Enthalpy-based Lattice Boltzmann Research Articles

Water–ice phase transition in frozen soils: a mesoscopic numerical study based on lattice Boltzmann method

ABSTRACT The phenomenon of water–ice phase transition in frozen soils is the key to explaining the mechanism of frost heaving and thawing settlement disaster. However, numerical analysis of water–ice phase transitions in frozen soils at mesoscale is rarely reported. This study combines the modified Gibbs-Thomson equation and the enthalpy-based lattice Boltzmann model, and develops a mesoscale numerical method to simulate the water–ice phase transition in the local pores of saturated frozen soil during freezing and thawing process. In order to accurately simulate this process, a new η coefficient is proposed to modify the Gibbs-Thomson equation, which is unrelated to the type of soil sample and gradation characteristics. According to the particle size distribution curve, the two-dimensional random circle generation method is used to reconstruct the soil pore structure. The freezing and thawing processes are verified with the experimental data. A larger non-uniformity coefficient C u and curvature coefficient C c of the grain size distribution result in a lower degree of subcooling and lower residual water content of the soil during the freezing process. The new model provides an effective means to understand the water–ice phase transition in frozen soil at a mesoscopic scale.

Corner melting in low Pr metals: A study using lattice Boltzmann method

Evolution of melting boundary in the solid–liquid phase-change problem involves nonplanar geometry due to the presence of Rayleigh–Benard convective cells in the melted region. The transition of flow behavior from steady to oscillatory in the melt zone is particularly an interesting phenomenon to study. In this work, numerical investigation of melting of low Prandtl number materials in a square cavity with two adjacent heated walls has been carried out using total enthalpy-based lattice Boltzmann method. The local thermal and fluid flow behavior within a moving melting front has been investigated. The influence of natural convection in the melt zone has been observed for two different cases: (1) heating from a corner formed by the left and the bottom walls and (2) heating from a corner formed by the top and the right walls. The effect of Rayleigh number in the range of Ra = 102–5 × 107 on the convective flow field is evaluated for a typical parametric value of Stefan number of 0.01 and Prandtl number of 0.025. Results show distinct convection rolls at the melt zone for the cases under investigations. Evolution of flow fields in the melt zone has been described by a set of isotherms and streamlines for both the cases. The interface fronts for both the cases are initially of convex shape, and around Fourier number of 0.5 turn into concave shape, as viewed from the direction of the movement of melting front. At higher Ra, the rates of melting for top-right side and left-bottom side heated cavities are nearly the same above Fourier number of about 1.2. The average heat flux from the walls scales with Ran , where n is a constant which varies between 0.98 and 1.11. In the melt region, the instability pattern of flow and thermal field changes with the change of effective melt area. Transition to periodic flow is observed at Ra of 7.5 × 106 for case 1 and 2.2 × 107 for case 2, respectively.

Solid–liquid phase transition simulated by the lattice Boltzmann model: from pore scale to representative elementary volume scale

Purpose This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems. Design/methodology/approach Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given. Findings This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices. Originality/value A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

Interfacial heat transfer and melt-front evolution at a Fractal Cantor structured interface under various PCM melting conditions

With the aim to investigate heat transfer characteristics of PCM on micro-textured hot surface, this study numerically investigates the heat transfer process of PCM at fractal Cantor structured surfaces using the total enthalpy-based lattice Boltzmann method, which is partly validated by experimental testing. The thermal slip length and liquid velocity distribution are assessed as evaluation criteria. Results show that Fractal Cantor structure can significantly stimulate localized thermal convection, thereby reducing the average thermal slip length from 0.3 mm to approximately 0.14 mm. When the Fourier number exceeds 0.1, both thermal conduction and convection should be considered within the melted layer. With the fractal level increasing, a more uniform melt-front evolution can be observed, consequently, minimizing the total melting time by 500 s with the fractal level of 3. Elevating Ste and gravity can significantly increase the flow rate of liquid PCM by augmenting superheat degree and buoyancy effect, thereby enhancing convective heat transfer strength and reducing thermal slip length. According to the orthogonal design, though the fractal level demonstrates minimal range values for both maximum velocity and Rayleigh number, it elevates the sensitivity to the variation of boundary conditions. Ste yields the most significant enhancement in heat transfer performance.

Comprehensive performance analysis and structural improvement of latent heat thermal energy storage (LHTES) unit using a novel parallel enthalpy-based lattice Boltzmann model

Latent heat thermal energy storage (LHTES) utilizing phase change material (PCM) is one of the critical enablers in developing sustainable and low-carbon energy systems. To fill the knowledge gap, this paper presents an enthalpy-based solid–liquid model through the lattice Boltzmann method (LBM) with a multi-relaxation-time (MRT) approach, aiming to simulate convective phase change in LHTES units with and without porous media in Cartesian or axisymmetric domains. To improve accuracy and efficiency, the model integrates a differential scanning calorimetry (DSC) correlated equation for enthalpy modeling, couples with a 1D heat-transfer-fluid (HTF) model for boundary treatment of HTF side, and employs a parallel LBM scheme for efficient parametric studies. The validation demonstrates the model’s success in predicting PCM phase change, with errors below 10%. A comprehensive numerical analysis is then conducted to quantitatively evaluate the effect of convection on PCM melting. Novel metrics, such as acceleration rates (ac) of PCM melting and threshold Rayleigh numbers (Radc) at various aspect ratios, are introduced. Furthermore, PCM melting in the porous cylindrical unit is explored. Findings reveal up to 86% acceleration in melting compared to pure PCM at 80% energy storage, and the porous media with porosity above 0.9 is recommended for thermal enhancement. Moreover, this paper analyzes the negative effect of uneven temperature distributions caused by convection on LHTES unit efficiency. A modified LHTES unit geometry is proposed to offset this negative effect, and the study demonstrates successful mitigation of uneven temperature distributions, achieving up to 57 % acceleration in PCM melting.

Lattice Boltzmann simulation of the melting enhancement of composite phase change material with highly conductive additives - Effect of discrete particulate phase and continuous conductive network

The melting process of paraffin-aluminum composite PCM in a 2D enclosure is numerically investigated by means of an enthalpy-based lattice Boltzmann method. The aluminum is deployed in discrete particles with size around 100 μm and the continuous fibrous network in the composite PCM, respectively. The effects of equivalent particle diameter, the volume fraction of aluminum additives as well as the local structural rearrangement are systematically investigated. The results demonstrate that the appending of discrete aluminum particles at a low volume fraction (ϕ ≤ 0.2 in this work) even has a negative effect on the melting process, because of the inhibition of the natural convection. By concentrating the particles in either back and top area, the melting performance could be slightly promoted. However, the improvement is very limited. Instead, it is more effective to utilize the continuous conductive fibrous network structure to accelerate the melting, which is suggested to be bespread over the entire PCM with larger local space in the direction of temperature gradient. Furthermore, it is discovered that the critical melting time reduces exponentially with the increase of fiber volume fraction. This work gives a comprehensive understanding of the differences between the discrete particles and continuous structures in the heat transfer enhancement of composite PCM, and offers an optimization strategy in the fabrication of fiber/foam structures.

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 numerical study of phase change material melting enhancement in a horizontal rectangular enclosure with vertical triple fins

In renewable energy systems, energy storage with phase change materials (PCM) is important, but these materials have poor thermal conductivity; therefore, approaches for improving the performance of these storage systems have become required. This research investigates numerically whether fins affect thermal energy storage (TES) units' behavior during phase changes. Three conductive fins at different positions were attached to the heated bottom wall to enhance the PCM melting process. Different dimensionless fin lengths (a/H = 0.25, 0.50, and 0.75) and dimensionless fin positions (b/L = 0.15, 0.25, 0.35, and 0.75) were considered as parameters to investigate their effect on melting rate. The main objective is to detect the best lengths of the fins and the optimum distance between them to achieve the highest storage performance. The enthalpy-based lattice Boltzmann technique is used to solve velocity and temperature fields for simulations. The results from other researchers validate the numerical predictions. It is found that significant enhancement in the heat transfer is shared between thermal conduction and convection at the initial and final stages of melting, respectively. Increasing the ratios fin lengths of a/H from 0.25 to 0.75, the whole melting period is shortened by 15.1%, 40.7%, and 70.1%, respectively. The best compromise positions ratio for short fins at a/H = 0.25 is b/L = 0.48 till the complete melting of PCM, while its b/L = 0.35 when the fine longer than a/H > 0.50.

Numerical investigation of the melting process in a half horizontal cylinder with radial fins

In the present study, the melting phenomenon in a half horizontal cylinder cavity with rectangular heat sources is investigated using numerical lattice Boltzmann method. The cylinder is modeled two dimensionally and its boundaries are insulated. Also, the high temperature rectangular heat sources with constant area are located in radial position on cavity. The enthalpy-based lattice Boltzmann method is used for simulating the phase change problem in the cavity. Melting of lead with Stefan number of 0.86 and Prandtl number of 0.0236 is simulated in the cavity. The effects of pertinent parameters such as the aspect ratio of the fins 1,2.5,5,7.5, the Rayleigh number 103,104,105 and the angular position of the heat sources 0,15,45 are studied on the melting phenomenon. The results show that increasing the aspect ratio of the fin with constant area reduces the melting time and increases the liquid fraction at the same time. Also higher value of the Rayleigh number improves the natural convection effect and raises the rate of melting. Finally, it is observed that the highest rate of melting is obtained when two fins are positioned at 45 degrees with aspect ratio of 7.5 at Rayleigh number of 105.

Study of Natural Convection Melting of Phase Change Material inside a Rectangular Cavity with Non-Uniformly Heated Wall

In the present numerical study, the convection diffusion phenomena associated with solid-liquid phase transition processes during phase change material (PCM) melting within a rectangular cavity is studied. The cavity is heated from left wall with a sinusoidal temperature distribution. Initially the enclosure was filled by solid gallium at melting temperature 29.78°C. The enthalpy-based lattice Boltzmann method (LBM) with D2Q9 particle velocity model is used to solve density, velocity and temperature fields. Influence of Rayleigh number ranging from 103 to 4×105 on streamlines, isotherms and liquid fraction is analyzed. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. It is found that the rate of the melting increases with the increase in the values of the Rayleigh number.

Numerical simulation of convective non-Newtonian power-law solid-liquid phase change using the lattice Boltzmann method

In this study, a two dimensional enthalpy-based lattice Boltzmann method was developed to simulate the non-Newtonian melting process inside an enclosure. To examine the effect of power-law indexes in the phase change process, Nusselt number and the position of melting front for flow exposed to different flow behavior indexes (0.8−1.8) and Rayleigh number (50000, 170000, 840000) were investigated. Results show that as flow behavior index increases for a flow with a given Rayleigh number, average Nusselt number at hot wall and the rate of melting decrease. In order to verify the accuracy of proposed numerical scheme, step-by-step verification of sub-models is explained in detail.

Comparative study on natural convection melting in square cavity using lattice Boltzmann method

The phase change process is of significant importance in the application of phase change material (PCM). In this paper, the natural convection melting in a square cavity was investigated and the enthalpy-based lattice Boltzmann model (TLBM) combined with the pseudo-potential LB model was developed to trace the solid–liquid interface. Four cases with different boundary conditions were calculated and the corresponding temperature contours, velocity vectors and average liquid fraction at various time were compared.Results show that TLBM has good accuracy in simulating the solid-liquid phase transition process. Variation in boundary conditions has appreciable impact on the natural convection process and melting behavior. Comparing model.1 (single heating wall) with model.2 (double adjacent heating walls with cold wall), the maximum liquid fraction is increased 16.7% in model.2 and the additional top heating wall acts to accelerate the average melting rate by 16.7%. The comparison between model.3 (double opposite heating walls) and model.4 (double adjacent heating walls without cold wall) shows that the natural convection heat transfer is intensive in model.3 and resulting in a 280% faster melting rate than that in model.4. Comparing the melting rate between the model.5 (all heating walls) and model.3, the increase of 54% due to the more heating walls in model.5 is observed.

Heater Position and Alumina Effects on Octadecane Melting in Sideways Cooled Cavities

In the present study, the enthalpy-based lattice Boltzmann method (LBM) with multidistribution function model is used to investigate the melting process engendered by a thin heater placed in the horizontal median plane of the cavity. The latter is cooled from its vertical walls by maintaining their temperature constant at , lower than the constant temperature of the heater (), while the top and bottom horizontal walls are insulated. The cavity is filled with a nonmelted octadecane laden with nanoparticles uniformly distributed in the basic phase-change material. Three positions of the thin heat plate are considered: heater centrally located or shifted toward the right vertical wall (two positions). The LBM with the multirelaxation time scheme is used to solve the flow problem, whereas the finite volume method is used to solve the energy equation. The simulations are performed for the three locations of the heater, with and without nanoparticles. The obtained results show that the addition of nanoparticles has a limited effect on the melting rate and stored energy, whereas the heater location has a strong effect on the heat evacuation rate from the sides.

Pore scale investigations on melting of phase change materials considering the interfacial thermal resistance

The performance of phase change materials (PCM) in the latent heat thermal storage system can be improved by doping highly conductive additives to enhance the thermal conduction. In this work, a pore-scale enthalpy-based lattice Boltzmann model is developed to investigate the melting performance of the PCM doped with porous media. The general conjugate boundaries between the doped additives and PCM are properly handled to ensure the continuity of heat flux even when interfacial thermal resistance or local thermal non-equilibrium state cannot be neglected. After code validations, the effects of doping additives on the melting rate of PCM are systematically investigated. The results show that although doping high thermal conductivity additives can enhance the heat conduction, it also significantly reduces the intensity of natural convection. Whether doping additives enhance the melting rate of PCM or not depends on the Rayleigh number and doping content. The melting rate of PCM can be optimized by a proper configuration of doping particles, with a high (low) doping content at the bottom (upper) parts of domain. Furthermore, the interfacial thermal resistance can significantly reduce the melting rate when the ratio of interfacial thermal resistance to bulk conductance resistance is larger than 0.01.

Magnetic regulating the phase change process of Fe3O4-paraffin wax nanocomposites in a square cavity

The addition of external force provides an alternative way to promote the application of phase change materials in thermal-energy storage, space heating, and cooling systems. However, the experimental investigation using external magnetic force to regulate the phase change process is still limited. Here, magnetic Fe3O4 nanoparticles were added to paraffin wax to form phase change nanocomposites with enhanced thermal properties and controllable magnetism. The thermal properties of nanocomposites were measured and the phase change processes under magnetic controlling were experimentally and numerically investigated. A two-dimensional enthalpy-based lattice Boltzmann model with considering the external magnetic force was proposed and the measured thermal properties were used in the simulation. Good agreement between the experiment and simulation was achieved. The effects of different mass fractions of Fe3O4 nanoparticles (0, 1, 2, 3 and 4 wt%), magnetic directions, magnetic field intensities (0, 20, 40, 60 mT) on the phase change characteristics are discussed. The heat transfer efficiency in a square cavity filled with the nanocomposites developed more quickly when the paraffin wax was doped with a higher Fe3O4 mass fraction. Moreover, the phase change characteristics were controlled by the intensity and direction of the magnetic field. This study presents a method to achieve magnetically regulating phase change heat transfer characteristics that have potential applications in the energy-storage industry.

MELTING WITHIN HORIZONTAL H-SHAPED ENCLOSURE WITH ADIABATIC CURVED BOUNDARY AFFECTED BY INCLINATION, MONO/HYBRID NANOFLUIDS AND FINS

From an energy saving viewpoint, full melting of phase change material in thermal storage systems should be achieved. Constrained ice melting with natural convection inside a horizontal H-shaped capsule with adiabatic curved sidewalls is not completed because energy input from hot surfaces overheats the liquid phase on top while stable thermal stratification on bottom persists. Although 90° inclination of capsule engenders full melting of pure ice, the melting process is still sluggish due to low thermal conductivity of ice/water. Hence, heat transfer enhancement techniques using mono Cu, hybrid Ag/MgO nanoparticles, and 310 stainless steel fins are incorporated into system. Existing enthalpy-based lattice Boltzmann method with double distribution function model in single-phase framework is implemented. Insertion of Ag-MgO hybrid nanoparticles within horizontal H-shaped enclosure does not eradicate persistent thermal stratification. Full melting time inside 90° inclined capsule is diminished 13.6 and 24.5%, respectively, when the volume fraction of hybrid nanoparticles is increased from 0.0 to 0.01 and 0.02. While mono Cu nanoparticles give a better thermal performance in contrast to Ag-MgO hybrid nanoparticles, their price is double. Lower volume fraction (0.01) of mono Cu nanoparticles is prescribed since storage capacity is less decreased. Compared to pure PCM melting, partial internal fins mounted on bottom hot surface diminish full melting time 28.0%. However, magnitude of maximum velocity in molten PCM demonstrates that existence of fins considerably limits growth of natural convection flow.

The enthalpy-based lattice Boltzmann method (LBM) for simulation of NePCM melting in inclined elliptical annulus

Constrained melting of ice as a PCM11Phase Change Material. in inclined elliptical annulus should be studied. Efficiency of heat transfer enhancement methods such as insertion of Cu nanoparticles and metallic porous matrix in this heat storage system must be determined. Porous material is made of alloys of Nickel and Steel. The enthalpy-based LBM22Lattice Boltzmann Method. with a D2Q9-DDF33Double Distribution Function. model at the REV44Representative Elementary Volume. scale is implemented. There is thermal equilibrium condition between porous media and PCM. Also, for NEPCM55Nanoparticles-Enhanced PCM. melting, the single phase flow model is adopted. Particle diameter in nanofluid is equal to 100 nm. The sub-cooling of solid PCM is ignored. Prandtl number, Stefan number, Rayleigh number and Darcy number are 6.2, 1, 2×105 and 10−3, respectively. The volumetric concentric of the nanoparticles is between 0 and 0.02. Porosity is between 1 and 0.9. It is found that inclination of the elliptical annulus does not engender any change in the liquid fraction. Inserting nanoparticles is best effective technique to enhance liquid fraction in oblate annulus due to enhanced conduction heat transfer. Use of porous matrix is recommended for prolate and inclined configurations. It obviates considerably stable stratification at bottom of elliptical annulus as a thermal storage unit.

Thermal performances of saturated porous soil during freezing process using lattice Boltzmann method

A stochastic growth method for generating the porous soil structure is proposed, and an enthalpy-based lattice Boltzmann phase transition model is introduced. Thermal performance of phase transition in saturated porous soil during freezing is investigated. The effects of thermal diffusivity ratio of porous medium to fluid, difference in specific heat capacity between liquid and solid phase, and porosity of porous medium are investigated. The results show that higher thermal diffusivity ratio will promote the low-temperature propagation and phase interface movement while higher specific heat capacity difference and porosity will hinder the temperature propagation and phase transition from liquid to solid. The solid–liquid interface moves from 39 to 51 mm with the ratio increasing from 2 to 5; the interface position decreases from 51 to 26 mm with the difference increasing from 2000 to 26,000; the interface moves from 59 to 47 mm when the porosity increases from 0.2 to 0.8.

Lattice Boltzmann Simulation of Metallic Powder Melting during Additive Manufacturing

Additive manufacturing (AM) is a prevailing topic. Among all the processes during AM, the initiation and evolution of melt pool is of vital importance. Lots of studies are devoted to the fundamental mechanism of melt pool, but most of them only focus on the macroscopic level. However, when it comes to the mesoscopic level, it can be founded that the melt pool is the result of melting and fusion of powders. To better understand the melt pool, it is necessary to understand the melting and fusion characteristics of powders. This paper aims to provide a new kind of mesoscopic perspective to the melt pool through the investigation on single powder melting. Enthalpy based Lattice Boltzmann method, combined with Neumann boundary, is adopted to model the powder melting under fixed and moving laser beam. Results indicate that for the fixed laser beam, the melting front presents a symmetric convex. The increase of the laser power input can increase the energy absorbed by the powder, speed up the melting process and enhance the flow inside the powder. For the moving laser beam, the melting front loses its symmetry. The increase of the scanning speed can decrease the energy absorbed by the powder, the melting volume fraction and the inside flow. The fast moving speed could easily result in partially melted powder. All these results could help us better understand the powder melting under different laser inputs, and thus arranging the laser power reasonably to make the best use of it according to various occasions.

Effect of heating modes on melting performance of a solid–liquid phase change using lattice Boltzmann model

The effects of heating modes on melting processes of pure tin and gallium are simulated using the enthalpy-based lattice Boltzmann method (LBM) with multi-relaxation time in a square cavity. Five different wall-heating modes including the uniform wall-temperature (UWT), increment wall-temperature (IWT), decrease wall-temperature (DWT), convex wall-temperature (CWT) and sink wall-temperature (SWT) are simulated at the left-wall and bottom-wall heaters of the cavity. The natural convective heat transfer is simulated with the change of Fourier numbers and Rayleigh numbers. The melting rate, melting efficiency and synergy angle are compared with the left-wall heater and the bottom-wall heater at the different heating modes. The dimensionless melting times decrease and the melting efficiencies increase with the increase of Rayleigh numbers. The dimensionless melting times are largest at the CWT heating mode, and lowest at the UWT heating mode. The synergy angles are lowest at the CWT heating mode and largest at the UWT heating mode at the bottom-wall and left-wall heaters. Comprehensive comparison shows that the melting process at the CWT heating mode is faster than the other heating modes because of the better field synergy at the hot wall.