Two-dimensional Lattice Boltzmann Method Research Articles

An improved axisymmetric interfacial lattice Boltzmann flux solver for large-density-ratio multiphase flows

In this paper, an improved axisymmetric interfacial lattice Boltzmann flux solver abandoning the previous predictor-corrector scheme is proposed. Unlike the previous model starting from the two-dimensional standard lattice Boltzmann method (LBM), the present method is developed using the axisymmetric LBM, which directly incorporates the axisymmetric effects into the distribution functions. As a result, the proposed solver does not need the corrector step involving complicated space derivatives. It makes this method simpler and more computationally efficient. In the present solver, the resultant governing equation is globally resolved by the finite volume method, while the fluxes are reconstructed by local application of the axisymmetric LBM. Therefore, the inconsistency between the local reconstruction and the global governing equation can be eliminated because the global equation can be strictly derived from the axisymmetric LBM, which holds stronger physical basis than the previous method. Numerical experiments about the interface capturing and the multiphase flows are conducted to test the proposed model. Results show that the present method is superior to the fractional step solver in terms of the accuracy, stability, and computational efficiency. In addition, this solver has the capacity of simulating large-density-ratio and complex interfacial change.

Study of sedimentation characteristics of an elliptical squirmer in a vertical channel

Abstract We used a two-dimensional lattice Boltzmann method to simulate the sedimentation motion of an elliptical squirmer in a vertical channel, taking into account the case of a circular squirmer, aiming to more realistically simulate the swimming of microorganisms in nature. The study in this was divided into two phases. The first phase comprised the numerical calculations of an elliptical squirmer with an aspect ratio of c = 2.0 and revealed three typical motion modes: steady inclined motion, wall-attraction oscillation, and large-amplitude oscillation. It was found that the formation of these three motion modes and transitions between modes are related to the pressure distribution formed between the elliptical squirmer and wall. In addition, significant differences exist between the motions of elliptical and circular squirmers. The force generated by the interaction between the elliptical squirmer and wall does not all point towards its center of mass, resulting in an additional torque on the elliptical squirmer; this is not the situation for the circular squirmer. The second phase of the study simulated squirmers with different aspect ratios (c = 1.0, c = 3.0). It was found that for an elliptical squirmer with an aspect ratio c = 3.0, the large-amplitude oscillation mode (among the above three motion modes) no longer exists. By combining the motion modes of a circular squirmer in the channel, it can be observed that as the aspect ratio c increases, the squirmer’s head direction tends to be more vertical, which may reduce the drag force during swimming.

Passive particles driven by self-propelled particle: The wake effect

This work focuses on numerically studying hydrodynamic interaction between a passive particle and a self-propelled particle, termed a squirmer, by using a two-dimensional lattice Boltzmann method (LBM). It is found that the squirmer can capture a passive particle and propel it simultaneously, provided the passive particle is situated within the squirmer’s wake. Our research shows that the critical capture distance, which determines whether the particle is captured, primarily depends on the intensity of the squirmer’s dipolarity. The stronger dipolarity of squirmer results in an increased critical capture distance. Conversely, the Reynolds number is found to have minimal influence on this interaction. Interestingly, the passive particle, when driven by the squirmer’s wake, contributes to a reduction in the squirmer’s drag. This results in a mutual acceleration for both particles. Our findings can provide valuable perspectives for formulating the principles of reducing the drag of micro-swimmers and help to achieve the goal of using micro-swimmers to transport goods without physical tethers.

Three-dimensional reconstruction and optimization of porous fuel electrode in reversible solid oxide cells based on the Lattice Boltzmann method

A reversible solid oxide cell can work as a fuel cell (FC) or an electrolyzer cell (EC) with superior efficiency in a single device, which has the potential to become the core of energy conversion and storage. Since the redox reaction occurs at the three phase boundary in the porous electrode, the microstructure of which has a significant effect on the dynamic performance of the cell. Current research on porous electrodes mainly focuses on parametric and steady-state analysis but lacks studies on dynamic performance. In this study, we investigate the mass transfer process and dynamic performance of rSOC fuel electrodes by 3D reconstruction and artificial generation combined with a two-dimensional lattice Boltzmann method. The results show that the effective diffusion coefficients and cell performance of the XCT cross-sectional and random sphere method are much higher than those of the Gaussian filter and fiber rod structure. The change in H2 concentration is larger for switching from FC to EC compared to switching from EC to FC, but the transient steady-state difference and relaxation time of the voltage is smaller. These results can be used as a reference for the design and optimization of the porous electrodes in reversible solid oxide cells.

Simulation of flow past a squirmer confined in a channel at low Reynolds numbers

The two-dimensional lattice Boltzmann method was employed to numerically investigate the flow around a circular squirmer in a channel at low Reynolds numbers. The study thoroughly examined the impact of various factors on flow structures and drag coefficients (C d) of the squirmer, such as the Reynolds number (Re), self-propelled strength (α), squirmer-type factor (β), blockage ratio (B), and orientation angle (θ). Notably, despite the low Reynolds numbers, a change in the orientation angle θ resulted in a lift in the squirmer, consequently affecting its lift coefficient (C l). The simulation findings underscored that a pair of up-down backflow regions are generated on the squirmer’s surface. Interestingly, the locations of these backflow regions varied significantly between the pusher type (β< 0), the neutral squirmer (β= 0), and the puller type (β> 0). These variations were closely tied to the pressure and velocity distributions on the surfaces of the respective squirmers. Furthermore, an increase in α might induce the formation of a new pair of backflow regions near the channel walls and subsequently elevate the C d . On the other hand, alterations in Re did not affect the flow structures but created a negative correlation with C d. Overall, the study unveiled unique dynamic characteristics, offering a contrast to the extensively investigated case of flow past a cylinder.

Channel flow boiling on hybrid wettability surface with lattice Boltzmann method

Channel flow boiling on the hybrid wettability surface is studied numerically using a two-dimensional pseudo potential lattice Boltzmann method (LBM) coupled with a thermal phase transition model. Heat transfer performance between single and hybrid wettability surfaces is compared first, and it is shown that the heat flux on the hybrid surface is higher than that of its single wettability competitor. After analyzing 36 groups of numerical results, it is found that the impacts brought by contact angle and geometrical parameters of the hybrid surface on heat flux is complex. By fixing the hydrophilic contact angle, the heat flux increases first but then decreases with the increase of hydrophobic contact angle. However, the heat flux decreases monotonously with increasing the hydrophilic contact angle under a fixed hydrophobic contact angle. The 30°/120° hybrid wettability surface shows the best heat transfer performance due to its better three-phase contact line spreading and accelerated bubble departure frequency. Aside from the contact angle, the flow boiling heat transfer performance dominated by bubble dynamics is also closely related to the widths of hydrophilic/hydrophobic regions, and there exist optimal widths under various wall superheats. Finally, the pressure drop inside channel is investigated, and it is shown that the hybrid surface is favorable to reduce pressure drop fluctuation on the premise of providing high vapor yield.

Simulation of Rayleigh convection during dichloromethane absorption by water using lattice Boltzmann method

Developing dichloromethane (DCM) waste gas purification and absorption technology is consistent with the demand of the circular economy and contributes to the goals of achieving carbon peaking and carbon neutrality. In addition, Rayleigh convection generated during the absorption of DCM by water is of great significance for understanding the interfacial mass transfer mechanism and enhancing the mass transfer efficiency. Thus, the absorption process of DCM discrete diffusion sources was simulated using the two-dimensional lattice Boltzmann method (LBM) with external forces to visualize the effect of Rayleigh convection evolution law on the mass transfer of the absorption process in this study. The concentration and velocity distribution with single or multiple diffusion sources were respectively simulated at 298.15 K and 1.00 atm. The results show that the convection structure of the simulated plume is similar to that of comparable studies, and the convective structure on both sides suppresses the development of the intermediate convective structure when convection occurs. At a constant gas-phase concentration (CB,g), the more the number of diffusion sources, the faster the convective structures integration, and the rapid integration of convective structures is associated with the sharp increasing instantaneous mass transfer flux. Meanwhile, increasing the gas phase concentration can effectively shorten the convection onset time (tc), increase the instantaneous mass transfer flux (Nins,t), and enhance the mass transfer efficiency by calculating the simulated transfer mass data. Furthermore, the critical onset time of Rayleigh convection first lengthens and then shortens with the number of diffusion sources (n) increasing. And the more the number of diffusion sources, the more significant the final cumulative (Nt) absorption amounts are. The simulation results can provide theoretical guidance for enhancing the mass transfer efficiency in the DCM absorption process.

Lattice Boltzmann modelling of colloidal suspensions drying in porous media accounting for local nanoparticle effects

A two-dimensional (2-D) double-distribution lattice Boltzmann method (LBM) is implemented to study isothermal drying of a colloidal suspension considering local nanoparticle effects. The two LBMs solve isothermal two-phase flow and nanoparticle transport, respectively. The three local nanoparticle effects on the fluid dynamics considered in this paper are viscosity increase, surface tension drop and local drying rate reduction. The proposed model is first validated by the study of the drying of a 2-D suspended colloidal droplet for two different Péclet numbers, where the evolution of the diameter squared agrees well with experimental results. The model is further validated looking at drying of a colloid in a 2-D capillary tube with two open ends. Compared with experimental results, the best agreement in terms of deposition profile and drying time is obtained when considering all three nanoparticle effects. Afterwards, we apply the model to investigate the complicated drying of a colloidal suspension in a 2-D porous asphalt, considering all three local nanoparticle effects. The drying dynamics, resultant nanoparticle transport, accumulation and deposition are first analysed for a base case. Then a parametric study is conducted varying the initial nanoparticle concentration, porous medium contact angle, nanoparticle contact angle and nanoparticle diffusion coefficient. The influence of these parameters on drying dynamics, drying rate, deposition process and final deposition configurations is analysed in detail, together with the mutual influence of local nanoparticle behaviour. Finally, a unified relation between the average drying rate and the studied parameters is proposed and verified, covering the full parameter ranges of simulations.

Effects of Compression and Porosity Gradients on Two-Phase Behavior in Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Water management within the gas diffusion layer (GDL) plays an important role in the performance of the proton exchange membrane fuel cell (PEMFC) and its reliability. The compression of the gas diffusion layer during fabrication and assembly has a significant impact on the mass transport, and the porosity gradient design of the gas diffusion layer is an essential way to improve water management. In this paper, the two-dimensional lattice Boltzmann method (LBM) is applied to investigate the two-phase behavior in gas diffusion layers with different porosity gradients under compression. Compression results in an increase in flow resistance below the ribs, prompting the appearance of the flow path of liquid water below the channel, and liquid water breaks through to the channel more quickly. GDLs with linear, multilayer, and inverted V-shaped porosity distributions with an overall porosity of 0.78 are generated to evaluate the effect of porosity gradients on the liquid water transport. The liquid water saturation values within the linear and multilayer GDLs are significantly reduced compared to that of the GDL with uniform porosity, but the liquid water within the inverted V-shaped GDL accumulates in the middle region and is more likely to cause flooding.

Lattice Boltzmann study of droplet evaporation on a heated substrate under a uniform electric field

In this paper, a two-dimensional hybrid thermal lattice Boltzmann (LB) method coupled with the leaky dielectric model was firstly presented to study droplet evaporation on a heated substrate under the influence of an electric field. Contact angle hysteresis and Marangoni effects are included. The accuracy of this model is validated by simulation a static droplet evaporation and droplet deformation in the electric field. Then, the validated model is used to explore the effects of the electrical field on droplet evaporation, by varying the electric field strength and direction. The electric field is seen to change the droplet morphology, internal flow, heat transfer and thus evaporation time. The droplet is elongated along the direction of the electric field, and the contact angle is reduced. A pair of vortices is formed inside the droplet, which is consistent with the Marangoni flow direction, while the pair of vortices outside the droplet is oriented in the opposite direction to the internal one. For all droplets, the average heat flux to the evaporating is linearly related to the contact line length density. Additionally, it is discovered that applying a vertical electric field increases the evaporation time of a sessile droplet, while applying a horizontal electric field decreases it. Our research aids in achieving precise regulation of droplet evaporation and gives a better understanding of the influence of electric fields on droplet evaporation.

The migration of viscous fish eggs in artificial reefs

Artificial reefs play a key functional role in marine ecosystem recovery and particularly in the rebuilding of fish populations. However, improving the reef design for viscous-egg-spawning fish is very challenging. Viscous eggs must adhere to a substrate to continue the hatching process, i.e., increasing the egg adhesion rate of the reef makes it a better fish spawning habitat. Therefore, the movement characteristics of viscous fish eggs in an artificial reef are a vital issue in marine ecology. In this study, a vertical two-dimensional lattice Boltzmann method was developed to simulate the complex hydraulic field in a reef zone and to predict the movement of fish eggs as affected by the hydrographic environment. A particle image velocimetry experiment on fish egg transportation was carried out to validate the model. These results revealed the effects of different hydrodynamic conditions on the migration of sticky eggs in the reef zone, to promote the sustainable development of fisheries and restore the marine ecology.

A two- and three-dimensional mesoscopic method for an updated non-homogeneous model of Newtonian and non-Newtonian nanofluids

A mesoscopic method based on a lattice Boltzmann method (LBM) for simulation of Newtonian and non-Newtonian nanofluids has been introduced. This investigation is a continuation of our recent study [G. H. R. Kefayati and A. Bassom, “A lattice Boltzmann method for single and two phase models of nanofluids: Newtonian and non-Newtonian nanofluids,” Phys. Fluids 33, 102008 (2021)], which proposed a two-dimensional LBM for a non-homogeneous model of nanofluids with Brownian diffusion and thermophoresis. Here, this model is improved by considering thermodynamic consistency, deposition rate, nanoparticle thermal dispersion, and hydrodynamic interactions around the nanoparticles, which are evaluated and reported in some thermodynamic and experimental observations. The proposed method is also developed for three-dimensional cases, applying all the above-mentioned elements. The revised macroscopic governing equations of mass (one for the carrier fluid and the other for the nanoparticles), momentum, and energy by considering the newly mentioned elements are presented, and then the proposed LBM, which has the ability to recover equations, is introduced while the derivations and proofs are provided. Different elements of the present code are validated with previous studies and demonstrated good agreement. To apply and evaluate the model in a case study, natural convection of Newtonian, shear-thinning, and viscoplastic nanofluids in a side-heated two-dimensional square enclosure and in a cubic cavity are investigated. The results for various volume fractions of nanofluids and Grashof numbers are shown in the formats of isotherms, streamlines, nanoparticle distributions, and local and average Nusselt numbers on the hot wall. In addition, the yielded/unyielded regions for viscoplastic nanofluids are defined and depicted.

Two-dimensional lattice Boltzmann method to study the influence of nucleation distance on heat flux during bubble coalescence

The lattice Boltzmann method studied the merging of double bubbles under different spacings in pool boiling. This paper analyzes the influence of bubble nucleation distance on heat transfer performance. According to the difference of nucleation distance within the scope of this article, the impact of bubble coalescence on bubble departure frequency can be divided into three regions: promotion, inhibitive, and promotion. The dynamic behavior of the bubble is linked with the heat flux, the heat flux evolution characteristics of different bubble separation distances are analyzed. The optimal nucleation distances were found to exist to achieve the maximum thermal transfer performance. The optimal distance is correlated with environmental factors such as superheat, heater length, and gravity. The main reason affecting the optimal separation distance is the bubble diameter. The larger the bubble leaves the diameter, the larger the optimal separation distance.

Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows

Rheological properties of the suspension flow, especially effective viscosity, partly depend on spatial arrangement and motion of suspended particles. It is important to consider effective viscosity from the microscopic point of view. For elliptical particles, the equilibrium position of inertial migration in confined state is unclear, and there are few studies on the relationship between dynamics of suspended particles and induced local effective viscosity distribution. Contribution of a single circular or elliptical particle flowing between parallel plates to the effective viscosity was studied, focusing on the particle–wall distance and particle rotational motion using the two-dimensional regularized lattice Boltzmann method and virtual flux method. As a result, confinement effects of the elliptical particle on the equilibrium position of inertial migration were summarized using three definitions of confinement. In addition, the effects of particle shape (aspect ratio and confinement) on the effective viscosity were assessed focusing on the particle–wall distance. The contribution of particle shape to the effective viscosity was found to be enhanced when the particle flowed near the wall. Focusing on the spatial and temporal variation of relative viscosity evaluated from wall shear stress, it was found that the spatial variation of the local relative viscosity was larger than temporal variation regardless of the aspect ratio and particle–wall distance.

Experimental and numerical studies on melting process of phase change materials (PCMs) embedded in open-cells metal foams

Of the composite PCMs that regulate temperature in thermal energy storage, metal foam is a good candidate because of its high conductivity. This paper aims to characterize the behavior of composite PCMs through the dual experimental and numerical approach. The approach takes into consideration the natural convection of PCMs and the porosity character of metal foams which is constructed by quartet structure generation set (QSGS) method. The model uses the two-dimensional lattice Boltzmann method based on the enthalpy method. The effects of foam porosity and characterized numbers on the heat transfer process in porous structures are investigated. The numerical and experimental results exhibit good agreement. The results indicates that for higher porosities of metal foams, the PCMs proves to speed up the melting rate. The significance of heat conduction in melting process of PCM in foam metal is observed. The approach adopted allows to highlight the behavior of the composite PCMs to better characterize its properties of heat-enhancement.

The study of nucleation site interactions on the mixed wettability rough surface

In order to achieve the best heat transfer performance on a mixed wettability surface, engineering of the wettability pattern is often used as heat transfer performance is significantly dependent on pitch distance between hydrophobic spots, which is maybe linked to the nucleation site interaction effects. In this work, the effects of nucleation site interactions between two hydrophobic cavities on a hydrophilic surface (a mixed wettability rough surface) are investigated, using a two-dimensional pseudopotential phase-change lattice Boltzmann method. The results of the mixed wettability rough surface are compared with completely hydrophilic rough surface and mixed wettability smooth surface to understand the effects of wettability and surface roughness. The focus is placed on the hydrodynamic interaction (which has promotive effect on the bubble formation activity) and thermal interaction (which has inhibitive effect). There exists an optimum pitch distance at which the heat flux and heat transfer coefficient are highest for mixed wettability surface, which are due to larger intensity of hydrodynamic interaction and nearly zero intensity of thermal interaction. Moreover, heat flux is found to be larger for the mixed wettability rough surface than the mixed wettability smooth surface. The bubble nucleation mechanism and time are found to be different for all surfaces.

Simulation of interfacial mass transfer process accompanied by Rayleigh convection in NaCl solution

Rayleigh convection caused by dissolved CO2 is critical for CO2 capture and storage technology in saline aquifers. However, the poor experimental measurements of theoretical model parameters limit a further analysis of the interfacial mass transfer process after the convection occurring. In this study, a two-dimensional lattice Boltzmann method (LBM) including electrostatic and volume forces is used to simulate Rayleigh convection for CO2 in a NaCl solution at 293.15 K, 1.00 atm. Through calculating the key parameter of the simulated onset time, it indicates that the CO2 interfacial concentration is only 15–20% of the saturated concentration at the true gas–liquid mass transfer interface. Besides, the simulated convective onset time would be delayed by increasing the salt concentration. The average instantaneous mass transfer factor is also decreased with the increased concentration and when the concentration of the NaCl solution is less than 3 mol L−1 (M), the mass transfer rate can be accelerated by more than 3.2 times. We propose a new method to obtain surface renewal time which is determined according to the concentration and velocity field simulated by LBM and find that changes in mass transfer rate follow the penetration theory in the molecular diffusion stage while abiding by the surface renewal theory in the interfacial convection stage. Our results can provide a valuable guide for relevant economic evaluation and appropriate geological sequestrated sites.

Lattice Boltzmann study of nucleation site interaction and nucleate boiling heat transfer on a hybrid surface with multiple cavity-pillar structures

In this work, nucleation site interaction and nucleate boiling heat transfer are studied on a hybrid rough surface, a surface with multiple cavities and a pillar on sides of each cavity, using a two-dimensional pseudopotential phase-change lattice Boltzmann method (LBM). To elucidate the effects of incorporation of pillars, the results of the hybrid rough surface are compared with a simple rough surface (a surface with multiple cavities). First, bubble nucleation, growth and departure processes are investigated above the simple and hybrid rough surfaces with three cavities and bubble interactions and their effects on cavity activation/deactivation at low superheat are discussed. The results showed a complete suppression of the central cavity at small pitch distance and left/right cavities at large pitch distance, which are caused by combined suppression effect of adjacent cavities and edge effects of the heater, respectively, for the simple rough surface. But, with the incorporation of pillars the heat transfer area is increased and the effects of induced flow are reduced, resulting in the activation of suppressed cavities, and thus, the higher heat flux is observed for the hybrid rough surface than the simple rough surface. The cavity suppression is also observed for unequal cavity depths or widths. The complete suppression of the central cavity occurs, when the central cavity is narrow or left/right cavities are deep. On the other hand, the highest heat flux is observed for the hybrid rough surface with central deep cavity and left/right shallow cavities due to the activation of all nucleation sites and additional heat transfer from the central deep cavity. Increasing pillar height or decreasing cavity-pillar spacing results in the stability and growth of residual bubbles to the next cycle without waiting periods, which increase the heat flux. Next, heat transfer in the nucleate boiling region is investigated by comparing saturated boiling curves obtained through simulations. The heat flux in the nucleate boiling including the critical heat flux (CHF) is higher for the hybrid rough surface than the simple rough surface. The heat flux also found to be increased in developing region of nucleate boiling, when pillar height is increased. The CHF increases with pillar height up to a certain height. But, with tall pillars at high wall superheats, the excessive nucleation of bubbles can also occur in the inter-pillar spacings, in addition to cavities, increasing the susceptibility of merger of closely spaced bubbles, which reduce the CHF.

Inertial focusing of neutrally buoyant particles in heterogenous suspensions

The modelling-based design of microfluidic devices leads to highly efficient process intensification, which provides insights into different temporal and spatial scales at which processes in various fields of application could be performed. This requires not only an understanding of the underlying mechanisms of different processes at the micro scale, but also the development of relevant computational tools. The macroscopic models are often unable to produce conclusive evidence for a given mechanism in systems with the complexity characterizing almost all chemical and biochemical processes. By contrast, mesoscale methods possess the unique ability to model relatively large physical systems, and, at the same time, effectively capture the essential features of the micro- and nanoscale structure, architecture, and relevant interactions. We demonstrate the feasibility and usefulness of this novel tool by considering a movement of neutrally buoyant particles in straight microchannels. The two-dimensional lattice Boltzmann method with immersed boundary conditions was used to study the influence of Reynolds number and particle diameter ratio on formation of particle trains. It was shown that an increase in particle diameter ratio leads to a less stable final particle configuration. An increase in Reynolds number was not found to significantly influence the train stability in the tested range.

Interaction between two unequal particles at intermediate Reynolds numbers: A pattern of horizontal oscillatory motion.

The two-dimensional lattice Boltzmann method (LBM) was used to study the motion of two interacting particles with different densities (ρ_{1} and ρ_{2}) and diameters (d_{1} and d_{2}), which were placed in a vertical channel under gravity. Both the density ratio (λ=ρ_{2}/ρ_{1}) and diameter ratio (r=d_{2}/d_{1}) between the particles were considered. The transition boundaries between the regime where the particles settle separately and the regime where the particles interact are identified by λ_{max}(r) and λ_{min}(r); they exhibit excellent power-law relationships with r. A pattern of horizontal oscillatory motion (HOM), characterized by a structure with a large (but light) particle right above a small (but heavy) one and strong oscillations of both particles in the horizontal direction, was revealed for r∼0.3 at intermediate Reynolds numbers. The results indicate that the magnitude of oscillations decreases with λ, whereas the frequency displays the opposite trend. A sudden increase in the terminal velocity of particles is seen, illustrating a transition from the classical pattern of drafting, kissing, and tumbling to the HOM at a certain λ. Upon increasing λ, the pattern of HOM may bifurcate into a vertical steady state at low Re or small r. Furthermore, the effects of the confinement ratio and particle-to-fluid density ratio were also examined. The existence of a critical confinement ratio is observed, beyond which the particles interact in a different manner.