Thermal Lattice Boltzmann Model Research Articles

A consistent thermal lattice Boltzmann method for heat transfer in arbitrary combinations of solid, fluid, and porous media

In this study, a thermal lattice Boltzmann model (TLBM) is developed for heat transfer in arbitrary combinations of solid, fluid, and porous media. The velocity and temperature field are modeled through a double distribution function (DDF) approach. By introducing a new temperature equilibrium DF, the present TLBM not only recovers the correct macroscopic energy equation via Chapman–Enskog expansion but also possesses a consistent definition of heat capacity ratio which is lacked in previous thermal models. To validate the proposed method, four benchmark cases are tested, including the heat conduction in dual heterogeneous media, Couette flow in partially porous channel, natural convection in a porous cavity, and natural convection in a partially solid and porous cavity. Good agreement is attained, which shows the applicability of the present model for simulating thermal flows in combined solid, fluid, and porous media conditions.

Pore-scale investigation on reactive flow in porous media with immiscible phase using lattice Boltzmann method

Reactive flow happens during carbonate rock acidification. In the present study, carbonate rock dissolution process is investigated by lattice Boltzmann method at pore scale. The two immiscible fluids flow, solute transport and heat transfer are 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 is updated by Volume of Pixel method. The results show that the immiscible phase has negative effect on dissolution, while positive effect on acid penetration. The immiscible phase effect is influenced by the inlet velocity, porous media porosity, surface wettability and temperature. The increasing inlet velocity and temperature accelerate the dissolution rate, but decrease the degree of immiscible phase suppression on dissolution. The surface wettability impact on dissolution process is influenced by the immiscible phase distribution. The porosity affects the degree of immiscible phase suppression on dissolution process slightly.

Axisymmetric lattice Boltzmann model for simulating the freezing process of a sessile water droplet with volume change.

Droplet freezing not only is of fundamental interest but also plays an important role in numerous natural and industrial processes. However, it is challenging to numerically simulate the droplet freezing process due to its involving a complex three-phase system with dynamic phase change and heat transfer. Here we propose an axisymmetric lattice Boltzmann (LB) model to simulate the freezing process of a sessile water droplet with consideration of droplet volume expansion. Combined with the multiphase flow LB model and the enthalpy thermal LB model, our proposed approach is applied to simulate the sessile water droplet freezing on both hydrophilic and hydrophobic surfaces at a fixed subcooled temperature. Through comparison with the experimental counterpart, the comparison results show that our axisymmetric LB model can satisfactorily describe such sessile droplet freezing processes. Moreover, we use both LB simulations and analytical models to study the effects of contact angle and volume expansion on the freezing time and the cone shape formed on the top of frozen droplets. The analytical models are obtained based on heat transfer and geometric analyses. Additionally, we show analytically and numerically that the freezing front-to-interface angle keeps nearly constant (smaller than 90°).

2D Simulation of boiling heat transfer on the wall with an improved hybrid lattice Boltzmann model

This paper investigates the energy non-conservation problem of the hybrid thermal lattice Boltzmann (LB) phase change model. To solve this problem, an infinite volume discrete scheme was introduced to deal with the diffusion term in the energy equation. After verifying this model with energy conservation law in the simulation of the one-dimensional heat conduction across the liquid-vapor interface and the liquid film evaporation on the heating wall, the improved hybrid thermal LB model was then applied in the two-dimensional simulation of bubble nucleation and boiling heat transfer. With an innovative nucleation site treatment on the wall, the complete boiling stages and the boiling curve were successfully reproduced without adding any heating fluctuations. The bubble nucleation, growth, departure, and coalescence were also well-captured. Some basic features of boiling heat transfer were clearly observed in the numerical results, including the bubble nucleation site activation, bubble departure frequency, character of bubble shape at different regime, and horizontal movement of bubble during the boiling process.

Heat transfer dynamics inside the Drop-on-Demand inkjet printhead with a hybrid thermal lattice Boltzmann model

The heat transfer dynamics inside the Drop-on-Demand (DoD) printhead play a significant role for improving temperature compensation and jetting reproducibility. A three-dimensional hybrid thermal lattice Boltzmann model is employed to explore the temperature distributions within the ink chamber in DoD droplet jetting process. The scenarios including heated walls resulting from deformation of lead zirconate titanate (PZT) and heat sources coupled with heated substrate are investigated. It is found that the isotherms evolutions are hindered from heat walls to the center of ink chamber by the velocity fields during the droplet jetting process. The thermal fields adjacent to the inlet and outlet regions are affected by the thermal boundaries with lower temperature and exhibit meniscus isotherms. Attributing to the combined effects of advection-dominated heat transfer and velocity fields of jetting dynamics, the overall temperature distributions obtain the quicker stabilized status for coupled heat sources. Moreover, the temperature distributions in the lower-center region exhibit the vorticial structure. In summary, we illustrate the temporal evolutions of temperature distributions within ink chamber and offer an in-depth exploration of heat transfer dynamics coupled with velocity fields. It could be beneficial for exploring the first droplet dissimilarities and improving the temperature compensation.

Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number

We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Bénard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-Bénard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106,3×106, and 107, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.

Hybrid recursive regularized thermal lattice Boltzmann model for high subsonic compressible flows

A thermal lattice Boltzmann model with a hybrid recursive regularization (HRR) collision operator is developed on standard lattices for simulation of subsonic and sonic compressible flows without shock. The approach is hybrid: mass and momentum conservation equations are solved using a lattice Boltzmann solver, while the energy conservation is solved under entropy form with a finite volume solver. The defect of Galilean invariance related to Mach number is corrected by the third order equilibrium distribution function, supplemented by an additional correcting term and hybrid recursive regularization. The proposed approach is assessed considering the simulation of i) an isentropic vortex convection, ii) a two dimensional acoustic pulse and iii) non-isothermal Gaussian pulse with Ma number in range of 0 to 1. Numerical simulations demonstrate that the flaw in Galilean invariance is effectively eliminated by the compressible HRR model. At last, the compressible laminar flows over flat plate at Ma number of 0.3 and 0.87, Reynolds number of 105 are considered to validate the capture of viscous and diffusive effects.

Lattice Boltzmann study of pool boiling heat transfer enhancement on structured surfaces

Pool boiling heat transfer enhancement on structured surfaces with columns is investigated by a thermal two-phase lattice Boltzmann model. The effects of geometrical parameters, including column height (H), width (W) and gap spacing (D), are discussed in detail. The size of columns is comparable to the diameter of a typical detached bubble (db). It is found that the heat transfer performance mainly depends on two factors: the heated surface area A and local convective flow field. When W and D are properly chosen as about W=D≈4db, increasing H enhances the heat transfer solely due to the increase of the surface area. When W and D are small, it is observed that the top of the columns and the channels are mostly covered by a layer of vapor, respectively, which weaken the convection. Under the circumstances, although surface area A increases, heat transfer enhancement is not so significant. For the surface tension effect, the enhancement of the structured surface decreases with the increase of capillary number compared to that of the plain surface. The mechanism is that at larger capillary number, the convection close to the channel may be partially blocked, which hinders the heat transfer. An optimal enhancement could be achieved when A is as large as possible and meanwhile the convection is not hindered by the bubbles behaviors. The finding here may shed some light on mechanism of heat transfer enhancement on structured surfaces with columns.

Single droplet condensation in presence of non-condensable gas by a multi-component multi-phase thermal lattice Boltzmann model

A multi-component multi-phase thermal lattice Boltzmann model considering vapor-liquid phase change is developed to study droplet condensation with the presence of non-condensable gas. Some tests, including an isolated droplet evaporation, are conducted to verify the capability of this model in simulating multi-component multi-phase flow with vapor-liquid phase change. After that, single droplet condensation considering non-condensable gas is investigated with different mass fraction of non-condensable component and contact angles. The results show that the influence of the non-condensable gas upon droplet condensation heat transfer is depended on the growth stage and the amount of the non-condensable gas. The mass transfer of vapor and non-condensable component will tend to an equilibrium state with the droplet condensation going. Furthermore, for different contact angles, the dynamic behavior of the contact line plays a critical role in the accumulation effect of the non-condensable component. And the heat transfer of droplet condensation is enhanced by the hydrophilic substrate rather than the hydrophobic substrate as expected, no matter adding the non-condensable component or not. In different conditions, the power law, which fits the droplet radius with time, is used to define the growth rate mathematically.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part II: Natural convection of nanofluids in a square enclosure

The novel solid-liquid local thermal non-equilibrium lattice Boltzmann model, developed in Part I of this paper series [1], is applied to the classical problem of natural convection of nanofluids in a square enclosure with vertical walls at differential temperatures. Effects of Rayleigh numbers, nanoparticles random motion, nanoparticles volume fraction and nanoparticles non-uniform distribution in natural convection of nanofluids are studied. Because random motions of nanoparticles are intensified with temperature, vertical velocity and temperature profiles in the nanofluid are asymmetric with respect to the hot and cold vertical walls. Distribution of nanoparticles in the nanofluid inside the enclosure is affected by both the Rayleigh number and random motion of nanoparticles, and nanoparticles’ distribution become relatively non-uniform at relatively high Rayleigh numbers. The non-uniform distribution of nanoparticles also affect local vertical velocity distribution, local temperature distribution, and the average Nusselt numbers. The effect of random motion of nanoparticles is shown to be responsible for enhanced convection at small Rayleigh numbers, the increasing viscosity of nanofluids is shown to be responsible for the deteriorating effects on heat transfer at intermediate Rayleigh numbers and non-uniform distribution of nanoparticles is shown to be responsible for ascending trend of Nusselt numbers at high Rayleigh numbers. The non-monotonous variation of the Nusselt number with respect to the Rayleigh number are in qualitative agreement with existing experimental data.

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part I: Model development, shear flow and heat conduction in a nanofluid

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for hydrodynamics and heat transfer in a nanofluid is developed in this paper. In this proposed model, interactions between fluid and solid nanoparticles, random motion of nanoparticles as well as heat transfer between nanoparticles and the base fluid are taken into consideration. This novel model is applied to two simple nanofluids problems: isothermal shear flow between two parallel plates moving at different velocities, and heat conduction between two parallel plates at different temperatures. For the problem of shear flow, it is found that nanoparticles random motion causes the instantaneous velocity distribution of a nanofluid to become non-linear in the shear flow between two parallel plates at microscopic level. At macroscopic level, it is found that as nanoparticles volume fraction increases, effects of nanoparticles random motion are enlarged and the time-average velocity distribution of a nanofluid deviates more from a linear distribution in a shear flow. For the problem of heat conduction between parallel plates at different temperatures, it is found that random motion of nanoparticles together with their high thermal diffusivity and thermal conductivity, causing the instantaneous temperature distribution in the nanofluid to become non-linear between two parallel plates at different temperatures. Temperature inside a nanoparticle is shown to be non-uniform, and temperature gradients in the fluid near a nanoparticles are elevated, thus heat transfer rate is enhanced near a nanoparticle. Time-average temperature gradients of a nanofluid at hot/cooled wall are higher than those of a pure fluid in heat conduction between parallel plates at different temperatures. Comparisons of calculated dynamic viscosity and thermal conductivity based on this novel model are found in good agreement with existing correlation equations. Thus, the accuracy of this novel solid–liquid local thermal non-equilibrium model for a nanofluid is validated.

Numerical analyses and optimization of tubular thermochemical heat storage reactors using axisymmetric thermal lattice Boltzmann model

Axisymmetric lattice Boltzmann (LB) model has gained great development in the field of fluid flow and heat transfer in recent decades. Compared with the standard LB method, the axisymmetric LB method can solve 3D axisymmetric problems with minimal meshes. This numerical method will be helpful in research on thermochemical heat storage, especially considering the profound understanding and optimization of reactor performance. In this study, we extended a previous axisymmetric LB model to simulate the charging/discharging processes of a MgO/Mg(OH)2 thermochemical reactor. We derived a new evolution function by including an unstable heat source term out of a chemical reaction. New isothermal and heat flux boundary treatment approaches were proposed to maintain the precision of this axisymmetric LB model in the presence of the heat source term. In addition, a local method for transient conjugate heat transfer simulation without the utilization of temperature gradient information at the fluid-solid interface was developed to predict heat transfer between the reactor bed and heat transfer fluid. With the proposed axisymmetric thermal LB model, the charging/discharging processes of a tubular MgO/Mg(OH)2 thermochemical reactor unit with a heat exchanger were simulated. Results showed that the average power output was maximized with a bed thickness of 1.0 cm. The length of the reactor unit should be considered by balancing power output and cost.

Numerical investigation of convective dropwise condensation flow by a hybrid thermal lattice Boltzmann method

The present paper, convective dropwise condensation flow over a cold spot is numerically investigated using a 2D hybrid thermal lattice Boltzmann (LB) model with vapor-liquid phase change. After validating the present LB model, dropwise condensation on a cold spot as the nucleation region is simulated so as to study the nucleation and growth of the isolated droplet. The well-known power law for the growth of a single condensing droplet is demonstrated. And then, both simulations of dropwise condensation and convective dropwise condensation are carried out to study the effect of forced convective flow on dropwise condensation. Aiming to consider the effect of contact angle, the droplet is growing in the constant contact radius (CCR) mode. The results indicate that the forced convectional flow complicates the internal flow of the droplet and the vapor flow. The detouring flow (including the lee-side vortex) around the droplet in an isothermal system is replaced by the suction flow owing to condensation. The interaction between the dragging force of the vapor flow and the surface tension gradient changes the size of two symmetric vortices within the droplet in dropwise condensation. The size of these two vortices inside the droplet depends on the velocity and direction of convective flow. By comparison, the heat transfer enhancement of the superimposed flow is not worth mentioning in spite of different flow mode. Not affected by the vapor flow, the heat transfer is weakened by increasing of the contact angle owing to the change of conduction resistance. The present study illustrates the mechanisms of convective dropwise condensation flow in detail.

Lattice Boltzmann simulation of tree-shaped fins enhanced melting heat transfer

A thermal lattice Boltzmann model is developed to simulate the melting process with natural convection in a cavity filled with tree-shaped solid fins, in which the velocity field and temperature field distribution functions are considered. The present model incorporates the total enthalpy and a free parameter in the equilibrium distribution function to handle conjugate heat transfer. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. Increasing the number of branching levels leads to a more rapid melting process, and selecting appropriate bifurcation angle has more efficient heat transfer performance.

Numerical simulation of MHD oscillatory mixed convection in CZ crystal growth by Lattice Boltzmann method

A two-dimensional axisymmetric swirling thermal lattice Boltzmann model is presented to study the magnetohydrodynamics (MHD) oscillatory mixed convection in the melt of Czochralski silicon crystal growth in this paper. The governing equations are all solved by lattice Boltzmann method. The D2Q9 model is applied to solve the radial and axial velocities of the melt. Two D2Q5 models are adopted to solve the azimuthal (swirling) velocity and the temperature. The comparison with experiment and finite volume method proves that the presented model can be used as an alternative for simulating the axisymmetric crystal growth. Furthermore, simulations of the melt flow structure and heat transfer under a vertical magnetic field are conducted. And the critical Reynolds numbers Recr, which lead to the onset of the oscillatory melt convection, are calculated in different Richardson numbers (Ri), Ri=0.1,0.5,1.0,1.5,2.0,3.0, and different Hartmann numbers (Ha), Ha=0,10,20,30,40,50. In addition, the magnetic stability diagram is established according to a series of computations and the relationship between crystal rotation parameter and the state of the melt convection are analyzed. Compared with the traditional three-dimensional computational model, the proposed model in this paper has less computation time in simulating the axisymmetric swirling flow without affecting the accuracy of the results. The obtained critical Reynolds number has certain reference for improving the crystal growth parameter in practice.

Two-phase lattice Boltzmann simulation of natural convection in a Cu-water nanofluid-filled porous cavity: Effects of thermal boundary conditions on heat transfer and entropy generation

The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (103 ≤ Ra ≤ 105) and Darcy number (10−1 ≤ Da ≤ 10−6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.

Boiling heat transfer on hydrophilic-hydrophobic mixed surfaces: A 3D lattice Boltzmann study

In this paper, the boiling heat transfer performance on a type of hydrophilic-hydrophobic mixed surfaces is numerically investigated using a three-dimensional (3D) thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The mixed surface is square-pillar textured with the pillar being composed of hydrophilic side walls and a hydrophobic top surface. Numerical simulations are carried out to investigate the influences of the contact angle of the hydrophilic region of the mixed surface, the pillar width, and the pillar height. It is found that an appropriate increase of the contact angle of the hydrophilic region, θphi, can promote the bubble nucleation on the bottom substrate and hence enhances the nucleate boiling on the hydrophilic-hydrophobic mixed surface, but a larger θphi may make the boiling enter the transition or film boiling regime. Moreover, it is shown that the heat flux initially increases with the increase of the pillar width and shows a declining trend after reaching its peak value. The optimal θphi and the optimal pillar width are found to decrease with the increase of the wall superheat, revealing that the hydrophilic region of the mixed surface should play an increasingly important role when the wall superheat increases. The orthogonal array tests are performed and it is found that the contact angle of the hydrophilic region is the most important influential factor among the three investigated factors.

Lattice Boltzmann simulation of melting in a cubical cavity with a local heat-flux source

A three-dimensional numerical study is conducted to investigate the effect of heat-flux source location on the melting of phase change material (PCM) in a cubical cavity. An enthalpy-based incompressible thermal lattice Boltzmann model (iTLBM) has been established and validated by two benchmark problems. In order to reveal the effect of heat-flux source location in melting rate in three-dimensional space, both horizontal and vertical locations are considered. The numerical results show that the size of local heater and its heat flux play an essential role in melting rate. Furthermore, the variation of the location of the heat-flux source from both sides to the middle region of the cavity leads to the increase of the total heat flux on the interface, which also results in the increase of melting rate. Finally, we also find that the melting rate increases as the location of the heat-flux source is changed from top to the bottom region of the cavity, which is attributed to the enhancement of convection heat transfer.

Simulation of stratified flows over a ridge using a lattice Boltzmann model

A three-dimensional thermal lattice Boltzmann model (TLBM) using multi-relaxation time method was used to simulate stratified atmospheric flows over a ridge. The main objective was to study the efficacy of this method for turbulent flows in the atmospheric boundary layer, complex terrain flows in particular. The simulation results were compared with results obtained using a traditional finite difference method based on the Navier–Stokes equations and with previous laboratory results on stably stratified flows over an isolated ridge. The initial density profile is neutral stratification in the boundary layer, topped with a stable cap and stable stratification aloft. The TLBM simulations produced waves, rotors, and hydraulic jumps in the lee side of the ridge for stably stratified flows, depending on the governing stability parameters. The Smagorinsky turbulence parameterization produced typical turbulence spectra for the velocity components at the lee side of the ridge, and the turbulent flow characteristics of varied stratifications were also analyzed. The comparison of TLBM simulations with other numerical simulations and laboratory studies indicated that TLBM is a viable method for numerical modeling of stratified atmospheric flows. To our knowledge, this is the first TLBM simulation of stratified atmospheric flow over a ridge. The details of the TLBM, its implementation of complex boundaries and the subgrid turbulence parameterizations used in this study are also described in this article.