Lattice Boltzmann Method Simulation Research Articles

Introducing a variable speed of sound in single-component lattice Boltzmann simulations of isothermal fluid flows

To simulate the hydrodynamics and mixing characteristics of chemical reactors by means of a lattice Boltzmann method (LBM), it is essential to consider components with varying molecular weights (and therefore speeds of sound). This option requires modification of the standard equilibrium distribution function and the use of an extended velocity set. In this paper, we show that, for isothermal incompressible single-component non-reactive flows, tuning the speed of sound with a modified equilibrium distribution and an extended velocity set allows for reproducing the proper flow characteristics with strongly reduced errors (compared to LBM simulations on standard lattices). This is done for two isothermal benchmarks, viz. a damped standing pressure wave and a decaying viscous Taylor–Green Vortex. The convergence as a function of the number of lattice nodes used improves substantially for varying values of the speed of sound.

Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model.

Lattice Boltzmann method simulations about shale gas flow in contracting nano-channels

Shale matrix consists of numerous interconnected nanoscale slit pores with size ranging from 4 nm to 200 nm, naturally resulting in variable cross-section scenarios for shale gas transport. Understanding the behavior of shale gas flow in variable cross-section channels would have practical benefits to further reveal the gas flow mechanism. Herein, using multiple-relaxation time lattice Boltzmann method (LBM) simulations, we investigate the flow characteristic of shale gas in sudden and gradual contraction channels. The influences of Knudsen number and cross-section shrinking coefficient on the shale gas transport are discussed in details. We find that the relationship between centerline velocity and Knudsen number is dependent on the gas flow regime. The nonlinear pressure deviation shows a negative correlation with the Knudsen number. The slip mass flux and the second-order permeability correlation factor are found to have positive correlations with the cross-section shrinking coefficient, demonstrating that the shale gas apparent permeability would be underestimated without considering the influence of cross-section contraction. Moreover, we reveal that the shrinking of pore channel has a great influence on Knudsen minimum effect. A high cross-section shrinking coefficient and dramatically varied cross-section type will lead to a low critical Knudsen number of Knudsen minimum effect. The LBM results and insight obtained here would be conductive to understanding shale gas transport in contracting nano-channels.

Computational analysis of magneto-hydrodynamic natural convection in partially differentially heated cavity: Effect of cooler size

This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103 ≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose.

A lattice Boltzmann method for simulation of multi-species shock accelerated flows

ABSTRACTA numerical scheme for simulating multi-species shock accelerated flows using lattice Boltzmann approach has been proposed. It uses the moment conservation approach of Yang, Shu, and Wu and extends it to multi-species fluid problems. The multi-species method of Wang et al. has been modified by use of a predictor–corrector approach. This has helped in preventing the pressure oscillations while handling multi-species. Simulation of 2D shock cylinder interaction with this solver has shown good agreement with the experimental data and could capture material discontinuity and unsteady shocks. The simulation of a single mode Richtmyer–Meshkov instability showed that the solver is able to capture the development of spike and bubble as per the experimental findings of Aure and Jacobs. The dissipation in the proposed scheme was further reduced by the use of fifth-order weighted essentially non-oscillatory (WENO). Validated with multiple problems, this method has been found to capture shock instability with good accuracy with a check on pressure oscillations.

Noise predictions of the advanced noise control fan model using lattice Boltzmann method and Ffowcs Williams–Hawkings analogy

The lattice Boltzmann method (LBM) is applied to simulate the complete three-dimensional transient flow and noise generated on the Advanced Noise Control Fan (ANCF) geometry. The ANCF is a model developed by NASA Glenn composed by a rotor–stator system enclosed by a duct. The experimental noise spectra provided by NASA at 30 microphones around the fan are used to validate the results obtained with the LBM. Overall, the predicted sound spectra pattern and the main tonal frequencies agree well with the noise measurements; in terms of tonal noise levels, the agreement varies depending on the frequency and microphone position. The noise at the 30 microphone positions is also computed by employing the porous Ffowcs Williams and Hawkings (FW–H) formulation with noise sources located on two integral surfaces placed at the ANCF openings. The good agreement obtained between the sound levels calculated with the FW–H formulation and those computed by the LBM show that the FW–H analogy may be applied in place of the LBM numerical simulation. In addition, the FW–H formulation is applied to compute the sound generation with sources located on different physical surfaces of the ANCF model such as the rotor, stator, hub, and nacelle, procedure known as noise source breakdown. A comparison of the FW–H results applied on different surfaces of the ANCF model with the noise computed by the LBM shows that most of the tonal noise levels observed at the far-field microphones (predicted by the LBM simulation) correspond to the noise sources generated on the stator vane surfaces. Such a study of the noise sources breakdown also evidences the interaction effect between the rotor and the stator, whose mechanism is the main contributor to the tonal noise generation content.

Improving wettability and preventing Li-ion batteries from thermal runaway using microchannels

Effects of using microchannels on the wettability of the porous electrodes and preventing the battery cell from thermal runaway have been studied. Two-dimensional Lattice Boltzmann Method (LBM) simulation was carried out to simulate the effects of embedded microchannels inside the electrodes on the electrolyte transport in the porous electrodes as well as their effects to lead the generated gases during thermal runaway out of the battery cell. The two-phase intermolecular potential model was utilized to investigate the microscopic behavior of the electrolyte flow in the porous electrodes. The results showed that embedding microchannels inside the electrodes significantly improves the wettability of the electrodes, especially for the electrodes with lower porosities. Furthermore, the use of microchannels inside the electrodes could considerably reduce possibility of occurrence of the thermal runaway. During thermal runaway, the electrodes with higher number of smaller microchannels could drive the generated gases out of the battery cell much quicker than the electrodes with lower number of larger microchannels.

A mesoscopic model for transient mass transfer of volatile organic compounds from porous walls of different structures

Transient mass diffusion and convection of volatile organic compounds (VOCs) from walls is an important issue for air quality in buildings. In the present work, a new model of these processes that captures mass transport within the wall structure is presented and applied for a ventilated enclosure. Porous wall structures composed of two solid phases (one carrying the VOC and one inert) and one fluid phase air are generated by the Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity. Mesoscopic scale parallel non-dimensional lattice Boltzmann method (P-NDLBM) simulations are performed for relevant ranges of wall porosity, Reynolds and Schmidt numbers for a two-dimensional enclosure with a top inlet and bottom outlets. The effect of the wall structure on mass transfer in the enclosure is investigated for two wall structures: type (A) a wall with randomly immersed particles, and type (B) a shape-separated wall structure. Results include transient VOC concentration and streamlines in the porous wall and the enclosure for a vary of porosities and diffusivities for each phase. The pore structure and porosity of the wall have significant impact on mass transfer. Type (B) structures are more favorable for rapid mass transfer within the wall.

A combined GCMC and LBM simulation method for CH4 capture in Cu-BTC particle adsorption bed

Two-dimensional Lattice Boltzmann Method (LBM) combined with grand canonical Monte Carlo (GCMC) approach is proposed to investigate the heat and mass transfer of methane (CH4) adsorption in Cu-BTC particle adsorption bed. In interfacial boundary, saturation adsorption capacities are obtained by GCMC method to replace empirical values. The diffusion and adsorption heat in particle interior are fully considered. Langmuir-Freundlich model and linear fitting formula are used to calculate the saturation adsorption capacities in Langmuir adsorption kinetics model and the adsorption heat in heat transfer in LBM model at mesoscopic level, respectively. At micro-scale level, GCMC method is used to obtain parameters of Langmuir-Freundlich and linear fitting formula. The effects of porosity and particle size on CH4 adsorption are discussed. Results show that the time for the saturation adsorption decreases with an increase in porosity and increases with increased particle size. In fluid region and particle interior, temperature peak decreases with increasing porosity and particle size. Nonuniformity of temperature exists both in fluid region and solid particles. The adsorption properties in Cu-BTC adsorption bed, such as the relation between external and internal heat and mass transfer, is predicted intuitively by GCMC and LBM combined simulation method.

Study on Gas Diffusion Layer Structure Tolerant to Flooding in PEFC by Scale Model Experiment and LBM Simulation

To improve the performance of a polymer electrolyte fuel cell (PEFC), it is essential to control liquid water behavior in the cell. Gas diffusion layer (GDL) plays an important role for the water transport. As the structure of GDL is quite complex and small with the scale order of 200 mm thickness, measurement of liquid water behavior in the GDL is difficult, and only a few results are reported with X-ray measurement and pore-network simulation. Therefore, the water transport in GDL is still unclear and there may be some room for improving the structure of GDL. The objective of this study is to evaluate the effects of different degree of isotropic fiber directions and uneven hydrophobic and hydrophilic structure of GDL for the water transport. For the analysis enlarged scale model experiment and high-speed Lattice Boltzmann Method (LBM) are applied. In the previous research of the authors, the effects of the GDL fiber direction on the cell performance was investigated using anisotropic GDL, and the results of the experiments showed that the cells with perpendicular fibers are more tolerant to flooding than cells with fibers parallel to the channel direction (1). The fiber direction is important factor for the water control in the GDL. The fiber direction perpendicular to the channel discharged liquid water under libs more smoothly. Similarly, there is a report which shows that better cell performance was obtained with the GDL with cyclic hydrophobic and hydrophilic lines (2). The fiber direction and wettability of GDL are important factors for the water control in the GDL, but the water behavior in the structures have not been observed and the effect of these factors on water transport is not clear yet. The authors proposed a scale model experiment with similarity to the actual behavior. In the experiment silicon oil is used for the liquid water and water for air. With this combination of the fluids, buoyancy effects are set similar with the actual system in enlarged models with 300 times of the actual size. Additionally, the authors have developed LBM model with high speed computation to make it possible to simulate the space covering the GDL width and channel. Figure 1 is a result comparing the scale model and LBM simulation. The figure shows the liquid water distribution in GDL. Figure 1 (a) is experimental results with an enlarged scale model and Fig. 1 (b) is simulation result by LBM. The two figures show similar water distribution. Figure 2 shows two different fiber structures with LBM simulation. Figure 2 (a) is the structure of anisotropic fiber and Fig. 2 (b) is the one of isotropic fiber. The fibers have a diameter of 8μm and orientation is set to give based on electrical resistivity with the actually measured GDLs with different isotropy. Sizes of the each GDL structure is 270μm × 270μm × 200μm and porosities is 75%. Liquid water is introduced from a hole placed at the bottom center of the boundary, which corresponds to MPL boundary. The contact angle of solid wall (GDL fibers, MPL, side wall) is set 130º. Figure 3 shows the difference in water distributions in two different fiber structures with LBM simulation. Figure 3 (a) shows the result for anisotropic and Fig.3 (b) shows the result for isotropic fiber. The water tends to spread along with fiber direction in the anisotropic GDL, whereas water transports upwards randomly in the isotropic GDL. It is known that water tends to retain in the GDL under ribs and smooth removal of the water is important to avoid flooding. The anisotropic GDL may guide the liquid water toward channel direction from under the rib, when the fiber direction is placed perpendicular to the rib direction. In the final full paper, the water transport characteristics with different fiber orientations and wettability will be demonstrated in detail. Reference (1) K. S. S. Naing, Y. Tabe, and T. Chikahisa, J. Power Sources, 196 (2011) 2584-2594. (2) A. Forner-Cuenca, J. Biesdorf, V. Manzi-Orezzoli, L. Gubler, T. J. Schmidt and P. Boillat, J. Electrochemical Society, 196 (13) F1389-F1398 (2016). Figure 1

Study on Gas Diffusion Layer Structure Tolerant to Flooding in PEFC by Scale Model Experiment and LBM Simulation

In a polymer electrolyte fuel cell (PEFC), it is important to control water drainage to supply oxygen smoothly to the catalyst layer (CL). Gas diffusion layer (GDL) plays an important role for the water management and it is significant to develop GDL’s that achieves ideal water transport. In this paper, as first step to develop the optimal GDL, the water transport in GDL’s with oriented fiber distribution and with periodic hydrophobic-hydrophilic pattern was investigated. Analysis was made by the lattice Boltzmann method (LBM) and the scale model experiment satisfying similarity conditions for the flow in GDL. In the oriented GDL, the water under rib was drained to the channel smoothly along with oriented fibers placed perpendicular to the rib. In the GDL with hydrophobic-hydrophilic pattern, the water was transported to the channel along hydrophilic band. In this case the hydrophilic region was saturated, while hydrophobic region was left water free.

Lattice Boltzmann method simulation for CuO-water nanofluid flow in a porous enclosure with hot obstacle

In this research, effect of Lorentz force on nanofluid natural convection inside a porous cavity is reported. Simulations have been done via Lattice Boltzmann Method. KKL model is employed to add Brownian motion effect on nanofluid properties. Impacts of Darcy number (Da), Rayleigh number (Ra), nanofluid volume fraction (ϕ) and Hartmann number (Ha) on heat transfer treatment are demonstrated. Outputs demonstrate that temperature gradient reduces with increase of Hartmann number but it enhances with augment of Darcy number.

A scalable interface-resolved simulation of particle-laden flow using the lattice Boltzmann method

Abstract We examine the scalable implementation of the lattice Boltzmann method (LBM) in the context of interface-resolved simulation of wall-bounded particle-laden flows. Three distinct aspects relevant to performance optimization of our lattice Boltzmann simulation are studied. First, we optimize the core sub-steps of LBM, the collision and the propagation (or streaming) sub-steps, by reviewing and implementing five different published algorithms to reduce memory loading and storing requirements to boost performance. For each, two different array storage formats are benchmarked to test effective cache utilization. Second, the vectorization of the multiple-relaxation-time collision model is discussed and our vectorized collision and propagation algorithm is presented. We find that careful use of Intel’s Advance Vector Extensions and appropriate array storage formats can significantly enhance performance. Third, in the presence of many finite-size, moving solid particles within the flow field, three different communication schemes are proposed and compared in order to optimize the treatment of fluid-solid interactions. These efforts together lead to a very efficient LBM simulation code for interface-resolved simulation of particle-laden flows. Overall, the optimized scalable code of particle-laden flow is a factor of 4.0-to-8.5 times faster than our previous implementation.

Analysis on the mechanism of evolutionary process of counter-rotating vortex pair in film cooling based on hybrid thermal lattice Boltzmann method

Massively parallel simulation applying multiple graphic processing units (multi-GPUs) is carried out to perform a deep going investigation on the counter-rotating vortex pair (CVP) in single-jet film cooling based on hybrid thermal lattice Boltzmann method (HTLBM) and large eddy simulation (LES). The mechanism of evolutionary process of CVP and its influence on the Reynolds shear stress and cooling performance are studied in detail. In the simulation, the blowing ratio of coolant jet is kept to BR=0.5 and the inclined angle is α=30°. The Reynolds number based on the crossflow velocity and diameter of the jet hole is Re=4000. The secondary anti-kidney vortices, tertiary kidney vortices and quaternary anti-kidney vortices are captured, which increase the spanwise coolant-film coverage on the surface of the bottom wall. The size of the primary CVP significantly influences the distribution of Reynolds shear stress Ruv and Ruw. The vortex strength of the primary CVP and the characteristics of minor counter-rotating vortices mainly impact on the streamwise and spanwise distribution of film cooling effectiveness, respectively.

Reducing memory requirements for large size LBM simulations on GPUs

SummaryThe scientific community in its never‐ending road of larger and more efficient computational resources is in need of more efficient implementations that can adapt efficiently on the current parallel platforms. Graphics processing units are an appropriate platform that cover some of these demands. This architecture presents a high performance with a reduced cost and an efficient power consumption. However, the memory capacity in these devices is reduced and so expensive memory transfers are necessary to deal with big problems. Today, the lattice‐Boltzmann method (LBM) has positioned as an efficient approach for Computational Fluid Dynamics simulations. Despite this method is particularly amenable to be efficiently parallelized, it is in need of a considerable memory capacity, which is the consequence of a dramatic fall in performance when dealing with large simulations. In this work, we propose some initiatives to minimize such demand of memory, which allows us to execute bigger simulations on the same platform without additional memory transfers, keeping a high performance. In particular, we present 2 new implementations, LBM‐Ghost and LBM‐Swap, which are deeply analyzed, presenting the pros and cons of each of them.

Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry

The aim of this work is the development of the lattice Boltzmann model for simulation of the mold filling process. The authors present a simplified approach to the modeling of liquid metal-gas flows with particular emphasis on the interactions between these phases. The boundary condition for momentum transfer of the moving free surface to the gaseous phase is shown. Simultaneously, the method for modeling influence of gas back pressure on a position and shape of the interfacial boundary is explained in details. The problem of the lattice Boltzmann method (LBM) stability is also analyzed. Since large differences in viscosity of both fluids are a source of the model instability, the so-called fractional step (FS) method allowing to improve the computation stability is applied. The presented solution is verified on the bases of the available reference data and the results of experiments. It is shown that the model describes properly such effects as: gas bubbles formation and air back pressure, accompanying liquid-gas flows in the casting mold. At the same time the proposed approach is easy to be implemented and characterized by a lower demand of operating memory as compared to typical LBM models of two-phase flows.

Numerical study of patterns and influencing factors on flow boiling in vertical tubes by thermal LBM simulation

Heat transfer and flow pattern of flow boiling in vertical tube are investigated numerically based on the phase-change Lattice Boltzmann method (LBM) which includes an improved pseudo-potential LB model and a thermal LB model. Two-dimensional numerical simulations are carried out under constant heat flux conditions for the first time. The processes of growth, slippage, detachment and coalescence of the bubbles are captured to verify the correctness of the model. The effects of gravity, contact angle and wall superheat on bubble departure diameter and nucleation waiting time are illustrated. The multiple flow patterns, single-phase flow, bubble flow, slug flow and DNB have been illustrated with the behaviors of bubble nucleation, growth, departure, and coalescence. Some basic features of flow boiling have been clearly observed in the simulation. The influences of several factors such as heat flux, Reynolds number, the width of flow channel, and the width of nucleation point on flow boiling especially on the point of DNB are investigated. The numerical results show that the DNB could be avoided by reducing the heating density, increasing the Reynolds number, increasing the width of the tube and reducing the heating concentration.

New Cascaded Thermal Lattice Boltzmann Method for simulations of advection-diffusion and convective heat transfer

A Cascaded Thermal Lattice Boltzmann Method (CTLBM) is presented for efficient simulations of fluid flow and heat transfer problems. Contrary to the Bhatnagar-Gross-Krook Single Relaxation Time (BGK-SRT or just BGK) and Multiple Relaxation Times (MRT) methods of the LBM used for thermal problems, the proposed CTLBM improves Galilean invariancy of the method. The cascaded collision scheme was proved to increase the stability of the LBM in the case of fluid flow. Here we prove the enhanced stability and accuracy of the CTLBM scheme for thermal problems by comparing our results to traditional thermal BGK and MRT lattice Boltzmann methods. The proposed numerical scheme employs cascaded D2Q9 model for fluid flow and cascaded D2Q5 model for the temperature to study advection diffusion of sine wave and forced convection phenomena in forced cooling of a cylinder with heated core. To validate the proposed scheme, we compare our numerical results to the exact solutions of the sine wave advection-diffusion in 1D system for Peclet numbers between 102 and 106. We also present comparisons of our CTLBM with BGK and two widely used MRT lattice Boltzmann methods for several lattice resolutions. For 2D case, we present numerical validation of forced cooling of a cylinder with heated core. To show the stability of the proposed CTLBM even for moderate lattice resolutions, we also present numerical simulations of forced convection across the row of hot tubes and double shear layer flow. The numerical simulations are faster and numerical results are in strong agreements with those available in the literature. The enhanced stability and accuracy of the cascaded scheme are clearly evident in the numerical results. Therefore, we show that the proposed CTLBM possesses higher stability and good accuracy with faster computation speed when compared to the other thermal BGK and MRT LBMs.

Lattice Boltzmann method simulation for MHD non-Darcy nanofluid free convection

Magnetohydrodynamic nanofluid convective flow in cubic porous enclosure is reported. Lattice Boltzmann Method is selected as mesoscopic approach. Brownian motion impact is taken into account via KKL model. Roles of Darcy number (Da), Hartmann number (Ha), Rayleigh number (Ra), and Al2O3 volume fraction (ϕ) are presented. Outputs are illustrated in forms of velocity contours, isokinetic energy, streamlines, isotherms and Nusselt number. Results indicate that temperature gradient over the hot surface augments with rise of Darcy numbers and ϕ while it reduces with augment of Lorentz forces. Nusselt number enhances with increase of buoyancy forces and permeability of porous media. Nanofluid motion enhances with augment of ϕ,Da,Ra while it decreases with augment of Ha.

Multiscale transport mechanism of shale gas in micro/nano-pores

A better understanding on the multiscale transport of shale gas will further the advancement of shale gas extraction. Traditional lattice Boltzmann method (LBM) simulations usually underestimate the shale gas transport capacity due to the missed consideration of gas adsorption in nanometer-sized slit pores. Here, we proposed a multiscale LB model considering the adsorption effect to simulate the shale gas transport in micro/nano-pores. The adsorption parameters between organic wall and gas molecules were determined by molecular dynamics (MD) simulations. Multiscale transport mechanism of shale gas in micro/nano slit pores ranging from nanometer to millimeter was studied by, including three different flow characteristics, namely, viscous flow, slippage, and surface diffusion. In microscale pores (pore width H>1μm), viscous flow is the dominated transport mechanism, where the velocity profile displays a typical parabolic shape without slip velocity. In larger nanoscale pores (10nm<H<1μm), slip velocity is no longer zero and increases as pore width decreases. The gas transport is dominated by viscous flow and slippage. In smaller nanometer-scale pores (H<10nm), relatively more gas molecules are adsorbed on organic pore wall, resulting in non-negligible surface diffusion which can increase the mass flux by as much as one order of magnitude. Moreover, apparent permeability obtained from our LBM simulations was compared with previous theoretical models, demonstrating the accuracy of the second-order relationship between the correlation factor and the Knudsen number.