Thermal Lattice Boltzmann Model Research Articles

LBM modeling of three-dimensional mixed convection in CZ crystal growth on curvilinear coordinates system

A three-dimensional (3D) thermal lattice Boltzmann model of crystal growth is presented to study the magneto-hydrodynamics (MHD) mixed convection in the melt of Czochralski silicon single crystal growth in this paper. In order to solve the problem of lattice Boltzmann method’s difficulty in solving the flow of 3D cylindrical cavity, the 3D physical model of crystal growth is transformed from the Cartesian coordinate system to the Curvilinear coordinate system. And the irregular grids in the Cartesian coordinate system are transformed into regular grids in the Curvilinear coordinate system to facilitate the establishment of the Lattice Boltzmann model. Under the above operations, two coupled distribution functions are established to solve the governing equations. Two D3Q19 models are adopted to solve the melt velocity and temperature. And the 3D lattice Boltzmann modeling of crystal growth with cylinder boundary is realized by interpolation in Curvilinear coordinate system. The comparison with the experiment and other references proves that the proposed model and boundary treatment scheme is correct and it proposes a new way for studying the 3D crystal growth or other similar 3D cylindrical cavity simulations. Furthermore, the unstable melt flow for two cases are also simulated in this paper and the critical Reynolds number are also obtained. Results show that the introduction of the transverse magnetic field enhances the stability of the crystal growth system and increases the adjustable range of crystal rotation parameter. The obtained conclusion has an important reference for adjusting the process parameters during the CZ crystal growth.

A thermal lattice Boltzmann model for evaporating multiphase flows

Modeling thermal multiphase flows has become a widely sought methodology due to its scientific relevance and broad industrial applications. Much progress has been achieved using different approaches, and the lattice Boltzmann method is one of the most popular methods for modeling liquid–vapor phase change. In this paper, we present a novel thermal lattice Boltzmann model for accurately simulating liquid–vapor phase change. The proposed model is built based on the equivalent variant of the temperature governing equation derived from the entropy balance law, in which the heat capacitance is absorbed into transient and convective terms. Then a modified equilibrium distribution function and a proper source term are elaborately designed in order to recover the targeting equation in the incompressible limit. The most striking feature of the present model is that the calculations of the Laplacian term of temperature, the gradient term of temperature, and the gradient term of density can be simultaneously avoided, which makes the formulation of the present model is more concise in contrast to all existing lattice Boltzmann models. Several benchmark examples, including droplet evaporation in open space, droplet evaporation on a heated wall, and nucleate boiling phenomenon, are carried out to assess numerical performance of the present model. It is found that the present model effectively improves the numerical accuracy in solving the interfacial behavior of liquid–vapor phase change within the lattice Boltzmann method framework.

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid–vapor phase change

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change.

Enhanced dropwise condensation on downward-facing cross-shaped pillar-structured surfaces with mixed wettability

In this paper, a novel downward-facing cross-shaped pillar-structured surface with mixed wettability is conceived for enhancing dropwise condensation. A three-dimensional thermal lattice Boltzmann model is employed to investigate the condensation performance on the downward-facing cross-shaped pillar-structured surface with mixed wettability and the associated enhancement mechanism of dropwise condensation. The numerical investigation shows that the cross-shaped pillar-structured surface with mixed wettability exhibits much better condensation performance than the square pillar-structured surface with mixed wettability and the flat surface with mixed wettability due to the synergistic effects of structural effects and mixed wettability, which can promote the droplet nucleation and accelerate the condensate removal. Moreover, for different contact angles of the pillar top (θtop), there exists a competition between the droplet nucleation and the condensate removal on the downward-facing cross-shaped pillar-structured surface. It is found that, when θtop=60°, an optimal droplet dripping rate can be achieved due to a suitable balance between a relatively large mass of detached droplets and a short condensation cycle time. Furthermore, the aspect ratio (γ) has an important influence on the droplet dripping rate, i.e., as γ increases, the droplet dripping rate first exhibits small fluctuations, then increases rapidly before γ=1.0, and after that experiences a slight variation. The large droplet dripping rate achieved at γ=1.0 is mainly attributed to the fact that an optimum structure of the concave corner can promote the droplet nucleation, increase the length of the triple-phase contact line, advance the appearance of droplet coalescence, and finally accelerate the condensate removal.

Effects of surface characteristics on bubble dynamics in nucleation boiling using LBM

In this paper, the hybrid thermal lattice Boltzmann model is adopted to investigate the nucleation boiling. The bubble dynamics behaviors including nucleation, growth, coalescence, and departure, are studied on structured surfaces. Three types of structured surfaces adopting the rectangular, triangular, and trapezoidal structured surfaces are designed with different surface wettability. The numerical results reveal that, firstly, for the single bubble, increasing the opening width of structured surfaces from inside to outside is beneficial for bubble evolution. Then, with the dimensionless separation distance less than 1 between the two nucleation sites for the double bubbles, it presents a more noticeable advantage in the bubble evolution with different surface characteristics. Finally, the dimensionless critical coalescence distance of double bubbles increases significantly with the increment of contact angle on the hydrophobic surface. Besides, the dimensionless bubble critical coalescence distances on the triangular and rectangular structured surfaces are larger than those on the trapezoidal structured surface for the hydrophobic surface.

Enhancing the Power Performance of Latent Heat Thermal Energy Storage Systems: The Adoption of Passive, Fractal Supports

We employ a three-phase thermal lattice Boltzmann model (LBM) to investigate the power performance of latent heat thermal energy storage (LHTES) systems based on the exploitation of phase change materials (PCMs). Different passive thermal supports are considered to increase the melting rate, including innovative, fractal, branch-like structures. Our simulations reveal that the adoption of fractal, branch-like metal supports consistently outperforms other configurations in terms of PCM melting rates. These results open the path towards novel strategies to enhance the power performance of PCM-based TES systems, offering potential benefits for energy storage applications.

A lattice Boltzmann investigation of liquid viscosity effects on the evolution of a cavitation bubble attached to chemically patterned walls

The thermal lattice Boltzmann model is applied to explore liquid viscosity effects on a single cavitation bubble attached to chemically patterned walls. A conversion method based on the surface tension and the non-ideal equation of state parameters is proposed. According to the force analysis, it is found that the local pressure difference and the unbalanced Young's force are two main controlling factors for contactpoint dynamics. The dynamic contact angle is larger than the equilibrium contact angle throughout the evolution process for a hydrophilic wall, which results in a hysteresis effect in the bubble growth process due to the unbalanced Young's force and accelerates the contact point retraction velocity in the collapse stage. For hydrophobic walls, the unbalanced Young's force accelerates the contact radius expanding, resulting in a larger maximum contact radius than for a bubble attached to a hydrophilic wall. The hysteresis effects caused by the unbalanced Young's force slow down the contact points retraction in the early collapse stage and accelerate the retraction later because of dramatic interface deformation. The bubble is punctured over a larger volume with a hydrophilic wall than with a hydrophilic wall, resulting in a smaller collapse intensity. An exponential relationship between the micro-jet volume and the cosine function of the equilibrium contact angle at the collapse point is found. Furthermore, the jet volume before bubble collapse decreases, and the collapse time delays with the increase in viscosity.

A numerical study on bubble dynamics and heat transfer of flow boiling in an inclined microchannel

Flow boiling, as an important heat transfer method, is widely applied in many devices. In this study, a gas-liquid thermal lattice Boltzmann model is adopted to study the flow boiling in an inclined microchannel. Specifically, the bubble growth processes and heat transfer efficiency are studied for different inclined angles. The numerical results show that the liquids occur phase change almost at the same time while the inclined angles are different. As the inclined angle increases, the bubble departure time decreases. Also, the heater temperatures change periodically for the studied cases. The maximum heater temperature is not affected by the inclined angle while the minimum heater temperature decreases when the inclined angle of the microchannel increases. Therefore, the larger inclined angle increases the flow boiling heat transfer efficiency.

Numerical Analysis for Argon Arc Plasma Jet Flow by Three-Dimensional Thermal Lattice Boltzmann Model

Numerical Analysis for Argon Arc Plasma Jet Flow by Three-Dimensional Thermal Lattice Boltzmann Model

Lattice Boltzmann Study of Microdroplet Evaporation Process in Pixel Pits

Inkjet printing has the advantages of high material utilization, low cost, and large-area production and is a promising manufacturing technology for organic light-emitting diode (OLED) displays. However, the droplet evaporation in micron-size pixel pits is highly influenced by the pit wall. Such a process is extremely difficult to control, leading to the appearance of defects such as the coffee ring in the printing process of OLED displays. In this work, a multiphase thermal lattice Boltzmann (LB) model based on multiple distribution functions is established to study the evaporation process of micron-size droplets in pits. According to the characteristics of the largest number of the three-phase contact line (TCL) appearing in the evaporation process, the evaporation modes can be divided into three types, i.e., one, two, and three TCLs. In the 1-TCL mode, the droplet stays in constant contact radius (CCR) for the shortest time; in 2-TCL and 3-TCL modes, the liquid film fracture behavior of evaporating droplets in the pit is well captured. The effects of the pit height and the contact angle on the droplet evaporation mode are investigated in detail. The phase diagrams of evaporation modes with different parameters are also established. The revealed evaporation mechanism is supposed to be useful for regulating the droplet evaporation behavior and controlling the cured film shape in the OLED printing process.

Natural convection of large Prandtl number fluids: A controversy answered by a new thermal lattice Boltzmann model

The purpose of this work is to deepen our understanding of natural convection with large Prandtl number fluids and to resolve some controversies in the previous publications. To achieve this purpose, a new thermal multiple-relaxation-time lattice Boltzmann model is proposed. Natural convection in a square cavity, a benchmark test case, is investigated numerically using the new model. The Prandtl number is up to 100. For the first time, it is numerically observed that there are two critical Prandtl numbers in the natural convection, which will affect the correlation between the Nusselt number and Prandtl number critically. Three heat transfer characteristic ranges of natural convection are defined in this work, according to the two critical Prandtl numbers. In each range, the dominant heat transfer mechanism is different, which can solve a long-standing issue in the discipline of heat and mass transfer: completely opposing statements on the correlation between the Nusselt number and Prandtl number for natural convection, were published in the open literature. For the first time, this work reveals cause behind the controversial reports and provides the guidance for the future research.

PORE SCALE INVESTIGATION ON THE EFFECT OF TEMPERATURE ON THREE-PHASE REACTIVE FLOW IN POROUS MEDIA USING THE LATTICE BOLTZMANN METHOD

In this study, the process of carbonate rock acidification with three-phase immiscible fluid [water, oil, and supercritical carbon dioxide (scCO<sub>2</sub>)] reactive flow in nonisothermal condition at pore scale was simulated by the lattice Boltzmann method (LBM). The three immiscible fluids' flow, solute transport, and heat transfer were solved by the Shan-Chen multiphase multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model, and multicomponent thermal lattice Boltzmann model, respectively. The solid phase was updated by the volume-of-pixel method. In addition, the effect of temperature on the multiphase multicomponent reactive flow was numerically investigated. The results show that the dissolution rate is determined by three-phase distribution. The increase of temperature can accelerate the dissolution rate and decrease the inhibition influence of the non-acid phase on dissolution. Furthermore, the influence of temperature decreases with the increase of inlet velocity and oil wettability.

Lattice Boltzmann mesoscopic study of effects of corrosion on flow boiling heat transfer in microchannels

The robustness of boiling heat transfer performance is crucial for the long-term applications, and it is necessary to understand the influence of corrosion on flow boiling heat transfer. In the present study, the corrosion process is first studied and the corrosion morphologies under typical reactive transport conditions and pit geometrical parameters are obtained using the corrosion lattice Boltzmann (LB) model. Then, the flow boiling heat transfer in the corroded microchannels is studied using the hybrid thermal multiphase LB model, and compared with the heat transfer performance and bubble dynamic behaviors of smooth intact microchannel. Effects of corrosion morphology, pit height, and staggered distance between pits on the flow boiling heat transfer characteristics are explored. The corrosion level plays an important role in the heat transfer performance. Although the corroded cavities with various corrosion levels can promote the bubble nucleation, the reduced heat transfer performance occurs at high corrosion level due to inefficient removal of the bubbles from the large corroded cavities. Increasing the pit height and staggered distance between pits can slow down the reduction of heat transfer performance. For the severe corroded microchannels, the heat transfer performance is deteriorated significantly due to the formation of the vapor film covered on the heating surface.

Thermal lattice Boltzmann model for liquid-vapor phase change.

The lattice Boltzmann method is adopted to solve the liquid-vapor phase change problems in this article. By modifying the collision term for the temperature evolution equation, a thermal lattice Boltzmann model is constructed. As compared with previous studies, the most striking feature of the present approach is that it could avoid the calculations of both the Laplacian term of temperature [∇·(κ∇T)] and the gradient term of heat capacitance [∇(ρc_{v})]. In addition, since the present approach adopts a simple linear equilibrium distribution function, it is possible to use the D2Q5 lattice for the two-dimensional cases considered here. Thus, the present model is more efficient than previous models in which the lattice is usually limited to the D2Q9. The proposed model is first validated by the problems of droplet evaporation in open space and droplet evaporation on a heated surface, and the numerical results show good agreement with the analytical results and the finite difference method. Then it is used to model the nucleate boiling problem, and the relationship between detachment bubble diameter and gravitational acceleration obtained with the present approach fits well with previous works.

MELTING HEAT TRANSFER IMPROVEMENT BY VENATION-FINNED POROUS NETWORKS

The venation-finned porous network has been demonstrated as a promising method to maximize the thermal transport access. To improve the heat storage efficiency, an innovative venation-finned porous network is employed here to enhance the melting performance of phase change materials (PCMs). The venation-finned porous network is quantitatively described by Murray’s law and Voronoi method, and a modified thermal lattice Boltzmann model of PCM melting processes in a square cavity is developed and numerically analyzed to optimize the venation-finned porous network. The melting performance of composite PCMs with three configurations (venation fin, porous network and venation-finned porous network) are compared and analyzed. Moreover, the effects of branching angle and Murray coefficient on melting performance are comprehensively studied. It indicates that venation-finned porous network is favorable to melting performance improvement due to venation’s inherent efficient heat transfer paths. Compared to venation fins and porous networks, the melting duration time of venation-finned porous networks is reduced by 78.4% and 21.4%, respectively. Furthermore, the branching angle of 45[Formula: see text] and Murray coefficient of 3 are suggested for maximizing the melting efficiency. Importantly, the melting mechanism is conduction and convective conjugated heat transfer in composite PCMs with venation fins, however, it is dominated by heat conduction for those with porous networks or venation-finned porous networks.

Analysis and reconstruction of the thermal lattice Boltzmann flux solver

AbstractThe thermal lattice Boltzmann flux solver (TLBFS) has been proposed as an alternative method to overcome the drawbacks of thermal lattice Boltzmann models. However, as a weakly compressible model, its mechanism of the good numerical stability for high Rayleigh number thermal flows is still unclear. To reveal the mechanism, the present article first derives the macroscopic equations of TLBFS (MEs‐TLBFS) with actual numerical dissipation terms by approximating its computational process. By solving MEs‐TLBFS with the finite volume method, the reconstructed TLBFS (RTLBFS) is proposed. Detailed analyzes prove that these actual numerical dissipation terms are the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows. More detailed numerical tests indicate RTLBFS has similar performances as TLBFS for stability, accuracy, and efficiency, which further validates the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows.

Droplet impact on a heated porous plate above the Leidenfrost temperature: A lattice Boltzmann study

In the past few decades, the droplet impact on a heated plate above the Leidenfrost temperature has attracted immense research interest. The strong hydrophobicity caused by the Leidenfrost effect leads to the droplet bouncing from a flat plate at a given contact time predicted by the classical Rayleigh theory. Numerous investigations were conducted to break the theoretical Rayleigh's limit to reduce the interfacial contact time. Recently, a droplet was observed to form a pancake shape and bounce as it impacted nanotube or micropost surfaces above the Leidenfrost temperature. This led to a significant reduction in droplet contact time. However, this unique bouncing phenomenon is still not fully understood, such as the influence of the plate configuration and the relationship between the droplet rebound time and evaporation mass loss. In this study, we carry out a numerical study of the droplet impact dynamics on a heated porous plate above the Leidenfrost temperature, using a multiphase thermal lattice Boltzmann model. Our model is constructed within the unified lattice Boltzmann method framework and is first validated based on theoretical and experimental results. Then, a comprehensive parametric study is performed to investigate the effects of the impact Weber number, the plate temperature, and the plate configurations on the droplet bouncing dynamics. Results show that higher plate temperature, larger Weber number, and smaller pore intervals can accelerate the droplet rebound and promote the droplet pancake bouncing. We demonstrate that the occurrence of the pancake bouncing is attributed to the additional lift force provided by the vapor pressure due to the evaporation of liquid inside the pores. Moreover, the droplet maximum spreading time and maximum spreading factor can be described by a power law function of the impact Weber number. The droplet evaporation mass loss increases linearly with the impingement Weber number and the plate opening fractions. This study provides new insights into the Leidenfrost droplet impingement on porous plates, which may potentially facilitate the design of novel engineering surfaces and devices.

Asymmetric Condensation Characteristics during Dropwise Condensation in the Presence of Non-condensable Gas: A Lattice Boltzmann Study.

In this work, the condensation characteristics of droplets considering the non-condensable gas with different interaction effects are numerically studied utilizing a multicomponent multiphase thermal lattice Boltzmann (LB) model, with a special focus on the asymmetric nature induced by the interaction effect. The results demonstrate that for isolated-like growth with negligible interactions, the condensation characteristics, that is, the concentration profile, the temperature distribution, and the flow pattern, are typically symmetric in nature. For the growth regime in a pattern, the droplet has to compete with its neighbors for catching vapor, which leads to an overlapping concentration profile (namely the interaction effect). The distribution of the condensation flux on the droplet surface is consequently modified, which contributes to the asymmetric flow pattern and temperature profile. The condensation characteristics for droplet growth in a pattern present an asymmetric nature. Significantly, the asymmetric condensation flux resulting from the interaction effect can induce droplet motion. The results further demonstrate that the interaction strongly depends on the droplet's spatial and size distribution, including two crucial parameters, namely the inter-distance and relative size of droplets. The asymmetric condensation characteristics are consequently dependent on the difference in the interaction intensities on both sides of the droplet. Finally, we demonstrate numerically and theoretically that the evolution of the droplet radius versus time can be suitably described by a power law; the corresponding exponent is kept at a constant of 0.50 for isolated-like growth and is strongly sensitive to the interaction effect for the growth in a pattern.

Transient thermal performance of multilayer thermal protection systems doped with phase change materials

In this article, the transient heat transfer process of the multilayer thermal protection system (TPS) doped with the phase change materials (PCM) is studied. The multilayer TPS consists of the C/SiC composite material, alumina aerogel, silica aerogel, and silica aerogel doped with the PCM. A thermal lattice Boltzmann model is adopted to consider the effect of interlayer thermal contact resistance on the transient thermal response of the TPS. An enthalpy-based lattice Boltzmann model is adopted to solve the solid–liquid phase change problem. The transient heat transfer characteristics of two kinds of TPSs in different layouts are analyzed in detail. The results show that whether the doped PCM enhances the thermal insulation performance of the TPS depends on the layout design of the multiple layers and service time. There exists an optimal layer thickness of the PCM that makes a TPS have the best thermal insulation performance, and the optimal value increases with the service time. The interlayer thermal contact resistance can have a significant effect on the transient thermal response of the TPS, and the optimal value of the PCM thickness will reduce.

A novel thermal lattice Boltzmann model with heat source and its application in incompressible flow

In this paper, the source term of energy distribution in double distribution function approach is analysed in detail and a new discrete model is proposed to eliminate the error terms in previous models. The newly proposed model contains two coupling terms, i.e. a velocity-source coupling term and a temperature-force coupling term. The velocity-source coupling term is related to the transport of source which affects the accuracy of simulations of convection, chemical reaction and so on. The temperature-force coupling term is related to the inner product of force and temperature gradient which affects the accuracy of simulations of boundary layer and the edge of plumes in convection. We extended two new heuristic treatments to handle the adiabatic and isothermal boundary conditions. Their efficiency and accuracy are analyzed theoretically and proved by some numerical validations. Finally, we simulated natural convection flows with compression work and viscous dissipation over a wide range of Eckert number using the present model and obtained a scaling law between average Nusselt number and Eckert number.