Boltzmann Model Research Articles

Mesoscale multi-component energy density transport for natural convective microchip cooling with solid–liquid–gas phase changes

A design of microchip cooling with natural convection driven multi-phase coolant flows is proposed by using thermoelectric modules as heat sinks. A new multi-component multi-phase (MCMP) thermal energy transport model is built for convective heat transfer with solid–liquid–gas phase changes. Different from previous lattice Boltzmann models based on temperature distributions, the present model is based on MCMP energy density distributions, which track sensible and latent heat transport for each phase. The local MCMP heat fluxes are related to mesoscale relaxation times and phase volume fractions. Transient solid–liquid–gas interfaces and local temperatures are obtained through the dynamical balance of mesoscale forces and fluxes among all phases together with MCMP enthalpy–temperature distributions. Comparisons of the on and off states of the heat sink modules show that the chip temperature can drop from about 300 to 110 °C, with the coolant liquid–gas phase change temperature of 80 °C at equivalent heat source and sink intensities of 100 W/cm2. Results also show that increasing heat sink intensity to 300 W/cm2 or decreasing gas–liquid phase change temperature to 60 °C can further decrease the chip temperature to 90 °C. The effects of sizes of chips, modules, and cooling units are also illustrated. It is observed that gas bubbles attached on chips impede heat transfer due to the low gas phase thermal conductivity, which means future improvements should also focus on removing or degrading attached gas bubbles. This model provides a quantitative tool for immersion chip cooling performances.

A lattice Boltzmann model for the interface tracking of immiscible ternary fluids based on the conservative Allen-Cahn equation

A lattice Boltzmann (LB) model for the interface tracking of immiscible ternary fluids is proposed based on the conservative Allen-Cahn (A-C) equation. A nonlocal equilibrium distribution function source term is adopted in the LB equation to eliminate the unwanted numerical items. With the new LB equation and the carefully designed equilibrium distribution function, Chapman-Enskog analysis shows that the present model can correctly recover the conservative A-C equation with second-order accuracy. A series of benchmark cases have been used to validate the accuracy and stability of the present model, including the classical diagonal translation of two concentric circular interfaces, the rigid-body rotation of Zalesak's disk, and the periodic shear deformation of two tangent circular interfaces. By coupling the dynamic LB model for Navier-Stokes equations, the stationary droplets, the spreading of a liquid lens, the spinodal decomposition, and the Raleigh-Taylor instability have also been simulated in the framework of ternary fluids. Utilizing the geometric interpolation method, the wettability effect of the horizontal boundary is considered and numerical tests with different wall contact angles have been performed to verify the applicability of the present model. All the numerical tests show that the present model can capture the interfaces among the immiscible ternary fluids accurately. Furthermore, using fewer discrete velocity directions, the present model shows higher numerical accuracy and stability compared with other existing numerical models. Therefore, it is promising to improve computational efficiency.

Investigation on latent heat energy storage using phase change material enhanced by gradient-porosity metal foam

Utilizing an optimized gradient porosity can help with the temperature uniformity and alleviate the temperature aggregation. In this paper, a solid–liquid lattice Boltzmann (LB) model at the representative elementary volume scale (REV-scale) is established to investigate the enhancement mechanism of gradient porosity on LTES units. Three gradient porosity including Chinese-fan-shape, vertical and concentric distribution has been investigated. The findings demonstrate that a well-designed gradient porosity can significantly decrease the melting time, with the best performance observed when using a fan-shape arrangement of a certain gradient. In comparison to a homogeneous porosity, the fan-shape arrangement of a specific gradient reduces the melting time by 36.1 % and ensures a more uniform temperature distribution. Increasing the number of layers from two to five has no remarkable improvement on melting, not exceeding 4.4 % in total melting time. Conversely, increasing the porosity gradient leads to an increase in melting time of no less than 36.1 %. Furthermore, an extended dimensionless number Ram in a range of 150 ∼ 600 is investigated. The results suggest that, with the increase of Ram the temperature aggregation is more significant, and the gains in melting rate are unable to offset the increased heating temperature's impact on the melting time.

Natural Convective Nanofluid Flows Immersed in Oscillating Magnetic Fields Simulated by a Sub-Continuous Lattice Boltzmann Model

Abstract Natural convective nanofluid flows immersed in oscillating magnetic fields are simulated with a sub-continuous nondimensional lattice Boltzmann model. The effective electrical conductivity model is built including coupled effects of nanoparticle concentrations and two Knudsen numbers. Effects of directions, frequencies, and strength amplitudes of the magnetic fields are studied in wide ranges of Hartmann numbers (0.1≤Haf,L≤600) and Rayleigh numbers (103≤Raf,L≤107). To achieve higher values of cycle averaged Nusselt numbers Nu¯̂f,L, optimal magnetic directions are along or opposite from the gravity directions. Effects of the magnetic frequency f˜B are negligible, in the conduction dominating lower Rayleigh number regime of Raf,L<104. In the convection dominating regime, Nu¯̂f,L increase with Raf,L in orders of Raf,L0.48 and Raf,L0.45 for vertical and horizontal magnetic directions, respectively, and maximum values of Nu¯̂f,L appear at the optimal magnetic frequency of f˜B=1/5cs*MaL(L/UL) for all magnetic directions. With Raf,L as high as 106, the oscillating amplitudes of the transient wall mean Nusselt numbers Nu¯f,L increase with increasing Haf,L, but the cycle averaged Nusselt numbers Nu¯̂f,L decrease from 9.35 to 1.42 with increasing Haf,L in the transient regime of 5≤Haf,L≤500. Meanwhile, heat transfer patterns transit back from convection to conduction dominating patterns with increasing Haf,L, as illustrated by transient streamlines and isotherms.

Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

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.

An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation

This paper is concerned with the lattice Boltzmann (LB) method for a class of time fractional partial differential equations (FPDEs) in the Caputo sense. By utilizing the properties of the Caputo derivative and discretization in time, FPDEs can be approximately transformed into standard partial differential equations with integer orders. Through incorporating an auxiliary distribution function into the evolution equation, which assists in recovering the macroscopic quantity u, the LB model with spatial second-order accuracy is constructed. The numerical experiments verify that the numerical results are in good agreement with analytical solutions and that the accuracy of the present model is better than the previous solutions.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.

Study on the melting process of oxide layer of micrometer-sized aluminum particles using Lattice Boltzmann method

The study of the oxide layer in aluminum-oxygen combustion is crucial for the subsequent reaction. In this article, a 2-D lattice Boltzmann model is established and the effects of different Rayleigh number, oxide thickness, Ste number, and porosity on melting speed and melting time are studied based on the enthalpy method. The results demonstrate that a low Rayleigh number has no noticeable impact on the melting process. However, a rise in the Rayleigh number can obviously advance the melting process when the Rayleigh number exceeds 105. The melting speed slows down and the melting time prolongs as the oxide thickness increases, but the effect of thickness on melting speed decreases progressively with increasing thickness. In contrast, rising Stefan number can promote the melting process, and the effect is more pronounced at lower Stefan number. High porosity is beneficial to the development of natural convection and is able to significantly boost the melting process.

Simulation of a sessile nanofluid droplet freezing with an immersed boundary-lattice Boltzmann model

The freezing process of a sessile nanofluid droplet has been reported to behave differently from a pure sessile water droplet in terms of freezing dynamics and the final shape of the ice droplet. When nanoparticles are added to the water droplet, instead of forming a pointed tip on the top, the completely frozen droplet exhibits a flat plateau shape. To investigate this unique scenario, we developed a lattice Boltzmann (LB) model that combines the multiphase solidification model (MSM) with the immersed boundary method (IBM). The MSM is based on our previous work of simulating the freezing of a pure droplet, while the IBM is used to handle the interaction forces between the suspended particles and the different phases in the freezing droplet. Using this LB model, we succeeded in simulating the formation process of the frozen plateau shape. The simulation takes into account the dynamics of the dispersed particles, including their expulsion from the propagation freezing front and their segregation, which brings the liquid water to the edge. We compared the simulated freezing shape profiles with the experimental images and found that the shape forms in a similar manner. We then used the developed model to explore more cases, considering the effects of droplet contact angles and particle volume concentration. Results show that the distribution of particles and final droplet height depend on the surface wettability, as the freezing front exhibits a concave/convex shape on hydrophilic/hydrophobic surfaces, resulting in different particle separation distributions on the freezing front interface. Furthermore, our simulation results confirm the experimental conclusion that the plateau size on the frozen top increases with particle concentration and appears to be independent of the initial droplet contact angle.

Thermodynamic effects of gas adiabatic index on cavitation bubble collapse

In this paper, an improved multicomponent lattice Boltzmann model is employed to investigate the impact of the gas properties, specifically the gas adiabatic index, on the thermodynamic effects of cavitation bubble collapse. The study focuses on analyzing the temperature evolution in the flow field and the resulting thermal effects on the surrounding wall. The accuracy of the developed model is verified through comparisons with analytical solutions of the Rayleigh-Plesset equation and the validation of the adiabatic law. Then, a thermodynamic model of cavitation bubble composed of two-mixed gases collapsing near a wall is established to explore the influence of the gas adiabatic index γ on the temperature behavior. Key findings include the observation that the γ affects the temperature of the first collapse significantly, while its influence on the second collapse is minimal. Additionally, the presence of low-temperature regions near the bubble surface during collapse impacts both bubble and wall temperatures. The study also demonstrates that the γ affects maximum and minimum wall temperatures. The results have implications for selecting specific non-condensable gas properties within cavitation bubbles for targeted cooling or heating purposes, including potential applications in electronic component cooling and environmental refrigeration.

Viscous effects on morphological and thermodynamic non-equilibrium characterizations of shock–bubble interaction

A two-fluid discrete Boltzmann model with a flexible Prandtl number is formulated to study the shock–bubble interaction (SBI). This paper mainly focuses on the viscous effects on morphological and thermodynamic non-equilibrium (TNE) characterizations during the SBI process. Due to the rapid and brief nature of the SBI process, viscosity has a relatively limited influence on macroscopic parameters but significantly affects the TNE features of the fluid system. Morphologically, viscosity affects the configuration of the vortex pair, increases both the amplitudes of gradients of average density and average temperature of the fluid field, and reduces circulation of the bubble. As a higher viscosity fluid absorbs more energy from the shock wave, it leads to an increase in both the proportion of the high-density region and the corresponding boundary length for a fixed density threshold. The spatiotemporal features of TNE quantities are analyzed from multiple perspectives. The spatial configuration of these TNE quantities exhibits interesting symmetry, which aids in understanding the way and extent to which fluid unit deviates from the equilibrium state. Theoretically, viscosity influences these TNE quantities by affecting the transport coefficients and gradients of macroscopic quantity. Meanwhile, the viscosity increases the entropy production rate originating from the non-organized momentum flux mainly through amplifying the transport coefficient and enhances the entropy production rate contributed by the non-organized energy flux by raising the temperature gradient. These multi-perspective results collectively provide a relatively comprehensive depiction of the SBI.

Effects of continuous wettability on the pool-boiling bubble dynamics and heat transfer characteristics of a triangular structure-roughened surface

A phase transition lattice Boltzmann model is used in the current study to simulate the pool boiling process on a triangular structure-roughened surface with conjugate heat transfer effect. Through the verification of the Laplace law and the theoretical film boiling results, the adopted model is ensured to predict pool boiling phenomena accurately with excellent stability. The bubble dynamics, including the nucleation, growth, coalescence and detachment of the bubbles on the triangular structure-roughened surface with continuous wettability, is discussed. Little research has been conducted on the continuous wettability effect on the pool boiling with triangular structures-roughened surfaces. The results show that a hydrophilic surface inhibits bubble growth but facilities bubble detachment with bubble nucleation at the concave corners; a hydrophobic surface increases bubble growth but inhibits bubble detachment with bubble nucleation at hydrophobic areas. It is found that when the direction of the self-drive favors bubble detachment from the surface, the surface which from contact angle θBottom=120° to θTop=90° under the study can achieve better heat transfer over a wider range of superheat, while setting the continuous wettability from θBottom=120° to θTop=60° can achieve a better heat flux density at lower superheat.

Pore-Scale Investigation of Mass Transport in Compressed Cathode Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs) are considered a promising energy source in the field of transport and distributed power generation. Fundamental research into their key components is needed to improve PEMFC performance and accelerate commercialization. Binder addition and compression induced by assembly pressure can significantly change the microstructure of the gas diffusion layer and affect mass transport. A two-dimensional multicomponent lattice Boltzmann (LB) model considering the cathode electrochemical reaction was developed, and a GDL was reconstructed numerically and considering a binder structure. The effects of the binder and compression on mass transport and electrochemical performance within the GDL were investigated. The results showed that an increase in binder volume fraction led to more chain-like structures and closed pores that were unfavorable for mass transport. Compression increased the mass transfer resistance of the GDL in the region under the rib, leading to a decrease in oxygen concentration and local current density.

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.

Pore-scale melting behaviors in composite phase change material with porosity gradients

Latent heat storage is a promising thermal energy storage solution to tackle the time–space conflict in energy demand. However, the low thermal conductivity of pure phase change material may limit the thermal energy storage performance of latent heat storage systems. In this work, porous support with gradient porosity and high thermal conductivity is incorporated into the phase change material to minimize the total melting time. A pore-scale lattice Boltzmann model for simulating the melting process of composite phase change material is established to investigate the effect of gradient porosity on the dynamic melting process. The results show that the two-dimensional gradient porosity structure can significantly improve the melting rate of composite phase change material. Compared with a uniform porosity structure, the melting time can be reduced by up to 8.58% in this work. By considering the changes in dominant heat transfer mechanisms during the melting process and the asymmetric evolution of the upper and lower parts of the melting front, the two-dimensional gradient porosity structure combines the advantages of horizontal and vertical one-dimensional gradient porosity structure. It is also found that the gradient porosity structures slow down the melting process of composite phase change material when the porosity is too small in the lower right corner of the square cavity or when the two-dimensional gradient porosity is divided too finely. The solid phase change material in this area mainly relies on thermal convection for melting, and it can significantly delay the melting time when the flow velocity is low, with a maximum extension of 26.58% of the melting time as compared to a uniform porosity structure.

Lattice Boltzmann modelling of salt precipitation during brine evaporation

Salt precipitation during brine evaporation in porous media is an important phenomenon in a variety of natural and engineering scenarios. This work establishes a multiphase multicomponent lattice Boltzmann (LB) method with phase change for simulating salt precipitation during brine evaporation. In the proposed LB models, the gas–brine multiphase flow, brine evaporation, salt concentration evolution, salt precipitate nucleation and growth are simultaneously considered. Simulations of the Stefan problem are first conducted to verify the proposed numerical models and determine the diffusion coefficient of brine vapour. Once the lattice Boltzmann models have been validated, salt precipitation during brine evaporation is simulated to investigate the competition mechanisms between salt precipitate nucleation and growth reaction. The results show that the typical salt precipitation patterns in existing experimental observation can be successfully reproduced, including the ring-like and pancake-like patterns. The difference in the salt precipitation patterns is explained by the competition mechanism between precipitate growth and nucleation according to the present study. Furthermore, the salt precipitation during gas injection into a microfluidic chip is investigated. The evolution of salt and brine saturation shows similar patterns to existing experimental results, and the effects of the gas injection rate on salt precipitation performance are clarified. The LB models in the present work can simulate salt precipitation with comprehensive consideration of multiphase brine evaporation, salt species mass transport, precipitate nucleation and growth, which have not been realized in previous studies. The numerical showcases demonstrate the excellent performance of the proposed models for the simulation of salt precipitation in porous media, which promise to guide practical engineering applications like CO2 sequestration.

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.

Condensation mode transition and droplet jumping on microstructured surface

Condensation enhancement on the micropillar structured surfaces is studied using a three-dimensional lattice Boltzmann model, and the optimal micropillar configuration is assessed. The impacts brought by varying micropillar geometric parameters on heat transfer and droplet dynamics during dropwise-to-filmwise transition are explored. Increasing micropillar width and spacing or decreasing height accelerates nucleation and improves nucleation density in the dropwise condensation stage, while radial contraction of the liquid film is hindered and the heat transfer area is increased in the filmwise condensation stage. Compared with its plain competitor, the maximum number of the isolated droplets is increased by 525%, the nucleation time is advanced by 57.1% and the heat flux is increased by 187.4% on the optimal micropillar surface. The entire condensation process spanning over nucleation, coalescence and jumping of multiple condensate droplets on the micropillar surface is realized using the present three-dimensional lattice Boltzmann model for the first time. The effects of height and spacing of micropillar arrays on jumping height and velocity are analyzed. The results show that the micropillar height poses little effect on the jumping height and velocity when the micropillar spacing is 0.1. When the micropillar spacing is 0.15, the jumping height and velocity first increase but then decrease with the increase of the micropillar height. Finally, the condensation heat transfer mechanism under different subcooling on the hierarchical surface is analyzed in detail.