior performance in capturing the large topological changes and small features of interfaces.

Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows.

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation(ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

Numerical Analysis of Radiation Heat Transfer Using the Lattice Boltzmann Method and the Finite Volume Method

This article reports the result of two popular numerical methods, viz., finite volume method (FVM) and lattice Boltzmann method (LBM) used to calculate the radiation heat transfer within an enclosure. 2-D rectangular enclosure with absorbing, emitting and scattering participating medium is considered. In terms of collision and streaming, the present approach of LBM for the radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analysis of conduction and convection. However, in the present LBM approach in order to mitigate the effect of isotropy in the polar direction the number of lattices employed is greater than those being used for 2-D system. Distribution of heat flux and emissive power for different values of extinction coefficient has been obtained using both methods. The good agreement has been found between LBM and FVM results. The number of iteration and CPU times has also been compared. It is found that for the convergence of solution the LBM required a greater number of iterations as FVM but LBM computationally much faster than FVM.

Consistent and conservative phase-field-based lattice Boltzmann method for incompressible two-phase flows.

In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equationcan be adopted, but also the mass and the momentum fluxes in the Navier-Stokes equationsare reformulated such that the consistency of reduction, consistency of mass and momentum transport, and the consistency of mass conservation are satisfied. We further develop a lattice Boltzmann (LB) method, and show that through the direct Taylor expansion, the present LB method can correctly recover the consistent and conservative phase-field model. Additionally, if the divergence of the extra momentum flux is seen as a force term, the extra force in the present LB method would include another term which has not been considered in the previous LB methods. To quantitatively evaluate the incompressibility and the consistency of the mass conservation, two statistical variables are introduced in the study of the deformation of a square droplet, and the results show that the present LB method is more accurate. The layered Poiseuille flow and a droplet spreading on an ideal wall are further investigated, and the numerical results are in good agreement with the analytical solutions. Finally, the problems of the Rayleigh-Taylor instability, a single rising bubble, and the dam break with the high Reynolds numbers and/or large density ratios are studied, and it is found that the present consistent and conservative LB method is robust for such complex two-phase flows.

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.

Investigating the effects of viscosity and density ratio on the numerical analysis of Rayleigh-Taylor instability in two-phase flow using Lattice Boltzmann method: From early stage to equilibrium state

The gravitational liquid-liquid two-phase flow was numerically investigated by using lattice Boltzmann method (LBM). The method was implemented for analyzing a model of Rayleigh-Taylor Instability (RTI). The feasibility of this present numerical approach was investigated by performing convergence test, and validating the obtained results with those obtained from experiments as well as other preceding numerical methods. Qualitative and quantitative comparisons were examined, whereby good agreements are noted for all cases. Parametric studies were also conducted by varying both of Reynolds and Atwood numbers to investigate the effects of viscosity and density ratio on the behavior of fluids interaction. Based on the obtained outcomes of this numerical approach, the present LBM was able to successfully simulate the complete phenomena during RTI, i.e.: the linear growth, secondary instability, bubble rising and coalescence, and liquid break-up, including turbulent mixing conditions as well as the equilibrium state. The finding obtained from this work might be beneficial in the investigation of parametric behavior in design of processes equipment such as for separator design.

Study on forcing schemes in the thermal lattice Boltzmann method for simulation of natural convection flow problems

AbstractThe present study addresses the effect of various schemes for applying an external force term on the accuracy and performance of the thermal lattice Boltzmann method (LBM) for simulation of free convection problems. Herein, the forcing schemes of Luo, shifted velocity method, Guo, and exact difference method are applied by considering three velocity discrete models of D2Q4, D2Q5, and D2Q9. The accuracy and performance of these schemes are evaluated with the simulation of three natural convection problems, namely, free convection in a closed cavity, in a square enclosure with a hot obstacle inside, and the Rayleigh‐Benard problem. The obtained results based on the present thermal LBM with different forcing schemes and velocity discrete models are compared with the existing experimental and numerical data in the literature. This comparison study indicates that imposing all employed forcing schemes leads to similar performance for the simulation of free convection problems studied at the middle range of Rayleigh numbers. It is found that the Luo forcing scheme is simple for implementation in comparison with the other three forcing schemes and provides the results with acceptable accuracy at moderate Rayleigh numbers. At higher Rayleigh numbers, however, the Guo scheme is not only numerically stable but a more precise forcing scheme in comparison with the other three methods. It is illustrated that employing the discrete velocity model of D2Q4 has more appropriate numerical stability along with less computational cost in comparison with two other discrete velocity models for simulation of natural convection heat transfer.

Consistent and Conservative Phase-Field Based Lattice Boltzmann Method for Incompressible Two-Phase Flows

In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum fluxes in the Navier-Stokes equations are reformulated such that the consistency of reduction, consistency of mass and momentum transport, and the consistency of mass conservation are satisfied. We further develop a lattice Boltzmann (LB) method and show that through the direct Taylor expansion, the present LB method can correctly recover the consistent and conservative phase-field model. Additionally, if the divergence of the extra momentum flux is seen as a force term, the extra force in the present LB method would include another term which has not been considered in the previous LB models. To quantitatively evaluate the incompressibility and the consistency of the mass conservation, two statistical variables are introduced in the study of the deformation of a square droplet, and the results show that the present LB method is more accurate. The layered Poiseuille flow and a droplet spreading on an ideal wall are further investigated, and the numerical results are in good agreement with the analytical solutions. Finally, the problems of the Rayleigh-Taylor instability and dam break with the high Reynolds numbers and/or large density ratios are studied, and it is found that the present consistent and conservative LB method is robust for such complex two-phase flows.

Simulation of collapsing cavitation bubbles in various liquids by lattice Boltzmann model coupled with the Redlich-Kwong-Soave equation of state.

A computational technique based on the pseudo-potential multiphase lattice Boltzmann method (LBM) is employed to investigate the collapse dynamics of cavitation bubbles of various liquids in the vicinity of the solid surface with different wettability conditions. The Redlich-Kwong-Soave equation of state (EoS) that includes an acentric factor is incorporated to consider the physical properties of water (H_{2}O), liquid nitrogen (LN_{2}), and liquid hydrogen (LH_{2}) in the present simulations. Accuracy and performance of the present multiphase LBM are examined by simulation of the homogenous and heterogeneous cavitation phenomena. The good agreement of the results obtained based on the present solution algorithm in comparison with the available data confirms the validity and capability of the multiphase LBM employed. Then, the cavitation bubble collapse near the solid wall is studied by considering the H_{2}O, LN_{2}, and LH_{2} fluids, and the wettability effect of the surface on the collapse dynamics is investigated. The obtained results demonstrate that the collapse phenomenon for the H_{2}O is more aggressive than that of the LH_{2} and LN_{2}. The cavitation bubble of the water has a shorter collapse time with an intense liquid jet, while the collapse process in the LN_{2} takes a longer time due to the larger radius of its bubble at the rebound. Also, this study demonstrates that the increment of the hydrophobicity of the wall causes less energy absorption by the solid surface from the liquid phase around the bubble that leads to form a liquid jet with higher kinetic energy. Therefore, the bubble collapse process occurs more quickly for hydrophobic surfaces, regardless of the fluids considered. The present study shows that the pseudopotential LBM with incorporating an appropriate EoS and a robust forcing scheme is an efficient numerical technique for simulation of the dynamics of the cavitation bubble collapse in different fluids.

Advances in mathematical modeling of hydrogen adsorption and desorption in metal hydride beds with lattice Boltzmann method

This study presents numerical modeling and simulations of thermal fluid flows in high-volumetric-density metal hydride beds during hydrogen (H2) adsorption and desorption within the lattice Boltzmann method (LBM) framework. A novel LBM is developed for predicting the flow and conjugate heat transfer in a practical lab apparatus involving a combination of solid chamber, free expansion zone, and porous media metal hydride that have not been addressed to date. With a correction term in the collision operator and a new equilibrium distribution function, the present model has a consistent expression of the heat capacity ratio for different fluid regions and derives the correct form of macroscopic energy and generalized momentum equations (including Darcy, Brinkman, and Forchheimer terms). The model is then validated through comparisons of the simulated results with previous experimental data under different initial pressure and temperature conditions for LaNi5–H2 storage systems as well Mg–H2 reactors, achieving excellent agreement. In addition, accounting for conjugate heat transfer and other porous forces in the present LBM yields improved predictions over prior numerical approaches.

Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method

The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions-simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.

Lattice Boltzmann method for fractional Cahn-Hilliard equation

Fractional phase field models have been reported to suitably describe the anomalous two-phase transport in heterogeneous porous media, evolution of structural damage, and image inpainting process. It is commonly different to derive their analytical solutions, and the numerical solution to these fractional models is an attractive work. As one of the popular fractional phase-field models, in this paper we propose a fresh lattice Boltzmann (LB) method for the fractional Cahn-Hilliard equation. To this end, we first transform the fractional Cahn-Hilliard equation into the standard one based on the Caputo derivative. Then the modified equilibrium distribution function and proper source term are incorporated into the LB method in order to recover the targeting equation. Several numerical experiments, including the circular disk, quadrate interface, droplet coalescence and spinodal decomposition, are carried out to validate the present LB method. It is shown that the numerical results at different fractional orders agree well with the analytical solution or some available results. Besides, it is found that increasing the fractional order promotes a faster evolution of phase interface in accordance with its physical definition, and also the system energy predicted by the present LB method conforms to the energy dissipation law.

Solving steady and transient radiative transfer problems with strong inhomogeneity via a lattice Boltzmann method

A complete lattice Boltzmann method (LBM) is developed to solve the steady and transient radiative transfer problems with strong inhomogeneity. The transient radiative transfer equation (RTE) is regarded as a hyperbolic conservation law equation and then solved by the LBM. A forward difference scheme is applied to the time derivative of the source term in the evolution equation, which makes the LBM accurate and stable for radiative transfer problems with strong inhomogeneity. The correctness and accuracy of the proposed LBM is verified first. Afterward, the LBM is applied to solve the one-dimensional radiative transfer problems involving strong inhomogeneous radiative intensity and discontinuous medium system, including a planar slab subjected to Gaussian-shaped source, an infinite slab with an inclusion layer, and a vacuum gapped medium system. The time-resolved radiation is presented and analyzed as well as the steady results. Finally, the present LBM is extended to multidimensional radiative transfer problems.

A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model

<p style='text-indent:20px;'>In this work, a multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is proposed to solve a coupled chemotaxis-fluid model. In the evolution equation of the proposed LBM, Beam-Warming (B-W) scheme is used to enhance the numerical stability. In numerical experiments, at first, the comparison between the classical LBM and the present LBM with B-W scheme is carried out by simulating blow up phenomenon of the Keller-Segel (K-S) model. Numerical results show that the stability of the present LBM with B-W scheme is better than the classical one. Then, the second order convergence rate of the proposed B-W scheme is verified in the numerical study of the coupled Navier-Stokes (N-S) K-S model. Finally, through solving the coupled chemotaxis-fluid model, the formation of falling bacterial plumes is numerically investigated. Numerical results agree well with existing ones in the literature.</p>

Lattice Boltzmann method for contact-line motion of binary fluids with high density ratio.

Within the phase-field framework, we present an accurate and robust lattice Boltzmann (LB) method for simulating contact-line motion of immiscible binary fluids on the solid substrate. The most striking advantage of this method lies in that it enables us to handle two-phase flows with mass conservation and a high density contrast of 1000, which is often unavailable in the existing multiphase LB models. To simulate binary fluid flows, the present method utilizes two LB evolution equations, which are respectively used to solve the conservative Allen-Cahn equation for interface capturing, and the incompressible Navier-Stokes equations for hydrodynamic properties. Besides, to account for the substrate wettability, two popular contact angle models including the cubic surface-energy model and the geometrical one are incorporated into the present method, and their performances are numerically evaluated over a wide range of contact angles. The contact-angle hysteresis effect, which is inherent to a rough or chemically inhomogeneous substrate, is also introduced in the present LB approach through the strategy proposed by Ding and Spelt [J. Fluid Mech. 599, 341 (2008)10.1017/S0022112008000190]. The present method is first validated by simulating droplet spreading and capillary intrusion on the ideal or smooth pipes. It is found that the cubic surface-energy and geometrical wetting schemes both offer considerable accuracy for predicting a static contact angle within its middle region, while the former is more stable at extremely small contact angles. Besides, it is shown that the geometrical wetting scheme enables us to obtain better accuracy for predicting dynamic contact points in capillary pipe. Then we use the present LB method to simulate the droplet shearing processes on a nonideal substrate with contact angle hysteresis. The geometrical wetting model is found to be capable of reproducing four typical motion modes of contact line, while the surface-energy wetting scheme fails to predict the hysteresis behaviors in some cases. At last, a complex contact-line dynamic problem of three-dimensional microscale droplet impact on a wettable solid is simulated, and it is found that the numerical results for droplet shapes agree well with the experimental data.

Macrosegregation simulation model based on Lattice-Boltzmann method with high computational efficiency

A macrosegregation simulation model is developed by coupling solute and energy conservation equations with Lattice-Boltzmann Method (LBM), newly developing technique of computational fluid dynamics. Effect of the solidification shrinkage is taken into account in the present LBM as well as effects of the Darcy’s flow and thermos-solutal convection. The present LBM-coupled model is based on modified lattice Bhadnager-Gross-Krook method, the numerical stability of which is better than that of the standard LBM. Accordingly, the present LBM-coupled model can be applied to simulations of macrosegregation behaviors in metallic alloy systems that cannot be handled by the previous LBM-coupled model. The validity of the model was demonstrated by comparing the results for steady-state flows with those of analytical solutions and a conventional model based on the Navier-Stokes equation. In addition, the computational speed of the present model is compared with the one of conventional model in cases of lateral directional solidification of Sn-Bi alloy and continuous casting of a steel slab. It is shown that the present LBM-coupled model enables remarkably faster computation than the conventional model especially in the latter case.

Investigation of nanofluids on heat transfer enhancement in a louvered microchannel with lattice Boltzmann method

Numerical studies of laminar forced convective heat transfer and fluid flow in a 2D louvered microchannel with Al2O3/water nanofluids are performed by the lattice Boltzmann method (LBM). Eight louvers are arranged in tandem within the single-pass microchannel. The Reynolds number based on channel hydraulic diameter and bulk mean velocity ranges from 100 to 400, where the Al2O3 fraction varies from 0 to 4%. A double distribution function approach is adopted for modeling fluid flow and heat transfer. Code validations are performed by comparing the streamwise Nusselt number (Nu) profiles and Fanning friction factors of the present LBM and those of the analytical solutions. Good agreements are obtained. Simulated results show that the louver microstructure can disturb the core flow and guide coolant toward the heated walls, thus enhancing the heat transfer significantly. Furthermore, the addition of nanoparticles in microchannels can also augment the heat transfer, but it creates an unnoticeable pressure loss. With both the louver microstructure and nanofluid, a maximum overall Nu enhancement of 7.06 is found relative to that of the fully developed smooth channel.

3D lattice Boltzmann simulation for a saturated liquid droplet at low Ohnesorge numbers impact and breakup on a solid surface surrounded by a saturated vapor

In this paper, new simulation results of a saturated liquid droplet impact dynamics on hydrophilic (θ = 80°) and hydrophobic (θ = 170°) solid surfaces surrounded by a saturated vapor are obtained based on a 3D lattice Boltzmann method (LBM). A novel piecewise relaxation time is proposed to overcome numerical instability at high liquid/vapor density ratios and low liquid droplet viscosities. Simulations are carried out for low Ohnesorge (Oh) numbers in the range from 0.01 to 0.05, corresponding to a water droplet diameter in the range of 1 µm to 130 µm. The impinging droplet deformation process including breakup phenomena is illustrated on hydrophilic and hydrophobic surfaces at different Weber (We) numbers. Droplet spread factors obtained from simulations match well with existing experimental data and theoretical values, validating the accuracy of the present 3D LBM. It is found that a water droplet, after reaching its maximum spread factor, breaks up into a toroid shape with a vapor cavity or a liquid film left at its center at large We numbers on a hydrophilic and a hydrophobic surface, respectively. A map in terms of We number versus Oh number is obtained for predicting the breakup occurrence. The critical We number is monotonically increasing with the increase of the Oh number, meaning that the smaller diameter water droplet requires a larger We number for breakup. Droplet breakup is more likely to occur on a hydrophobic surface than on a hydrophilic surface at larger Oh numbers, while the behavior is opposite at lower Oh numbers.