Thermal LB Model Research Articles

Pore-Scale Study of the Thermochemical Process in Porous Media With Immiscible Phase by Lattice Boltzmann Method

Abstract Reactive flow happens in carbonate rocks which are porous media during acidification. In this study, a thermochemical dissolution model based on the lattice Boltzmann method (LBM) is established to investigate the complex thermochemical process in porous media with immiscible phase at pore scale. In the model, the immiscible fluid flow, solute transport, and heat transfer are solved by Shan–Chen multicomponent LB model, mass transport LB model, and multicomponent thermal LB model, respectively. The porous media is generated by the quartet structure generation set, and the evolution of solid phase is addressed by volume of pixel (VOP) method. The detailed thermochemical process in porous media with immiscible phase is revealed, and the effects of velocity, concentration, and temperature on mass and heat transfer are further analyzed. The results show that increasing inlet velocity, inlet concentration, and temperature accelerates acidizing process and influences the temperature evolution in porous media significantly.

A 3D thermal LB model on non-orthogonal grid and its application for natural convection in irregular domains

In this paper, a 3D thermal LB model on non-orthogonal grid is derived, as well as the corresponding boundary treatment method for irregular boundary. Numerical validation is then performed by modeling natural convection in a 3D annulus. It is proved that the thermal flow structure in the annulus is accurately predicted with less grids. After that, present method is applied to study natural convection in a 3D cavity with inclined side walls. Two opposite inclined walls on the left and right sides are kept at different constant temperatures, while the remained four walls of the cavity are either adiabatic (Type 1) or own linear temperature variations (Type 2). It is found out that natural convection in the inclined cavity exhibits distinct 3D features under Type 2 thermal boundary setting, yet it can be viewed as a 2D process under Type 1 condition. Moreover, a large Prandtl number (Pr = 10.0) can generally suppress the 3D effect stemmed from thermal boundary setting. The aforementioned results indicate that present model and boundary treatment method are reliable to deal with 3D natural convection in irregular domains.

Thermal and hydraulic properties of sphere packings using a novel lattice Boltzmann model

A novel LB model is introduced to deal with the thermal and hydraulic properties in porous media. The pressure and density are separated in the proposed incompressible LB model and solid volume fraction is embedded in the formulations. Moreover, a modified thermal LB model is proposed that is shown to be more accurate than the Gue’s type of models. This model treats the energy equation with the second order of accuracy without any additional terms. The model is employed in a packing of monodisperse spherical particles within a rectangular channel. The results of new model have been improved as compared to the analytical solution.

Pinning-Depinning Mechanisms of the Contact Line during Evaporation of Microdroplets on Rough Surfaces: A Lattice Boltzmann Simulation.

In this study, pinning and depinning of the contact line during droplet evaporation on the rough surfaces with randomly distributed structures is theoretically analyzed and numerically investigated. A fast Fourier transformation (FFT) method is used to generate the rough surfaces, whose skewness ( Sk), kurtosis ( K), and root-mean-square ( Rq) are obtained from real surfaces. A thermal multiphase LB model is proposed to simulate the isothermal pinning and depinning processes. The evaporation processes are recorded with the variations in contact angle, contact radius, and drop shape. It is found that the drops sitting on rough surfaces show different behavior from those on smoother surfaces. The former shows a pinned contact line during almost the whole lifetime. By contrast, the latter experiences a stick-slip-jump behavior until the drop disappears. At mesoscopic scale, the pinning of the contact line is actually a slow motion rather than a complete immobilization at the sharp edges. The dynamic equilibrium is achieved by the self-adjustment of the contact line according to each edge.

Pseudo-potential MRT - thermal LB simulation of flow boiling in vertical tubes

The flow boiling in vertical tubes is simulated by the MRT pseudo-potential - thermal LB model to study the effect of contact angle. No empirical correlations are given in this simulation. To validate the model, the relationship between the acceleration of gravity and the departure velocity of bubble in the departure period is compared with the empirical formula. The effect of dynamic contact angle on boiling is investigated. The simulation results of the dynamic contact angle and the static contact angle show that the dynamic contact angle has great influence on the bubble behavior. The key features of dynamic contact angle, i.e. the advancing contact angle, receding contact angle and contact angle hysteresis, are investigated. The mechanisms of differences of entire bubble period and bubble departure diameter under various contact angles are discussed. The heat transfer coefficient, the critical heat flux and the flow pattern of different surfaces are investigated. The results suggest that the critical heat flux of hydrophilic surface are higher than that of hydrophobic surface.

Numerical study of patterns and influencing factors on flow boiling in vertical tubes by thermal LBM simulation

Heat transfer and flow pattern of flow boiling in vertical tube are investigated numerically based on the phase-change Lattice Boltzmann method (LBM) which includes an improved pseudo-potential LB model and a thermal LB model. Two-dimensional numerical simulations are carried out under constant heat flux conditions for the first time. The processes of growth, slippage, detachment and coalescence of the bubbles are captured to verify the correctness of the model. The effects of gravity, contact angle and wall superheat on bubble departure diameter and nucleation waiting time are illustrated. The multiple flow patterns, single-phase flow, bubble flow, slug flow and DNB have been illustrated with the behaviors of bubble nucleation, growth, departure, and coalescence. Some basic features of flow boiling have been clearly observed in the simulation. The influences of several factors such as heat flux, Reynolds number, the width of flow channel, and the width of nucleation point on flow boiling especially on the point of DNB are investigated. The numerical results show that the DNB could be avoided by reducing the heating density, increasing the Reynolds number, increasing the width of the tube and reducing the heating concentration.

Lattice Boltzmann technique for heat transport phenomena coupled with melting process

In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar–Gross–Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.

Simulation of steady fluid–solid conjugate heat transfer problems via immersed boundary-lattice Boltzmann method

In this paper, we extend the lattice Boltzmann method (LBM) in combination with the immersed boundary method (IBM) to simulate the steady-state fluid–solid conjugate heat transfer problems in complex geometries. The no-slip boundary condition is handled by the immersed boundary method. The “pseudo-solid-specific-heat” technique is used to ensure the continuity of heat flux at the fluid–solid interface. The present LB thermal field solver retains the simple structure of standards thermal LB model. The performance of the present method is validated by several heat conduction/convection problems. The numerical results agree well with exact solutions or published results.

Lattice Boltzmann simulation for solid–liquid phase change phenomenon of phase change material under constant heat flux

Phase change material (PCM) is receiving significant attention for the ability of storing thermal energy in recent years. In order to better understand the heat and mass transfer of PCM during solid–liquid phase change process and then improve the application of PCM, in this paper, the solution of solid–liquid phase change problem of PCM is investigated by using lattice Boltzmann method (LBM). A thermal LB model for describing the solid–liquid phase change phenomenon has been established and verified by the solution of conduction phase change under constant heat flux. Three kinds of heat flux distribution on left wall have been investigated: uniform distribution, linear distribution and parabolic symmetry distribution. The simulation results showed that concentrating more energy on upper region of left wall can reinforce the clockwise convective circulation. More input energy concentrating on the middle of left wall is the effective way to accelerate the rate of solid–liquid phase change and maintain the temperature of PCM.

Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

We discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice Boltzmann model. Their accuracy is investigated in the case of Couette flow by considering the slip regime. The best results are recovered with versions 2 and 3, which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain. Version 2 is found to be more economical since it involves no interpolation procedure. This version was thereafter used to investigate the temperature profile in Couette flow for various values of Prandtl number, as well as the capability of the thermal LB model to capture the Knudsen minimum in Poiseuille flow.

Lattice Boltzmann scheme for simulating thermal micro-flow

Gaseous flow and heat transfer in micro-channels are simulated by the lattice Boltzmann method (LBM). Thermal LB model with viscous heat dissipation has been adopted in the simulation. A new boundary treatment is proposed based on macro variables in order to capture the velocity slip and temperature jump. The numerical results show the velocity and temperature profiles are in agreement with the analytic results in different cases, which exhibits the availability of this model and boundary treatment in describing thermal micro-flow with viscous heat effect. The variation rules of temperature jump with different parameters are also discussed in this study.