Multi-relaxation Time Lattice Boltzmann Method Research Articles

Sensitivity analysis of natural convection in a porous cavity filled with nanofluid and equipped with horizontal fins using various optimization methods and MRT-LB

In the present study, natural convection heat transfer is investigated in a porous cavity filled with Cu/water nanofluid and equipped with horizontal fins. Optimization and sensitivity analysis of the fin’s geometry, porous medium and nanofluid properties to maximize heat transfer rate is the aim of this work. To achieve this purpose, a design space is created by input parameters which include length, number of fins, distance between fins, porosity, Darcy number and volumetric fraction of the nanoparticles. Several tools have been used to implement optimization methods including the Taguchi method (TM) for design points generation, sensitivity analysis of design variables by using signal-to-noise ratio (SNR) and analysis of variance (ANOVA), response surface method (RSM) for interpolation and regression by using nonparametric regression, and genetic algorithm (GA) for finding optimum design point. The double multi-relaxation time lattice Boltzmann method (MRT-LBM) is used to analyze and simulate the flow field and heat transfer in each design point. The results show that the optimal configuration leads to an average Nusselt number of 5.56. This optimal configuration is at the length of fins L/2, the number of fins 2, the distance between fins L/12, porosity 0.8, Darcy number 0.1, and the volumetric fraction of the nanoparticles 0.02. By using the SNR results, the Darcy number and the number of fins have the most and the least effect in maximizing the average Nusselt number, respectively. The ANOVA results and global sensitivity analysis (GSA) findings further validated this conclusion.

A machine learning based-method to generate random circle-packed porous media with the desired porosity and permeability

The generation of digital porous media facilitates the fabrication of artificial porous media and the analysis of their properties. The past random digital porous medium generation methods are unable to generate a porous medium with a specified permeability. In this work, a new method is proposed to generate a random circle-packed digital porous medium with a specified porosity and permeability. Firstly, the process of generating the random circle-packed digital porous medium with a specified porosity is detailed. Secondly, the permeability of the digital porous medium is calculated by the multi-relaxation time lattice Boltzmann method. A total of 3,000 digital porous medium samples are generated, and their microstructure data and permeabilities are prepared for the training of a convolutional neural network (CNN) model, which is then applied to effectively predict the permeability of a digital porous medium. Finally, our method is elaborated and the choice of target permeability in this method is discussed. Our approach has the potential to be applied to the generation of other types of porous media.

Suitability of body force model for pressure-difference driven flow in porous media

Pore-scale direct numerical simulation is an important tool for studying the flow of porous media nowadays. This work validates the suitability of body force model for simulating pressure-difference-driven porous flows in pore-scale simulations. The multi-relaxation time lattice Boltzmann method (MRT-LBM) with the color-gradient continuum-surface-force (CG-CSF) model is employed to calculate the absolute and relative permeability of randomly generated porous media. Results show that for single-phase flows, the relative errors are below 5% for most homogeneous porous structures while as high as 80% for structures with preferential paths. This study also reveals the pore-scale flow mechanisms and proposes a new heterogeneity parameter quantified by the standard deviation of the pressure at the boundary. For multiphase flows, errors of the body force model are significant at low Ca due to irreversible phase distribution difference appearing at the early stages. The findings of this work could be applied to other transport processes in porous media. It is crucial to consider the structural heterogeneity and proper parameters when employing the body force model in pore-scale simulations.

Three-dimensional Lattice Boltzmann study on structure optimization and heat dissipation performance of pin-fin heat sink integrated with phase change material

Phase change material (PCM) cooling is an excellent approach for reducing the excessive temperature of electronic devices. However, the heat transfer capacity of a heat sink is diminished by the low thermal conductivity of a PCM. Although this issue can be ameliorated by using extended pin-fins and nanoparticles, the latent heat storage capability of a PCM is decreased. To optimize the heat transfer efficiency of PCM heat sink with pin-fins, in this study, the effects of pin-fin shapes (circle, triangle, square, pentagon, hexagon, and octagon), novel arrangements with triangular fins, and the volume fraction of nanoparticles are investigated using the 3D enthalpy-based multi-relaxation time lattice Boltzmann method. The results showed that the PCM heat sink with triangular pin-fins exhibited optimal thermal performance due to the largest heat transmission area between the PCM and pin-fins. After conducting optimization research on triangular pin-fin arrangements, the full melt time was shortened by 14.3 % and the heat dissipation power was increased by up to 15.2 %, when compared with the PCM heat sink with triangular pin-fins. Furthermore, nanoparticles with a volume fraction of <0.1 were beneficial for balancing the elevated heat dissipation capacity and reducing the latent heat duration of the nano-enhanced PCM.

Study of magnetohydrodynamics-based-mixed convection & entropy generation within the rectangular enclosure with two obstacles for Cu-SiO2 multiwalled carbon nanotubes ternary hybrid nanofluids

This work employs the multirelaxation time lattice Boltzmann method (MRT-LBM) to investigate the heat transfer and entropy generation characteristics due to mixed convection in a rectangular enclosure with a discrete heater subjected to an external magnetic field. The enclosure contains Cu-SiO2 multiwalled Carbon nanotubes ternary nanofluid. In particular, the effect of Hartmann number (0 ≤ Ha ≤ 90), Richardson number (0≤ Ri ≤ 10), the volume fraction of nanofluids (0 ≤ ϕ ≤1), and the location of obstacles over the various aspects of thermohydrodynamics and entropy generation characteristics have been elaborated. Three cases are categorized based on the arrangement of the obstacles in the enclosure. Case 1 and Case 3 represent the alienated arrangement of the obstacles where the first obstacle is located below and above the second, respectively, while Case 2 represents the in-tandem arrangement of the obstacles. The results illustrate the reversal of flow velocity at Ha = 90 for all Ri. It is observed that case 2 is best suited for Nusselt number enhancement. It is seen that when Ri = 0.1 and 1 Case 2 and at Ri = 10, Case 1 augments heat transfer for Ha = 0.

Studying the Marangoni effect in double emulsions with a hybrid multi-relaxation time lattice Boltzmann method–finite difference method

Two-phase mass transfer is a critical process in preparing the inertial confinement fusion target microsphere. It is essential to reveal the effect of Marangoni convection on the flow and mass transfer in double emulsions to prepare high-quality microspheres. This paper develops a two-dimensional two-phase flow and mass transfer model based on multi-relaxation time lattice Boltzmann method and finite difference method. The study of the Marangoni effect within the double emulsion under a shear flow is carried out. The results indicate that the slope parameter (which measures the sensitivity of surface tension to the variation of solvent) and initial solvent concentration crucially affect the mass transfer behavior and the magnitude of the Marangoni convection of double emulsions. When the slope parameter is zero, there is no Marangoni convection in the flow field, the magnitude of the vorticity field is minimal, and solvent diffuses uniformly and slowly to the outer water phase. However, at low values of slope parameter, the Marangoni vortex formed within the emulsion is weak, and few plumes appear in the concentration field; at higher values, the magnitude of the vorticity field increases, and a large number of plumes appear and merge. Compared with the slope parameter, the mass transfer process is less sensitive to the initial solvent concentration. Plumes appear and merge at three different initial solvent concentrations. The time required for double emulsions to develop into equilibrium is inversely proportional to the initial solvent concentration.

Investigation of mass transfer model of CO2 absorption with Rayleigh convection using multi-relaxation time lattice Boltzmann method

• MRT-LBM is used to simulate CO 2 absorption with Rayleigh convection. • The characteristics of flow and concentration fields are presented. • The gas-liquid interface division results of Rayleigh convection are presented. • A penetration/surface divergence hybrid mass transfer model is proposed. CO 2 absorption into absorbents is a widely used method to reduce carbon emissions, in which the concentration gradient near the gas–liquid interface may induce Rayleigh convection (RC). Once RC occurs, the mass transfer rate will be significantly enhanced. Therefore, it is necessary to explore the mass transfer enhancement mechanism further and develop a penetration/surface divergence hybrid mass transfer model. In this study, we conduct research on the process of CO 2 absorption into ethanol with RC. Firstly, we use a multi-relaxation time lattice Boltzmann method to simulate the absorption process and obtain the flow and concentration fields. And we also verify the reliability of the numerical simulation results by comparing with the experimental results. Then, we analyze the characteristics of non-uniform flow and concentration fields in RC. Moreover, we divide the near-interface region into diffusion-dominated and convection-dominated mass transfer zones by checking whether the horizontal average velocity is greater than 1.0×10 –4 m∙s –1 . Furthermore, based on the differences in mass transfer mechanisms of the aforementioned two zones, we propose a penetration/surface divergence hybrid model to predict the instantaneous mass transfer coefficient. The prediction results demonstrate that the hybrid model can precisely predict the instantaneous mass transfer coefficient of the entire CO 2 absorption process. Our proposed hybrid model provides a promising way to deal with the complex mass transfer problems with non-uniform flow and concentration fields.

LBM study of ice nucleation induced by the collapse of cavitation bubbles

In this study, we extended the conventional lattice Boltzmann method (LBM) to numerically examine ice nucleation induced by the collapse of a cavitation bubble. Specifically, a pseudo-potential multi-relaxation-time lattice Boltzmann method (MRT-LBM) coupled with a thermal LBM and a criterion for pressure-dependent ice nucleation onset was developed to investigate the cavitation bubble dynamics including growth and collapse, and the subsequently induced ice nucleation. Using the present model, the water vapour-liquid coexistence curve was extended to temperatures lower than 42% of its critical point, excellently matching the Maxwell construction curve. Two practical application scenarios of ice nucleation were investigated: I, near a solid boundary and II, within a pressurised space. Effects of key system parameters including the stand-off distance (λ), differential pressure (Δp) and initial bubble size (R0) on the maximum collapse pressure (pmax) were examined. The results show that under the same conditions, a much higher pmax is generated in scenario II than that in scenario I, thus more readily initialises ice nucleation. After initialisation, part of the initially formed ice melts when the local temperature exceeds the ice melting temperature due to the rapid dissipation of pressure wave. To ensure the complete freezing of water, a large initial supercooling is required for scenario II.

Accurate hydrodynamic force and torque correlations for prolate spheroids from Stokes regime to high Reynolds numbers

Detailed simulations of flow around various prolate spheroids are performed using multi-relaxation time lattice Boltzmann method (LBM). The simulations are performed in the Reynolds numbers range 0.1≤Re≤2000 at different incident angles 0∘≤ϕ≤90∘ for various prolate spheroids of aspect ratios 1≤λ≤8. The Re is based on the volume equivalent sphere diameter. From the simulations, accurate correlations for average drag, lift and torque coefficients (CD, CL, and CT respectively) are proposed. The mean deviations between the correlations and the simulation data for CD, CL, and CT are 2%, 6.5%, and 4.7% respectively. Furthermore, the correlations are fitted with the physics in mind such that they can be extrapolated beyond the regimes simulated. The fits are designed such that correlations reduce to analytical (CD and CL) solutions available for prolate spheroids in the limit Re≈0. At high Re, the correlations mimic the asymptotic flattening of CD as for spheres and therefore, we expect the correlations to be valid until the critical Re (≈105). Furthermore, extensive comparison of our correlations with other high-fidelity simulations from literature demonstrate the accuracy of our work compared to other correlations from literature. This work enables researchers to perform accurate unresolved Euler-Lagrangian simulations for a wide range of elongated particles.

Simulation of Natural Convection by Multirelaxation Time Lattice Boltzmann Method in a Triangular Enclosure

The natural convection of incompressible flow confined within an enclosed right-angled triangular and isosceles cavity was investigated numerically using the multirelaxation time lattice Boltzmann method (MRT-LBM). According to the left and inclined walls thermal boundary conditions, two cases were considered in this study. In the first case, the inclined side of the enclosure was adiabatic, and the horizontal wall was heated, while the left one was kept at a cold temperature. However, the states of the left and inclined walls were interchanged in the second case. As the flow is only transported under the convection force, this study was carried out for the Rayleigh number ranging from Ra=103 to 106. The effects of the Rayleigh number on velocity and temperature profiles, streamlines, isotherms, and average Nusselt number were investigated. The position of cold and adiabatic walls had a great effect on the results. The results obtained are in good agreement with those of the literature and show the robustness of the MRT-LBM approach. In both cases, the heat-transfer rate increases with the increase in the Rayleigh number.

Natural convection in an L-shaped enclosure using multi-relaxation time lattice Boltzmann method

Natural convection in an L-shaped enclosure using multi-relaxation time lattice Boltzmann method

Multi relaxation time Lattice Boltzmann analysis of lid-driven rectangular cavity subject to various obstacle configurations

We have simulated two-dimensional laminar heat transfer in a lid-driven rectangular enclosure encapsulating heated obstacle filled with a regular viscous fluid. A square and rectangular-shaped heated blockage with different eccentric configurations is used in the physical domain to study mass and heat transfer in flow and temperature fields. We have applied D2Q9 and D2Q5 models of the Multi-Relaxation Time Lattice Boltzmann method to compute and simulate our results. The effect of dimensionless parameters like Grashof number (Gr=103, 104, 105, 106), Richardson number (Ri=0.01, 0.1, 1, 5, 10, 50, 100), Prandtl number (Pr=0.71, 1, 7) and of different eccentric placements of heated obstacle is studied on mixed convection heat transfer. The assigned value of the Reynolds number is 1000. We have also studied the impact of different aspect ratios (AR=2, 0.5, 5, 0.2) of the enclosure and the sizes of heated obstacles on fluid flow. We have also computed the local Nusselt number (Nulocal) average Nusselt number (Nu¯) along the cold wall of the enclosure.

A NEW FRACTAL APPARENT PERMEABILITY MODEL FOR LIQUID FLOW IN TORTUOUS NANOPORES FROM LATTICE BOLTZMANN SIMULATIONS TO THE THEORETICAL MODEL

Tortuous pores are ubiquitous in natural porous media; however, the linear effects of tortuosity on the liquid flow behaviors are usually considered through capillary bundle models, which lead to inaccurate permeability prediction. Additionally, in the nanopores, due to the existence of heterogeneous viscosity and boundary slip, the effects of tortuosity on nanoconfined liquid flow behaviors are more complicated. In this paper, we comprehensively use the theoretical models and a nanoscale multi-relaxation-time lattice Boltzmann method (MRT-LBM) to characterize water flow behaviors in the tortuous nanopores, where heterogeneous viscosity and boundary slip are considered. The results show that the increase of tortuosity causes more negative effects, which results in a decreasing apparent permeability. The conventional model of the influence of tortuosity on the apparent permeability is linear[Formula: see text], which greatly underestimates the effect of tortuosity on apparent permeability. Then, a new fractal apparent permeability model [Formula: see text] based on modified tortuous effects is obtained by fitting the results from the MRT-LBM simulations. Based on the new fractal apparent permeability models, the results show that with an increasing fractal tortuosity dimension, the apparent permeability decreases rapidly first and then this trend becomes moderate. Our works can provide a more accurate basic model for studying liquid flow in porous media based on the capillary bundle model or pore network model.

A simulation method for muscle-driven swimming and its applications

A novel muscle-driven method (MDM) with its corresponding Compute Unified Device Architecture parallel computational code is newly developed to mimic shortening and lengthening of muscles, in a fish-like swimming body, which causes the body flapping in the transversal direction and create a thrust force to propel the body to cruise in the longitudinal direction. In this method, the fish body is discretized as mass points connected by elastic springs and muscle deformation is critically realized by using a constraint algorithm, called RATTLE, to control relative deformation distances between neighboring mass points of the muscles, while turbulent fluids are treated by a multi-relaxation time lattice Boltzmann method with a large eddy simulation. A validation for the MDM is extensively conducted by comparing our simulation results with the existing experimental and theoretical results. Subsequently, the frequency, amplitude, and wavelength of lengthening of muscles and the stiffness and mass density of the body are systematically varied at different levels and their effects on flapping and cruising motion and flow structures are studied at different Reynolds numbers.

Multiphase and Pore Scale Modeling on Catalyst Layer of High-Temperature Polymer Electrolyte Membrane Fuel Cell

Phosphoric acid as the electrolyte in high-temperature polymer electrolyte membrane fuel cell plays an essential role in its performance and lifetime. Maldistribution of phosphoric acid in the catalyst layer (CL) may result in performance degradation. In the present study, pore-scale simulations were carried out to investigate phosphoric acid’s multiphase flow in a cathode CL. A reconstructed CL model was built using focused ion beam-SEM images, where distributions of pore, carbon support, binder, and catalyst particles can be identified. The multi-relaxation time lattice Boltzmann method was employed to simulate phosphoric acid invading and leaching from the membrane into the CL during the membrane electrode assembly fabrication process. The predicted redistribution of phosphoric acid indicates that phosphoric acid of low viscosity or low wettability is prone to leaching into the CL. The effective transport properties and the active electrochemical active surface area (ECSA) were computed using a pore-scale model. They were subsequently used in a macroscopic model to evaluate the cell performance. A parametric study shows that cell performance first increases with increasing phosphoric acid content due to the increase of ECSA. However, further increasing phosphoric acid content results in performance degradation due to mass transfer limitation caused by acid flooding.

Simulating the molecular density distribution during multi-phase fluid intrusion in heterogeneous media

A computational recovery of multi-phase intrusion was discussed with the modified multi-relaxation time Lattice Boltzmann method (MRT-LBM). Originally proposed dual-matrix computation is developed to address the different phase separation and interface tracking for the multi-phase problem. A comprehensive validation is performed with the previously theorized observation of the mercury-water system. Results show that the dual-matrix computation is feasible to provide converged output under narrowed density difference down to 18%. The wetting and non-wetting behaviour resulted from form solid–fluid interaction is realized with arbitrary boundaries, in which the contact variance is up to 4.14%. The linear relations described by Laplace's law and Washburn's equation were three-dimensionally recovered with determination coefficients of 96.34% and 94.19%, respectively. A third fluid intrusion status of partial-intrusion is captured in addition to complete-intrusion and non-occupation in porous boundary, demonstrating the advanced function of the phase-separation and interface tracking in problems with further increased heterogeneity.

Investigation of critical non-linear flow behavior for fractures with different degrees of fractal roughness

Non-linear flow behavior in rough fractures with shear dislocations is numerically investigated in this study with the validated multi-relaxation time lattice Boltzmann method. Fracture flow tests with different degrees of fractal roughness are simulated and the results show that the surface roughness has an inhibiting effect on fracture flow. With increasing roughness parameter, the effective transmissivity decreases accordingly. Deviation of fracture flow from the linear regime appears earlier for fractures with rougher surfaces and the non-linearity of fracture flow is enhanced with the tortuous flow-path and corner eddies during the closure process. The non-linearity of fracture flow was found to be anisotropic when applying the pressure gradient parallel and perpendicular to the shear direction. Though the anisotropic feature shows a non-monotonic trend during the closure process, it is enhanced with the increasing roughness parameter. Evaluation of the Forchheimer law in quantifying the non-linear fracture flow is also conducted. The relative difference between the Forchheimer linear transmissivity and intrinsic linear transmissivity is about 1–3%. Assuming that the Forchheimer linear transmissivity is equal to intrinsic linear transmissivity, the linear pressure drop can be underestimated. Relating the non-linear parameters with the dimensionless effective hydraulic aperture, a new model is proposed to predict the critical hydraulic behavior of rough fractures.

Innovations in Non-Linear Oscillations of a Pendent Drop From a Capillary Tip During Formation and Detachment - An LBM Simulation

Individual drops are suitable tools to study the liquid-fluid interfacial properties. In this work, forcedisplacement equation and non-linear oscillations of a pendent drop are numerically investigated. The presented novel force-displacement function allows following the dynamics of a pendent drop and realizing its elastic behavior. The growth and detachment of drop, which is pending due to gravity from a capillary tip, is considered (assuming high density and high viscosity ratios and immiscible two-phase flows). Twodimensional multi-relaxation time lattice Boltzmann method (MRT-LBM) was used to simulate growth, detachment, and oscillations of the drop using a conservative model for high-density ratio. The forcedisplacement function of a pendent drop (FDFPD), which is non-linear, was introduced. Using FDFPD, the non-linear elastic specifications of the pendent drop were determined. It was realized that the drop shows three different elastic behaviors simultaneously (hardening, linear, and softening). The drop superharmonic and subharmonic frequencies were calculated, using the natural frequency of the linear portion of FDFPD. Besides, the drop would grow as long as its displacement is between the extrema of FDFPD. In addition, a dynamic criterion for the onset of detachment was established. Also, increasing the Bond number from 0.11 to 1.96, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the linear portion of FDFPD. It was shown that increasing Capillary number from 1.8E-5 to 7.3E-4, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the non-linear portions of FDFPD.

Direct numerical simulations of turbulent periodic-hill flows with mass-conserving lattice Boltzmann method

The multi-relaxation time lattice Boltzmann method is used to perform direct numerical simulations of laminar and turbulent pressure-driven flows within a channel with hill-shape periodic constriction for the first time. The simulations are conducted on a graphics processing unit cluster with two-dimensional domain decomposition to accelerate the computation. The hill-shape boundary is represented using the interpolated bounce back scheme. However, the scheme generates mass leakage across the boundary, which is more pronounced in the turbulent flow regime, and this may produce diverging solutions for turbulent flows. The mass leakage due to the local mass imbalance along the curved boundary is solved by modifying the distribution functions locally or globally, and both predict similar velocity distributions. Since the global correction method is more computing time-consuming, the local correction method is adopted. The present numerical implementation’s capability is first validated by performing direct numerical simulations of turbulent channel flow at Reτ = 180, and the current predicted results agree well with the benchmark solutions. Direct numerical simulations are further conducted for the turbulent flow over the periodic hill at Reh = 2800. Both the mean velocity and turbulent stress compare favorably with the benchmark solutions. The present simulation also correctly predicts the turbulence splatting effect near the windward hill. Both phenomena are in good accordance with the benchmark solutions.

Effect of Inlet Air Locations on Particle Concentration using Large Eddy Simulation based on Multi Relaxation Time Lattice Boltzmann Method

In this work, turbulent indoor airflow was considered by Large Eddy Simulation (LES) based on Multi Relaxation Time Lattice Boltzmann Method (MRT-LBM). The Lagrangian approach was utilized to investigate the effect of inlet air location on transport and concentration of different sizes of particles (1-10 µm) in a modeled room. Simulation results showed that for the displacement ventilation system with the inlet air register on the floor, the number of 10µm particles that exit through the outlet is more than the case for the mixing ventilation system with the inlet register on the ceiling. Also, for the latter case, when the inlet air is on the ceiling, the number of suspended 10µm particles in the room is less than for the displacement ventilation system with inlet register on the floor. In addition, the results showed that the location of the inlet air register does not have a considerable effect on the small 1µm particle motion, and the numbers of the particles that remain suspended in the room are roughly the same for both ventilation systems.