Pseudopotential Lattice Boltzmann Research Articles

Numerical study of flow boiling on microcavity surface under the action of an electric field using lattice Boltzmann method

The microcavity setting promotes bubble nucleation, and the presence of an electric field enables bubble detachment. In this study, the synergistic effect of electric field and microcavity in improved flow boiling heat transfer was analyzed based on the pseudopotential lattice Boltzmann method. The investigation was focused on the influence of wall superheat, Reynolds (Re) number, electric field intensity, liquid subcooling, and gravitational acceleration on the flow boiling performance under two forms of electric field distributions for uniform conducting microcavity surface (MC–UCS) and conducting–insulating microcavity surface (MC–CIS). Compared with the MC–UCS, the MC–CIS maintained a stable wetting state in the microcavity through inhibition of sliding and merging of bubbles. The increase in electric field intensity and Re number improved convective heat transfer in the microcavity but at the expense of a larger frictional pressure drop. The boiling phenomenon on the microcavity surface weakened with the increase in liquid subcooling, which caused difficulty for the electric field to improve the heat transfer performance by improving bubble behavior. Electrical force can replace buoyancy force to perturb the vapor–liquid interface under low gravitational acceleration. This condition allows the fluid shear force to drive bubbles away from the microcavity surface quickly. The results can provide theoretical and technical guidance for the realization of the enhanced synergistic heat transfer between electric fields and microstructures.

Three-dimensional central-moment pseudopotential lattice Boltzmann model with improved discrete additional term

In this work, a three-dimensional central-moment pseudopotential lattice Boltzmann model is developed to simulate a two-phase flow and wetting phenomena. In this model, an improved discrete additional term is proposed to regulate the thermodynamic consistency and surface tension. Different from the discrete additional terms in previous models where only low-order terms are derived at the macroscopic Navier–Stokes equation level, high-order terms are correctly constructed at the mesoscopic lattice Boltzmann equation level in the present improved discrete additional term so that the high-order central moments can be modified in the collision step. With the improved discrete additional term, the simple relationship between the interaction force and the pseudopotential functions is well preserved. On this basis, a simplified wetting boundary scheme is further proposed, which eliminates the complex process for choosing proper characteristic vectors and interpolation. Numerical simulations demonstrate that the proposed model can achieve better performance in thermodynamic consistency, Galilean invariance, numerical stability and computational efficiency, and have great ability to simulate two-phase flow and wetting phenomena on realistic conditions.

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

Three-dimensional mesoscopic investigation of directional coalescence of two droplets impacting on a wall with wettability difference

In this work, a three-dimensional (3D) nonorthogonal pseudopotential lattice Boltzmann method (LBM) was proposed to investigate the coalescence dynamics of two droplets impacting on a wall with wettability difference. The influences of the wettability difference, Weber number, offset distance on the low-wettability side on the coalescence dynamics and the contact-line evolution processes were systematically examined. Both symmetric and asymmetric distributions of the droplet-coalescence behaviors were considered. Our findings reveal that the wettability difference has a significant influence on the asymmetric-retracting and wetting-equilibrium stages, identifying three modes: pin-slip, slip and no-rebound, and slip and rebound. The rebound time is dominated by the high-wettability wall. At a larger Weber number, droplets exhibit a large retracting velocity, which results in increased pumping velocity and earlier rebound time. In addition, a dramatic retraction of the three-phase contact line (TPCL) on the low-wettability wall is observed, leading to the detachment of the liquid bridge from the low-wettability wall, and the formation of a cavity. With increasing offset distance on the low-wettability wall, three different evolution modes are found: coalescence-rebound, coalescence-separation, and non-coalescence. A power function relationship is reported between the Weber number We and the offset distance L* both on the high-wettability wall and low-wettability wall for three modes of coalescence behavior with We∼L*α. The value of the exponent α ranges from 4.6 to 7.4. This study showcases the effectiveness of the 3D nonorthogonal pseudopotential LBM in predicting the complex interface phenomena and characteristics of the multiphase flow structures under investigation.

Effect of electric field on bubble dynamics in channel flow boiling using lattice Boltzmann method

The application of an electric field in flow boiling has been proven to effectively enhance heat transfer and reduce pressure drop instability. This study aims to elucidate the mechanism of the impact of electric fields on flow boiling bubble dynamics through the pseudo-potential lattice Boltzmann method (LBM). The interplay between the externally imposed electric field incoming velocity in different gravity conditions examined. These factors can regulate flow boiling heat transfer in horizontal channel. The results demonstrate a competitive relationship between electric field and gravity and between incoming velocity and gravity. Therefore, under higher gravity condition, an electric field is less effective to enhance flow boiling heat transfer than in low gravity condition and vice versa. Additionally, there exists a synergistic relationship between incoming velocity and the electric field that mitigates their competition. Moreover, when considering multipoint nucleation processes, applying an electric field can attenuates bubble–bubble interactions and inhibit large bubble formation so as to accelerates bubble condensation in supercooled flows and enhance boiling heat transfer. This work provides comprehensive physical insights into the mechanism of electric field to enhance the heat transfer in flow boiling, which is instructive for the development of electrohydrodynamic technique in flow boiling enhancement.

Dynamics of liquid bridges between patterned surfaces

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates consisting of alternating hydrophilic and hydrophobic stripes, using a multicomponent pseudopotential lattice Boltzmann method. This extends our earlier work where the substrates were uniformly hydrophilic or hydrophobic. In steady-state conditions, we calculate the following, as functions of pattern wavelength: (i) the velocity fields of moving bridges, in particular their (time-averaged) terminal velocities; (ii) the deformation of moving bridges, as measured by the deviation of bridge contact angles from their equilibrium values; (iii) the minimum applied force that breaks a moving bridge. In addition, we found that a bridge moving between patterned substrates cannot be mapped onto a bridge moving between uniform substrates endowed with some effective contact angle, even in the limit of very small pattern wavelength compared to bridge width.

Lattice boltzmann investigation of droplet interactions with non-uniform chemically patterned surfaces

In this study, we employed a non-orthogonal, three-dimensional, multi-relaxation-time pseudo-potential lattice Boltzmann method, and investigate the behaviors of droplets impacting chemically patterned surfaces. We considered two interfaces: a hydrophobic/neutral strip on a hydrophilic wall (surface A), and a hydrophilic strip on a hydrophobic wall (surface B). The dynamics of impact, including the evolution of the morphology and the droplet spreading factor, were investigated under the influence of the difference in wettability, Weber number (We), and strip width. An increase in the wettability difference of surface A delayed droplet detachment and reduced the amplitude of oscillations, where this can be attributed to the surface tension and viscous dissipation, which had more time to weaken the strength of the jet. The magnitude of droplet detachment time initially increased with We but eventually decreased. As We is further increased, the ratio of viscous loss to the initial kinetic energy of the droplet is decreased and resulted in a shorter detachment time. The unbalanced Young's force significantly affected the evolution of the droplet on surface B. The mass of the droplet accumulated near the borderline of the strip and expanded along the y-axis under the influence of the inertial force, where this led to a larger spreading factor along the y-axis. In addition, the mass of the droplet on the hydrophobic wall affected the strength of the unbalanced Young's force. As the strip width increased, the spreading factor initially increased but then decreased along the y-axis owing to the combined action of inertial forces.

Lattice Boltzmann simulation of flow boiling heat transfer process in a horizontal microchannel with rectangular cavities

Bubble nucleation, growth and separation from cavities on the bottom of a microchannel for subcooled flow boiling are investigated by pseudo-potential lattice Boltzmann method. The influence of subcooling temperature, wall superheat, wettability, cavity size, and cavity number on the flow boiling heat transfer is systematically studied. The results show that the bubble equivalent diameter is 1.9 times larger at subcooling temperature 0.05Tc than that at 0.15Tc, and the heat flux is also 8 % higher at subcooling temperature 0.05Tc than that at 0.15Tc. It is found that the flow boiling changes from nucleate boiling to film boiling with the increase of wall superheat. When the wall wettability changes from the hydrophobic wall (θ = 120°) to the hydrophilic wall (θ = 30°), the average Nusselt number (Nuav) is reduced by 23 %. We also optimize cavity height and the uniformly distributed cavity number in the microchannel. It is found that the Nuav is increased by 9.7 % when the cavity height changes from h = 20lu (lattice unit) to h = 60lu. However, there exists an optimal cavity height about h = 60lu, where the heat transfer performance cannot be improved with the cavity height over this value. In addition, the number of cavities in the microchannel can improve the boiling heat transfer. When the cavity number changes from 1 to 4, the Nuav is increased by 10 %.

A finite difference formulation inspired by the pseudopotential lattice Boltzmann method

A finite difference formulation inspired by the pseudopotential lattice Boltzmann method

Investigating snap-off behavior during spontaneous imbibition in 3D pore-throat model by pseudopotential lattice Boltzmann method

As a result of complex pore-throat geometry and precursor corner flow, the snap-off of the non-wetting phase occurs during the spontaneous imbibition (SI) of wetting phase. However, accurate modeling of such pore-scale flow behavior remains a big challenge, and its influencing factors remain unclear. In this study, an improved pseudopotential lattice Boltzmann method (LBM) is used to analyze the snap-off behavior during the SI process in three-dimensional (3D) pore-throat models with rough surfaces. The influence of the pore-to-throat size ratio (λ), contact angles (θ), and Ohnesorge number (Oh) on the occurrence of the snap-off are investigated and based on which a 3D phase diagram is established. The snap-off is more likely to occur with the increase in λ and Oh and decrease in θ, respectively. Only when the λ is ≥2 and the θ is <13°, the snap-off may occur. With the increase in θ from 0° to 13°, the snap-off is suppressed due to the relatively small advancing difference between the corner flow and the bulk meniscus. Volume fraction of the entrapped gas bubble in the pore increases with the increase in λ and Oh and the decrease in θ. The time when snap-off occurred increases with the increase in λ and θ, and decrease in Oh. These results are fundamental for investigating snap-off phenomena in real 3D pore space and guide how to avoid or facilitate the occurrence of snap-off and to control the degree of snap-off.

Impact dynamics of droplets on circular bodies: Exploring the influence of wettability, viscosity, and body dimensions using the lattice Boltzmann method

This study used the multi-relaxation time pseudopotential lattice Boltzmann method to examine the impact dynamics of droplets on circular bodies, focusing on the influence of the surface wettability, the viscosity of droplets by choosing three distinct Reynolds numbers (Re = 100, 300, and 500), and the body diameters. Initially, the study examined impact behavior under non-wetting and wetting conditions, revealing distinct behaviors characterized by dimensional stretch lengths in horizontal and vertical directions. Furthermore, the study evaluated the impact of viscosity by varying the Reynolds number, providing a better understanding of droplet behavior on the solid body. In addition, the effect of changing the diameter of the circular body was examined. This research underlines the importance of surface wettability in the dynamics of contact with the droplets impinging on it. In particular, higher wettability correlates with a monotonic increase in viscosity by acting on the Reynolds number. In addition, the droplet profile responds to changes in Reynolds number, albeit with relatively limited deformation, even in the case of intense interaction with the wetting surface. These results highlight the complex interplay between wettability, droplet dynamics, viscosity, body dimensions, and surface interactions during impact processes.

Framework for simulating the partially miscible multi-component hydrocarbon fluids in porous media via the pseudo-potential lattice Boltzmann model

framework for simulating the partially miscible multi-component hydrocarbon fluids in porous media via the pseudo-potential lattice Boltzmann model

Turbulent flow boiling simulation based on pseudopotential lattice boltzmann method with developed wall boundary treatments and unit conversion

The lattice Boltzmann method (LBM) is widely studied for complex flow simulations, including liquid–vapor phase change phenomena. Although previous studies extended the LBM simulation capability from single-phase to two-phase boiling simulations, most of them are restricted to no-flow (pool boiling) or low-flow-rate (laminar flow) boiling conditions owing to the stability problem in collision at low viscosity, representing high Reynolds numbers. However, a high Reynolds number flow is essential for investigating the effects of turbulence on bubble dynamics. Recently, the central moment-based collision method is used to enable high Reynolds numbers for bulk flow; however, extending the method for multiphase-flow simulation with high Reynolds numbers is limited owing to the boundary treatment near the wall. In this study, we augment the previous boundary treatment in LBM simulation with a forcing term, which increases the stability of the simulation even under two-phase conditions. With the improved boundary treatment, the flow boiling phenomena at high Reynolds numbers (up to Re = 107,000) are successfully reproduced. Moreover, in this study, unit conversion is reconsidered with the relationship between conversion factors because the poor outcomes of bubble dynamics are attributed to misinterpreted unit conversion. The new unit conversion method satisfies the necessary conditions for mapping the physical bubble behavior to lattice frame, reproducing bubble dynamics effectively following the Reynolds number, with reasonable spatial and temporal resolution. Consequently, the flow boiling simulation can accurately predict the bubble departure diameter from the real experimental results and the heat transfer trend as a function of the Reynolds number.

Adaptive thermodynamic consistency control via interface thickness in pseudopotential lattice Boltzmann method across wide temperature ranges

Multiphase flow phenomena are ubiquitous in real-life applications, and the pseudopotential-based lattice Boltzmann multiphase simulation method has gained extensive usage in fields such as fuel cells, energy storage materials, and boiling heat transfer. Over the past two decades, significant improvements have been made to the pseudopotential model. These advancements have greatly enhanced its accuracy in simulating various processes. In this paper, we employ a numerical stability-based unit conversion scheme to ensure an accurate representation of real-world material properties. Additionally, we introduce a more precise non-ideal two-parameter gas state equation Modified Peng-Robinson (MPR) that closely aligns with experimental data, surpassing the commonly used single-parameter Peng-Robinson state equations. Furthermore, we compare the accuracy of the two-state equations for polar and non-polar substances, finding improved accuracy for non-polar substances and a higher degree of fidelity for polar substances when using the MPR equation. We analyze the constant correction coefficients chosen for thermodynamic consistency regulation from the perspectives of vapor-liquid interface thickness and numerical stability, both when held constant and when employing a dynamic correction approach that balances vapor-liquid interface width, numerical stability, and thermodynamic consistency. Finally, we validate to ensure its practical applicability.

Effect of heating wires with electric potential on pool-boiling heat transfer under an electric field

In this study, we investigated the influence of heating wires with electric potential on a pool-boiling system under an electric field. We employed a numerical method that combines the pseudopotential lattice Boltzmann model, leaky dielectric model, and finite-difference model. Heating wires with different positions and electric potentials above a horizontal heater were explored. A detailed analysis of the boiling process occurring on the heater was performed at various electric-field intensities and for different boiling regimes, both with and without wires. For the pool-boiling system without heating wires, the results revealed that the critical heat flux (CHF) increased with the electric-field intensity, and the superheat required for the system to attain film boiling increased with electric field intensity. Placing heating wires on the heater surface resulted in the deterioration of heat transfer in the system without an electric field. However, the optimal distance between the heating wires and the heater remarkably promoted heat transfer during the film-boiling regime. The introduction of heating wires with electric potential into the system disrupted the original electric-field distribution, consequently impacting the boiling process and heat transfer. Compared with the system without both heating wires and an electric field, the system without heating wires exhibited a 7.9 % increase in the largest CHF at a low electric-field intensity of CaE = 0.2. However, at the same electric-field intensity, the largest CHF increased by up to 39.4 % when heating wires with an electric potential were employed. These findings provide a theoretical foundation for the practical application of effectively employing wires with electric potential to enhance boiling heat transfer.

Three-dimensional modelling of cavitation bubble collapse using non-orthogonal multiple-relaxation-time lattice Boltzmann method

In this study, we employ a three-dimensional (3D) non-orthogonal multiple relaxation time (MRT) pseudo-potential lattice Boltzmann (LB) model to simulate the dynamics of cavitation bubble evolution. We benchmark the model against the Laplace law and the Rayleigh–Plesset (R–P) equation, confirming its efficacy in accurately capturing cavitation phenomena. We then apply the model to examine the collapse dynamics of a singular bubble located near a plane wall boundary and right-angled wall corner. Additionally, the dynamic interactions among five cross-shaped bubbles revealed the dimensionless jet volume Vj*, which is the ratio of the jet volume to the maximum bubble volume, exhibits a power relationship with the bubble distance δ. The simulation results demonstrate the accuracy of the model in discerning the effect of the wall boundary and the protective mechanisms inherent to multi-bubble interactions. These results further validate the aptness of the model for cavitation bubble dynamics simulations. Moreover, the tested case studies provide a foundational basis for future research into more complex cavitation behaviours. In summary, the developed 3D non-orthogonal MRT pseudo-potential LB model is capable of reproducing fluid flows, capturing pressure waves, and measuring wall pressures. Our work provides a deep insight into cavitation bubble dynamics and a solid basis for both applied and fundamental research.

Contact-point analysis of attached-wall cavitation evolution on chemically patterned surfaces using the lattice Boltzmann method

In this study, we aim to investigate the contact-point characteristics of cavitation bubble evolution on different chemically patterned surfaces using the thermal pseudopotential lattice Boltzmann method (LBM). The local temperature variation is considered in the contact-point dynamics simulation. Force analysis is performed on the contact points, and two main controlling factors for contact-point dynamics are identified, namely, the local pressure difference and the unbalanced Young’s force. A dimensionless temperature is used to describe the heat exchange efficiency between the wall and fluids for different wall wettability and temperatures. The attached-wall bubble on the wet wall has an unbalanced Young’s force, which is directed toward the inside of the bubble throughout the entire growth and collapse stages at the contact point, resulting in a smaller contact radius and stronger collapse intensity and making the wet wall more suitable for wall cooling. Significant pressure differences are observed at the contact points owing to local momentum concentration. In contrast, the non-wetting wall surface is more suitable for wall heating because of its smaller collapse intensity and larger contact radius on the wall.

Hybrid outflow boundary condition for the pseudopotential LBM simulation of flow boiling

The pseudopotential lattice Boltzmann method (LBM) has been successful in simulating the pool boiling with a density ratio up to 1000. However, the flow boiling simulation of using the same LBM is rare and the density ratio is limited to about 17. The current study investigated the challenge of flow boiling by first simulating the isothermal bubble outflow, where large pressure deviation from the initial saturation pressure is observed due to perturbation of the bubble outflow. Pressure drifts continuously as there is no constraint at both inlet and outlet when using the usual convective outflow boundary condition (OBC). The subsequent flow boiling simulation shows that boiling will be suppressed by the drifting/increasing pressure. A hybrid OBC is proposed to stabilize the pressure by imposing a fixed pressure either on the whole outlet when the bubbles are still far away from the outlet, or on a part of the outlet when the bubbles are crossing the other part of the outlet where the convective OBC is still used. With the improvement by using the hybrid OBC, the heat transfer coefficient of saturated nucleate boiling in a channel flow is studied and the results are in good agreement with the experiments. More realistic problems with structured wall surface, various surface properties and density ratios are simulated to show the algorithm stability and robustness. The current study has extended the density ratio to about 125, which is much larger than the previous record of about 17.

Assessment of the pseudopotential lattice-Boltzmann method for modeling multiphase fuel droplets

An improved pseudopotential lattice–Boltzmann model was proposed for simulating multiphase flow dynamics to describe fuel droplets, and its thermodynamic consistency was tested against the Peng–Robinson equation of state. The studied liquid fuels included paraffinic hydrocarbons with a different number of carbon atoms (C[Formula: see text]–C[Formula: see text]), methanol (CH[Formula: see text]OH), hydrogen (H[Formula: see text]), ammonia (NH[Formula: see text]), and water (H[Formula: see text]O). To improve accuracy and reduce the magnitude of the spurious currents, the multi-relaxation times collision operator was implemented and the forcing term was computed using the hybrid pseudopotential interaction force with an eighth-order isotropic degree. The pseudopotential lattice–Boltzmann model accurately predicted the equilibrium densities and captured satisfactorily the thermodynamic vapor-liquid coexistence curve given by the analytical solution of the Peng–Robinson equation of state for acentric factors ranging from [Formula: see text]0.22 to 0.56, keeping the maximum average error for the liquid and vapor branches below 0.8% and 3.7%, respectively. Nevertheless, Peng–Robinson was found to be insufficiently accurate to replicate the actual thermodynamic state, especially for H[Formula: see text]O and CH[Formula: see text]OH, for which the results strongly deviated from the experimental vapor-liquid equilibrium densities and reached average errors for the vapor phase of nearly 28%. Furthermore, the surface tension ([Formula: see text]) was retrieved using the multiphase pseudopotential lattice–Boltzmann results and served to verify the thermodynamic consistency of the pseudopotential lattice–Boltzmann with respect to the parachor model. Lastly, the pseudopotential lattice–Boltzmann model was also shown to predict accurately the transient behavior of oscillating droplets. Overall, the enhanced model satisfactorily predicted the properties and behavior of the substances for a wide range of conditions.

A non-uniform magnetic field coupled lattice Boltzmann model and its application on the wetting dynamics of a ferrofluid droplet under gravity effects

To extend the mesoscopic model for simulating the wetting dynamics of ferrofluid droplets, an improved multicomponent multiphase pseudopotential lattice Boltzmann (LB) model coupled with the magnetic field solver is constructed in this work. Through a series of validation studies, the accuracy and reliability of the proposed coupled model are ensured. The ferrofluid droplet is subjected to the effects of non-uniform magnetic field and gravity. The influences of various magnetic Bond numbers (Bom) and gravitational Bond numbers (Bo) on the wetting dynamics of a ferrofluid droplet on a hydrophobic surface are discussed, and the mechanism behind the morphological evolution of the ferrofluid droplet is unveiled. The results show that the curvature of the phase interface is a key factor influencing both the magnetic field intensity distribution around the phase interface and the pressure distribution inside the ferrofluid droplet, thus changing the evolution of the droplet morphology. The variation of Bom has a monotonic impact on the morphological evolution of the ferrofluid droplet and its equilibrium state, while the effect of the Bo depends on the magnitude of Bom. At Bom=49.98 and Bo=4.1, the ferrofluid droplet splits from the central position and into three parts in the end. The amplitude and duration time of the oscillation of the ferrofluid droplet increase with Bom. This study can provide a model reference and some key theoretical understandings for the numerical study of the wetting dynamics of ferrofluid droplets.