Lattice Boltzmann Method Approach Research Articles

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

Integration of vorticity–velocity formulation in a lattice Boltzmann method for porous media

A lattice Boltzmann method (LBM) is proposed to address the two-dimensional macroscopic equations of velocity–vorticity for porous media in incompressible flows. The macroscopic equations of two-dimensional porous media using the representative element volume scale approach, employing various models, are shown. The momentum equations are transformed and presented in the velocity and vorticity format. Additionally, the energy and concentration equations are thoroughly examined. Subsequently, the LBM is presented to restore the dimensional macroscopic equations of the velocity–vorticity format for various porous models, accounting for external forces. The paper provides proof and derivations of the equations for the LBM, which are then demonstrated and discussed. The suggested approach is evaluated across a variety of well-established benchmark examples within the realm of fluid flow, heat, and mass transfer in porous media. Importantly, the LBM approach significantly reduces computational time compared to previous methods in the field by eliminating pressure in the momentum equation, thereby reducing the number of unknown variables and transforming the equation into a convection–diffusion form. This modification leads to a linear equilibrium distribution function and a noteworthy decrease in computational costs.

Numerical simulation of the flow and output of a Savonius hydraulic turbine using the lattice Boltzmann method

The flow and output of a Savonius hydraulic turbine rotor were simulated using the lattice Boltzmann method (LBM). The rotor, characterized by a configuration featuring two semi-circular arc-shaped blades, operated at a Reynolds number of 1.1 × 105. The simulations were conducted in a two-dimensional domain, focusing on the incompressible flow within the cross-sectional area of the rotor perpendicular to its rotational axis. The LBM approach was coupled with a rotor rotation analysis. In the LBM framework, the non-orthogonal central moment model was employed for the precise computation of particle collisions. Additionally, the direct forcing method was used to consider the rotating blades and shaft. Consequently, the torque exerted on both advancing and returning blades and rotor output was successfully simulated. These simulations unveiled the inherently unsteady rotational behavior of the rotor, stemming from the variable torque acting upon the blades. Moreover, the computational results exhibited a notable agreement between the simulated flow pattern around the rotor and the experimental visualization. Furthermore, an approximately identical correlation between the rotor speed and power output was established, mirroring the experimental results. These findings underscore the robust applicability of LBM in facilitating the design and operational analysis of Savonius hydraulic turbines.

Swirling flow of two immiscible fluids in a cylindrical container: Lattice Boltzmann and volume-of-fluid study

An experimental and numerical study of a multicomponent swirl flow of a liquid in a closed cylinder is carried out for various values of the relative cylinder elongation and the Reynolds number. The experimental technique for flow characteristics measurement is based on the PIV (particle image velocimetry) technique. To study the flow characteristics in detail, we simulated the problem numerically using the Palabos and Basilisk software open-source packages. The current implementation of the Palabos package uses the LBM (lattice Boltzmann method) approach, in which the collision integral is determined by the MRT (multiple-relaxation-time) approximation, and the intercomponent interaction is established according to the Shan–Chen pseudopotential approximation. The Basilisk package uses VOF (volume-of-fluid) approach to approximate the fluid interface. In this paper, for the first time, the data considering the emergence conditions for the zone of axial isolated recirculation in a multicomponent vortex flow were obtained at different viscosity ratios of two fluids. It is shown that with a decrease in the viscosities ratio, the recirculation zone existence curve shifts closer to that corresponding to the case of a one-component flow. In the course of numerical analysis, we found that both numerical implementations of this problem describe flow characteristics with high accuracy. Both methods recreate the recirculation zone on the cylinder axis observed experimentally. However, the velocity shift on the interface is observed only in the LBM approach.

Hydrothermal behavior of nanofluid flow in a microscale backward-facing step equipped with dimples and ribs; Lattice Boltzmann method approach

Hydrothermal behavior of nanofluid flow in a microscale backward-facing step equipped with dimples and ribs; Lattice Boltzmann method approach

Mesh-Free Analysis of a Vertical Axis Wind Turbine Using Lattice Boltzmann Method and Various Turbulence Models

This study aims to investigate the aerodynamic analysis of a Darrieus-type vertical axis wind turbine (VAWT) using the Lattice Boltzmann Method (LBM). The objective is to assess the accuracy and performance of the meshless LBM approach in predicting torque coefficients, velocity, turbulence intensity, and vorticity distributions for VAWT aerodynamic analysis. Two turbulence modelling approaches, Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS), are employed to model the flow domain. The central problem revolves around comparing the performance of different turbulence models based on their agreement with experimental results for power and torque coefficients. The findings demonstrate the effectiveness of the WALE turbulence model in achieving the best agreement with experimental data. Overall, the study provides valuable insights into applying LBM in VAWT aerodynamic analysis and highlights the advantages of the meshless approach compared to traditional CFD methods.

Numerical approach to simulate placement of wellbore plugging materials using the Lattice Boltzmann method

An approach is introduced using the multi-component lattice Boltzmann method (LBM) to numerically simulate multi-layered wellbore plug placement and investigate the effects of the rheological and physical properties of cement slurry and bentonite clay gel as plugging materials. As a proof of concept, this approach is applied to simulate the placement of a layer of cement slurry within a layer of bentonite clay gel to form three distinct alternating material layers in a wellbore. Prior to investigating this system, the LBM approach is validated through physical lab-scale plug placement tests. Then, a computational field-scale case study is examined to evaluate how variations in plug material properties and placement processes affect the resulting multi-layered wellbore plug. The analyses show that cement slurry density is the property that most affects the wellbore plugging process. At lower concentrations of bentonite clay gel, more cement slurry is needed to create the three-layer system, since the cement slurry penetrates further into the bentonite clay gel. Alternatively, for high concentrations of bentonite clay gel, higher density cement slurry can be placed as a distinct layer without having a significant increase in the amount of cement slurry needing to be pumped. For the cases considered, variations in yield stress and viscosity of the cement slurry have negligible effects on the plugging process. Lastly, although the pumping velocity controls the rate of cement slurry layer placement, it has a relatively small effect on the placement process. Overall, the LBM approach is shown to be an effective method to evaluate wellbore multi-layered plugging processes.

Unsteady characteristics of pressure and swirl distortion in helicopter intake: A lattice Boltzmann method approach

The present paper focuses on the analysis of the unsteady characteristics of pressure and swirl distortion and their relationship inside a complex air intake, including a plenum chamber, using Large-Eddy Simulation based on the lattice Boltzmann method (LBM). The steady-state analysis of the pressure field and swirl angle in the Aerodynamic Interface Plane (AIP) shows a complex pressure and swirl distortion pattern, as well as a high level of unsteadiness. Additionally, two vortical structures with equal intensity located on the top and bottom sides of the AIP plane were identified. The unsteady pressure distortion analysis highlighted fluctuations between two positions of the maximum circumferential pressure distortion in the AIP plane. One of these positions presents mean and peak distortion values lower than the other position. Furthermore, an alternating vortex pattern between two swirl patterns in the AIP plane is also identified. Finally, the relationship between pressure and swirl unsteadiness was investigated, and a link between the swirl distortion pattern and pressure distortion was identified. The identification of this relationship will allow geometrical changes in the air intake, leading to a reduction of the average circumferential distortion level, as well as a reduction of the maximum peak level achievable during a flight phase.

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.

Coupling of first collision source method with Lattice Boltzmann Method for the solution of neutron transport equation

Despite significant progress in the solution of Neutron Transport Equation (NTE) using Lattice Boltzmann Method (LBM), it suffers from the ray effect a problem similar to SN methods. The ray effect is prominent in the problems where source is localized and medium has low scattering cross-section. Due to ray effect spatial distortion in the scalar flux and angular flux is observed. This effect arises because NTE is solved in discrete directions, allowing neutrons to travel only in a few directions. Therefore, first collision source (FCS) method is applied for SN method. Presently, FCS method is applied to LBM and result are obtained for two-dimensional source problems. It is observed that by applying FCS to LBM, ray effect is mitigated. Compared to SN method, LBM approach is relatively simple in implementation and can be effectively used. Therefore, it has potential to provide easy and convenient solution of neutron transport equation.

Lattice Boltzmann approach for the fluid-structure interaction of a neo-Hookean medium.

In this paper, a lattice Boltzmann method (LBM) for the fluid-structure interaction of an incompressible neo-Hookean medium is proposed. The objective is to use the lattice Boltzmann method to model the fluid and the solid domains at the same time, and thus avoid coupling two solvers, one for the fluid and one for the structure. The specific case of a neo-Hookean incompressible medium allows us to use a Eulerian formulation for the structure problem, which resembles the Navier-Stokes equation. Then, a macroscopic multiphase equationcan be used to model the fluid and structure problems together. Next, the LBM approach is deduced from this macroscopic multiphase formulation of the fluid-structure interaction problem. It consists in extending the LBM to the solid domain by adding a tensor term in the equilibrium function of the collision operator. The effect of the added tensor term is to cancel in the solid domain the viscous fluid constraints and add neo-Hookean constraints. Thus, only the third moment of the LBM is modified, the first two being conserved, and only the constraints in the macroscopic Navier-Stokes equationare changed. The LBM scheme obtained can then model the interaction of a fluid and a structure composed of an incompressible neo-Hookean medium with a single solver for the fluid and the solid. Two additional equationsare used, one to track the fluid and solid domains with the Cahn-Hilliard equation, and the other to compute the solid displacement field by a finite-difference scheme. The proposed method is applied successfully on three cases from the literature.

Permeability prediction of low-resolution porous media images using autoencoder-based convolutional neural network

Permeability prediction of porous media from numerical approaches is an important supplement for experimental measurements with the benefits of being more economical and efficient. However, the accuracy and reliability of traditional numerical approaches are strongly dependent on the high-resolution images of porous media, which greatly limits their implementation for engineering applications. Herein, a semi-supervised machine learning approach is proposed to predict the permeability of porous media from low-resolution images. This approach consists of an autoencoder (AE) module trained with unlabeled data to assist the backbone convolutional neural network (CNN) in the prediction by providing a mapping of the low-resolution porous media to high-resolution features. The low-resolution information from CNN trained with small amount of labeled data and high-resolution information from AE trained with larger amount of unlabeled data are comprehensively considered in this approach. The prediction performance of AE-CNN from low-resolution images is examined against the results from traditional approaches of CNN and lattice Boltzmann method (LBM) by the mean-square errors (MSE) and R-Squared (R2) calculations. Using 5-fold cross-validation method, the average value of R2 is 0.896 on the test dataset by AE-CNN, compared to 0.869 for the traditional CNN without the AE. The MSEs for AE-CNN are 0.022 and 0.064 on the training and test datasets respectively in the best-performance fold, while without AE, the MSEs for only CNN are 0.034 and 0.083 on the training and test datasets respectively in the best-performance fold, implying that AE modules can substantially improve the prediction performance from low-resolution images of porous media. As for the simulation results of LBM approach, its prediction reliability (average R2: 0.42; MSE: 0.37 and 0.36 in the best-performance fold) is extremely lower than that of CNN-based machine learning algorithms owing to huge numerical error at the blurred boundaries of low-resolution images.

Aerodynamic analysis of hospital ventilation according to seasonal variations. A simulation approach to prevent airborne viral transmission pathway during Covid-19 pandemic.

During the Covid-19 pandemic, location of the SARS-CoV-2 infected patients inside the hospital is a major issue to prevent viral cross-transmission. The objective of this study was to evaluate the risk of contamination through aerosol by using a global approach of the multiple environmental parameters to simulate, including seasonal context. A computational fluid dynamic (CFD) simulation based on the Lattice Boltzmann Method approach was used to predict airflow on the entire floor of a private hospital in Paris. The risk of contamination outside the rooms was evaluated by using a water vapor mass fraction tracker. Finally, the air contamination was estimated by a “cough model” producing several punctual emissions of contaminated air from potentially infected patients. In a winter configuration, the simulation showed a well-balanced ventilation on the floor and especially inside the rooms. After cough emissions from COVID-positive rooms, no significant contamination was observed in the circulation area, public waiting space and nurse office. On the contrary, in a summer configuration, the temperature difference due to the impact of the sun radiation between both sides of the building created additional air transport increasing the contamination risk in neighboring rooms and public spaces. Airborne spread was limited to rooms during winter conditions. On the contrary, during summer conditions, market airflow with potentially contaminated air coming from rooms located on the side of the building exposed to solar radiation was evidenced. These observations have implications to locate infected patients inside the building and for the conception of future health care structures.

Practical aspects of absolute permeability finding for the lattice Boltzmann method and pore network modeling

The importance of pore-scale models deals with their ability to estimate macroscopic parameters such as capillary pressure, absolute and relative permeabilities that are important input data of any reservoir model while studying the microscopic structure of the given samples.The current paper aims to discuss practical aspects of two widely applied techniques for absolute permeability estimation, lattice Boltzmann method (LBM) and pore network modeling. Both approaches analyzed three sandstone and one carbonate samples with different pore structures from the open database of Imperial College London. First, a direct pore-scale modeling via LBM approach was built based on the single relaxation time concept. Later on, pore networks were extracted by using the fast and efficient SNOW algorithm which could be considered as an improved version of a well-known watershed segmentation approach. The paper does not only compare the accuracy of two methods, but rather summarize in which cases a direct pore-scale modeling can be substituted by the simplified pore network approach. It also highlights importance of new insights, for instance, consideration of image resolution and representative elementary volume of the samples as a part of their analysis.Results demonstrate that direct pore-scale modeling allowed to reach a reasonable accuracy in absolute permeability estimation for three studied sandstone samples, although this method will not properly work for bigger pore volume while running simulations on CPU. At the same time, pore networks were able to find values of absolute permeability with reasonably low errors for all samples by varying the filtering parameters while preparing images.

A Lattice-Boltzmann-based perturbation method

In this work, we report on the development and initial validation of a new hybrid numerical model for the simulation of incompressible flow. A kinetic Lattice Boltzmann method (LBM) model using a reduced domain is nested within an inviscid flow field to provide increased simulation fidelity where desired, while leveraging the computational efficiency of inviscid solutions. We formulate a fully (or strongly) coupled approach, in which a Helmholtz decomposition is applied to the flow, separating the inviscid and viscous perturbation parts. The latter component is driven by the inviscid field through nonlinear inviscid-perturbation interaction terms that, in conventional Navier-Stokes solvers, would be expressed as volume forces. In the present work an equivalent LBM approach is presented where, as opposed to a body-force coupling, a strong coupling within the LBM collision operators is presented. The resulting hybrid LBM is applied to validation cases for a wave driven boundary layer and the flow past a cylinder.

Particle-resolved direct numerical simulation of collisions of bidisperse inertial particles in a homogeneous isotropic turbulence

A particle-resolved study of a collision system composed of heavy particles and light particles in a homogeneous isotropic turbulence has been performed. Direct numerical simulations (DNS) of this system were conducted using lattice Boltzmann method (LBM). The effects of hydrodynamics on the collision particles were accounted by directly resolving the flow around finite-size particles with an interpolated bounce-back scheme. A large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. Both kinematic and dynamic collision kernels were evaluated to study the correlation of total collision events and turbulent kinetic energy (TKE) dissipation rate. The results show that collisions between particles increase with the increase of TKE dissipation rate as radial relative velocities between particles increase with it. It is found that the dynamic collision kernels do not match with the kinematic collision kernels which is derived from point-particle method. Quantitatively, they were approximately 4 to 10 times smaller than the corresponding dynamic collision kernels. Therefore, it is not reasonable to estimate the kinematic collision kernel in particle-resolved simulations as its rationales are not valid. However, the collision behavior can still be accounted for by means of the dynamic collision kernel since it is obtained from the direct statistical analysis of the collision events.

Lattice Boltzmann study of flow pulsation on heat transfer augmentation in a louvered microchannel heat sink

The present study reports the effects of flow pulsation on laminar forced convective heat transfer in an innovative louvered microchannel heat sink (MCHS) with lattice Boltzmann method (LBM). Two to eight louver-like microstructures are arranged in tandem within a microchannel, corresponding to a pitch ratio (PR) of 0.25 to 1.75. The Reynolds number (Re) based on channel hydraulic diameter and periodically averaged bulk mean velocity ranges from 100 to 300. The pulsating inlet velocity is in triangular waveform with Strouhal number (St) varying from 0 to 2.8. In terms of numerical models, a double distribution function LBM approach is employed for modeling both fluid flow and heat transfer. Simulation results show that the profiles of Nusselt number (Nu) and Fanning friction factor (f) with St are all multi-peak for the present louvered MCHS. This finding is different from the previous single-peak trend. The correlations of overall Nu and f ratios (Nu¯/Nu0 and f¯/f0) versus Re, PR, and St for the present MCHS are established for the first time. Furthermore, the present design attains a maximum Nu¯/Nu0 of 6.16 at St = 1.8, PR = 0.58, and Re = 300, which is the highest for f¯/f0<50 among previously reported ribbed and baffled MCHSs.

Numerical Study of Mass Transport and Electrochemical Kinetics inside Porous Structure Layers of PEMFC Using Direct Simulation Approach

The enhancement of the mass transports in porous layers of a polymer electrolyte fuel cells (PEFCs) is essential for developing material and design system to improve the PEFC performance and durability. The oxygen transport resistance is a large fraction of the mass-transport overpotential at the cathode. Condensed water in the flow field and porous layers reduces oxygen transport to the oxygen reduction reaction (ORR) region. Experimental investigation of locally saturated porous media in the operating cell is difficult. The Computational Fluid Dynamics (CFD) is mathematical modeling tool, which can be considered the incorporation of theory and experimentation in the field of kinetics, heat, and mass transport of the PEFCs. The purpose of this work is to use direct modeling-based, Lattice Boltzmann Method (LBM) within the detailed structure of porous layers to understand the kinetics and multi-scalar/multi-physics transports in a polymer electrolyte fuel cells (PEFCs). The model geometries consist of gas diffusion layer (GDL), micro porous layer (MPL), and Catalyst layer (CL), as shown in Fig. 1. The studies include the understanding of water evolution, water saturation, breakthrough pressure, heat transfer, species transport, and electrochemical kinetics inside porous layers under different conditions and situations that could occur in fuel cells. This work will show the enhancement of direct CFD simulation with LBM (CFD-LBM) approach [1-4], which incorporates with detailed structure of porous and catalyst layers from both micro- and nano- X-ray CT. This approach will consist of the kinetic model in the catalyst layer, which will involve coupling electrochemical kinetic to investigate the electrical potentials, electrical current, electron transfer, and exchange current in the catalyst layers, as shown in Fig. 2. The output of this work will be used for the optimization of catalyst layer thickness, with durability and water management improvement, for novel porous materials, particularly in the catalyst layer.

Accurate meso-scale simulation of mixed convective heat transfer in a porous media for a vented square with hot elliptic obstacle: An LBM approach

In the present study, heat and fluid flow of water in a vented cavity with elliptical hot obstacle is numerically investigated using Lattice Boltzmann Method (LBM). This flow is assumed to be laminar, 2D and incompressible. The main purpose in this work is to investigate the effect of utilizing porous medium on mixed convective heat transfer in an obstructed vented cavity. The simulations are performed for Richardson number of 0.1, 1 and 10, porosity of 0.5, 0.7 and 0.9, and solid-to-fluid conductivity ratios of 10, 33.3, 66.7 and 100. The results are presented by streamlines, temperature contours, and Nusselt number curves. Results show that by increasing Richardson number, due to the dominance of natural convective heat transfer compared with that of the forced case, the heat penetration in fluid layers in all areas of the cavity is increased. Moreover, as the Richardson number increases, due to limitation of forced heat transfer, the temperature gradients in the cavity rise and the growth of thermal boundary layer becomes significant. This behavior has an undesirable effect on heat transfer of hot obstacle especially around the cavity outlet and right side of the obstacle. By decreasing the cavity porosity, the areas around the hot obstacle will experience higher heat penetration into the fluid and consequently the heat transfer is reduced. In this study, the highest Nusselt number is obtained for Richardson number of Ri=0.1 and porosity of Po=0.5 and the increase in Richardson number and porosity coefficient results in reduced Nusselt number in all areas around the hot obstacle. The porosity changes have more significant effect on heat transfer in smaller Richardson numbers. This results in Nusselt number higher about 79% in best condition at conductivity ratio of 33.33 (Ri=0.1) while it changes the Nusselt number about 17.4% at conductivity ratio of 10 (Ri=10).

Lattice Boltzmann simulation of intraparticle diffusivity in porous pellets with macro-mesopore structure

Intraparticle diffusion inside porous pellets plays a controlling step in most reactive transport processes. In order to investigate microscopic diffusion process in porous pellets with macro-mesopore structure, a three-dimensional lattice Boltzmann method (LBM) approach with multi-relaxation-time (MRT) collision operator was utilized to calculate the intraparticle diffusivity. With respect to the hierarchical pore structure, the modified random generation of macro-meso pores (RGMMP) algorithm was proposed to obtain pore structure of porous pellets. In this work, a resin catalyst that has macro-mesopore structure was selected as a validation example. Based on the LBM approach, the effects of four geometrical parameters of the modified RGMMP algorithm on the intraparticle diffusivity, namely the total porosity, the ratio of mesopore porosity to macropore porosity, the ratio of average macropore diameter to mesopore diameter and the macropore growth direction were investigated, so as to elucidate the mass transfer mechanism in porous pellets with macro-mesopore structure. These theoretical findings are useful for the pore structure optimization design of porous pellets with macro-mesopore structure.