Thermal Lattice Boltzmann Model Research Articles

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

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

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

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

LAMMPS lb/fluid fix version 2: Improved hydrodynamic forces implemented into LAMMPS through a lattice-Boltzmann fluid

The first version of this code (Mackay et al., 2013) [10] implemented long-range hydrodynamic interactions into the open-source molecular dynamics package LAMMPS. This was done through the creation of a fix, lb/fluid which was subsequently included as a user-package in the main LAMMPS distribution. Here we substantially update this package by making improvements to its accuracy, adding significant new features, and by simplifying the use of the package. A new two-pass interpolation and spreading scheme is introduced which results in the improved accuracy and numerical stability. New features include new output options, several added computes, and mesh geometry option suitable for micro- and nano-fluidic device simulations. The original package could require fairly careful calibration to obtain accurate thermostating and accurate reproduction of properties related to the hydrodynamic size of objects such as colloids. This process has now been largely automated so that the default settings should suffice for most applications. Program summaryProgram title: fix lb/fluidCPC Library link to program files:https://doi.org/10.17632/2289cnrdtz.1Licensing provisions: GPLv3Programming language: C++Journal reference of previous version: Comput. Phys. Commun. 184 (2013) 2021–2031.Does the new version supersede the previous version?: YesReasons for the new version: The new version improves accuracy, adds new features, and simplifies the use of the package.Summary of revisions: A new two-pass interpolation and spreading scheme is introduced to relate properties on the fluid mesh to off-lattice particle properties. New features include output options, several added computes, and mesh geometry suitable for micro- and nano-fluidic device simulations. Calibration processes have been largely automated so that the default settings should suffice for most applications.Nature of problem: The inclusion of long-range hydrodynamic effects into molecular dynamics simulations requires the presence of an explicit solvent. Prior to the implementation of this fix, the only option for incorporating such a solvent into a LAMMPS [1] simulation is the explicit inclusion of each of the individual solvent molecules. This is obviously quite computationally intensive, and for large system sizes can quickly become impractical.Solution method: As an alternative, we have implemented a coarse-grained model for the fluid, simplifying the problem, while retaining the solvent degrees of freedom. We use a thermal lattice-Boltzmann model for the fluid, which is coupled to the molecular dynamics particles at each fluid time step.

Improved three-dimensional thermal multiphase lattice Boltzmann model for liquid-vapor phase change

Modeling liquid-vapor phase change using the lattice Boltzmann (LB) method has attracted significant attention in recent years. In this paper, we propose an improved three-dimensional thermal multiphase LB model for simulating liquid-vapor phase change. The proposed model has the following features. First, it is still within the framework of the thermal LB method using a temperature distribution function and therefore retains the fundamental advantages of the thermal LB method. Second, in the existing thermal LB models for liquid-vapor phase change, the finite-difference computations of the gradient terms ∇·u and ∇T usually require special treatment at boundary nodes, while in the proposed thermal LB model these two terms are calculated locally. Moreover, in some of the existing thermal LB models, the error term ∂_{t_{0}}(Tu) is eliminated by adding local correction terms to the collision process in the moment space, which causes these thermal LB models to be limited to the D2Q9 lattice in two dimensions and the D3Q15 or D3Q19 lattice in three dimensions. Conversely, the proposed model does not suffer from such an error term and therefore the thermal LB equation can be constructed on the D3Q7 lattice, which simplifies the model and improves the computational efficiency. Numerical simulations are carried out to validate the accuracy and efficiency of the proposed thermal multiphase LB model for simulating liquid-vapor phase change.

Analysis and reconstruction of the simplified thermal lattice Boltzmann method

The previous thermal lattice Boltzmann models are generally based on the lattice framework, which leads to some intrinsic drawbacks including the limitation of uniform mesh, coupled time step with mesh spacing, extra memory size, and complex boundary treatment. Aiming to decrease memory size and achieve good numerical stability for high Rayleigh number thermal flows, the simplified thermal lattice Boltzmann method (STLBM) was proposed. However, STLBM still has two fundamental problems. Firstly, as a weakly compressible model, its reason for the good numerical stability at high Rayleigh number thermal flows has not been revealed in the perspective of macroscopic scale yet. Secondly, it still depends on the uniform mesh, which makes the implementation of non-uniform meshes time-consuming and complicated. To tackle the two problems, the macroscopic equations of STLBM (MEs-STLBM) with actual numerical dissipative terms are derived firstly by approximating its actual computational process. By solving MEs-STLBM with the least-squares-based finite difference (LSFD) method, the limitation of the uniform mesh of STLBM can be easily overcome. Numerical investigation proves that the numerical dissipative terms in MEs-STLBM are the reason for the good numerical stability at high Rayleigh number thermal flows. By retaining these numerical dissipative terms, the discretized MEs-STLBM can recover the accuracy and numerical stability of STLBM well. Besides, they have significantly higher computational efficiency than STLBM.

An Efficient Thermal Lattice Boltzmann Method for Simulating Three-Dimensional Liquid-Vapor Phase Change

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid-vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid-vapor phase change, the present approach has two advantages: for one thing, the current approach does not require calculating the gradient of volumetric heat capacity [i.e., $\nabla \left( {\rho {c_v}} \right)$], and for another, the current approach is constructed based on the seven discrete velocities in three dimensions (D3Q7), making the current thermal LB model more efficient and easy to implement. Also, based on the scheme proposed by Zhou and He [Phys Fluids 9:1591-1598, 1997], a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. The current method is then validated by considering the temperature distribution in a 3D saturated liquid-vapor system, the $d^2$ law and the droplet evaporation on a heated surface. It is observed that the numerical results fit well with the analytical solutions, the results of the finite difference method and the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid-vapor phase change.

Mesoscopic characterization of bubble dynamics in subcooled flow boiling following a pseudopotential-based approach

The present study explores the capability of the pseudopotential-based thermal lattice Boltzmann model in emulating the underlying thermohydrodynamics of subcooled flow boiling in a narrow fluidic channel. In contrary to the conventional Eulerian-averaging-based approach, it adheres to the mesoscopic Boltzmann statistical averaging, which allows natural phase separation and no need of assuming the initial interface. A narrow fluidic channel, with specified inlet temperature and flow rate, and exit pressure, housing a microheater at the bottom wall, is considered as the computational domain of interest. Adopted boundary conditions ensure subcooled flow boiling through the channel, and the present algorithm successfully emulates the corresponding characteristics. The complete dynamics of bubble ebullition at the nucleation site, and subsequent flow regimes are adequately reproduced. Both bubbly and slug flow patterns are illustrated through the temporal evolution of the interface, and associated pressure drop and heat transport characteristics. Dependence of the departure characteristics on the flow rate, wall superheat and surface wettability is found to be consistent with available literature, which substantiates the competence of the present algorithm.

Evaluation of porous rib and flow pulsation on microchannel thermal performance using a novel thermal lattice Boltzmann method

In this study, a new thermal lattice Boltzmann model (TLBM) is developed to simulate conjugate heat transfer in a microchannel heat sink (MCHS) with porous ribs and pulsatile flow inlet. The examined parameters include the rib to channel height ratio (Hr*), Strouhal number (St), and Reynolds number (Re), which are varied from 0.25 to 0.75, 0 to 3.2, and 100 to 300, respectively. The proposed TLBM is based on the double distribution function framework and capable of addressing heat transfer in combined fluid and porous media conditions. The simulation data show that the flow pulsation inside MCHS with porous ribs not only improves the bulk mean temperatures but also eliminates the rib recirculation zones at some phases, which promotes both the local and overall heat transfer. For fixed Re, the overall Nusselt number (Nu‾/Nu0) and Fanning friction coefficient (f‾/f0) increase and then decrease with increasing St. The maximum values appear at St = 2. For fixed Re and St, the thermal performance factor (TPF) displays a single peak trend with Hr* and the optimal TPF of 2.2 occurs at Hr*=0.5. In addition, compared with the previous ribbed, baffled, and porous MCHSs, the proposed porous rib design under pulsating conditions reports the highest Nu‾/Nu0 of 13.4 in the range of f‾/f0≤200. Finally, the correlations of Nu‾/Nu0 and f‾/f0 with Re, St, and Hr* for the present MCHS are established for the first time, with average differences below 6.7% and 12.4%, respectively.

CONDENSATION PHASE CHANGE BEHAVIORS ON A ROUGH SURFACE CHARACTERIZED BY FRACTAL CANTOR

Understanding the fundamental mechanisms of vapor condensation on rough surfaces is crucial to a wide range of industrial applications. A hybrid thermal lattice Boltzmann model of the condensation heat transfer process on downward-facing rough surfaces characterized by the Cantor fractal is developed and numerically analyzed to investigate the condensation phase change behaviors on rough hydrophobic and hydrophilic surfaces. The dynamic behaviors of vapor condensation, including the evolutions of vapor–liquid interface, heat flux, condensate mass, and temperature distribution, on the hydrophilic and hydrophobic rough surfaces are presented and compared with corresponding smooth surfaces. The results indicate that the rough surface preferred a filmwise condensation under hydrophilic conditions but a hybrid dropwise–filmwise condensation under hydrophobic conditions. On the rough hydrophobic surface, the liquid film can rapidly adsorb droplets, maintaining a high-efficiency dropwise condensation. The absorption of droplets accelerates the liquid film growth and detachment process on the rough hydrophobic surface, which reduces the time-averaged thermal resistance of the filmwise region. These two behaviors together enhance condensation heat transfer on the downward-facing rough hydrophobic surface. Besides, stable dropwise condensation could also be formed on smooth hydrophilic surfaces and has better heat transfer performance than corresponding hydrophobic surfaces under the same heat transfer condition.

Evolution of solid–liquid interface in bottom heated cavity for low Prandtl number using lattice Boltzmann method

The influence of natural convection cells on heat transfer and the evolution of melt interface is studied for low Prandtl number fluid (Pr = 0.025) in phase-change Rayleigh–Benard convection using the lattice Boltzmann method. The thermal lattice Boltzmann model is used to evaluate the effect of Rayleigh number (Ra = 6708, 11 708, and 21 708) and cavity aspect ratio (γ = 0.062 5, 0.125, 0.25, 0.5, and 1) on the onset of convection, number of convection cells, and Nusselt number in the classical Rayleigh–Benard convection. The modified equilibrium distribution function-based thermal lattice Boltzmann model is applied to evaluate the effect of Stefan number (Ste = 0.025, 0.05, and 0.1) in the phase change Rayleigh–Benard convection. Distinct flow configurations depend on the Rayleigh number, aspect ratio, and Stefan number. The number of convection cells follows an inverse relation with the aspect ratio. Nusselt number increases with decreasing cavity aspect ratio and increasing Rayleigh number in the classical Rayleigh–Benard convection. With the variation in the aspect ratio based on the melt layer height during melting of phase change material, the number of convection cells changes resulting in the change in the evolution of the melt interface and convective heat transfer. Melting in a cavity of aspect ratio less than 0.5, the evolution of melt interface remains symmetrical. For an aspect ratio greater than 0.5, the interface evolution becomes unsymmetrical depending on the transition to single convection cell-dominated heat transfer.

Hybrid quasi-steady thermal lattice boltzmann model for investigating the effects of thermal, surfactants and contact angle on the flow characteristics of oil in water emulsions between two parallel plates

In this work, a two-dimensional hybrid quasi-steady thermal lattice Boltzmann model with temperature-dependent interfacial tension, surfactant and contact angle modules, is used to study the combined multi-physics effects on oil in water (O/W) systems flowing between two-parallel oil-wet plates. The proposed model is used to execute a parametric study for investigating the effects of the droplet radius, source terms, temperature, and surfactants parameters such as concentrations, elasticity, and diffusion coefficients on the flow characteristics of oil in water (O/W) emulsions inside microchannels. Flow conditions such as droplet Reynolds number0.41≤Re≤48, Webber number0.041≤We≤28 dimensionless surfactant surface concentration0.1≤Γ∗≤0.5, and surface Péclet number0.011≤Pes≤31are used in the simulations. The presence of surfactant noticeably enhances the droplets' transportation inside the channel, due to increased droplets' contact angle and deformation. Contaminated droplets with surfactant retain a greater bulk mass center velocity than clean ones to the tune of 2–5 times depending on the simulation conditions. The rise in temperature has a major impact on improving the suspended phase bulk velocity and power number ratio (system's efficiency indicator) for cases with and without surfactant. However, the presence of surfactant at elevated temperatures ameliorates the amount of useful work absorbed by the droplets from the flow significantly. Using specific conditions from the parametric study such as high temperature and surfactants characterized by low diffusion coefficient, results in an effective droplets breakup. The daughter droplets depart from the channel walls by shear lift, which enhances the suspended fluid transportation and increases the power number ratio up to 5.7 times.

Pore-scale investigation on reactive flow in porous media considering dissolution and precipitation by LBM

The reactive transport process in oil gas reservoirs is complicated due to the coupling between dissolution and precipitation. In the present study, based on lattice Boltzmann method, the coupled dissolution and precipitation process in randomly generated porous media by quartet structure generation is investigated at the scale of geological pores. The fluid velocity, temperature and concentration in porous media are solved by multicomponent flow lattice Boltzmann model, multicomponent thermal lattice Boltzmann model and mass transport lattice Boltzmann model, respectively. The solid phase is updated by volume of pixel method. The results show that the dissolution reaction rate has a positive impact on the consumption of reactants. For different precipitation reaction rates, there exists an optimal value resulting in abundant precipitate and sparse solid distribution. Reaction equilibrium constant affects reaction rates slightly but influence the solid morphology heavily. The coupled dissolution and precipitation process accelerates with the increase of Peclet number, but the precipitate produced increases with the decrease of Peclet number.

Multiple-relaxation-time lattice Boltzmann analysis of entropy generation in a hot-block-inserted square cavity for different Prandtl numbers

This work analyses the effects of three different Prandtl number fluids (Pr = 0.025, 5.83 and 151) on convective heat transfer inside a closed square cavity with an adiabatic left wall and three other cold walls. A centrally positioned square hot block with respective blockage ratios of 0.25 and 0.5 heats the cavity, which induces natural convection inside it for Grashof numbers Gr = 104, 105 and 106. Besides, two different cases of mixed convection based on the direction of moving right wall are investigated for varying Richardson numbers (0.01 ≤Ri≤ 100) at Gr = 104. We implement multiple-relaxation-time based thermal lattice Boltzmann model to study these flow configurations. The comprehensive analysis of the results suggests that the block size and Pr have a considerable influence on the flow and heat transfer behaviour. The average Nusselt number over the block surface Nuh‾ and total entropy generation throughout the cavity Stot‾ increase with an increase in Pr and Gr due to the augmentation of convective heat transfer. For all three cases, Nuh‾ at BR = 0.25 is higher compared to BR = 0.5. In mixed convection, the heat transfer irreversibility mostly dominates the entropy generation at all Pr irrespective of Ri values as indicated by large average Bejan number. The present code is carefully validated with the well-established results obtained through conventional numerical techniques.

Pore-scale investigation on the effect of gas-liquid phase separation on reactive flow in a horizontal rough fracture using the lattice Boltzmann method

In this study, the effect of the gas-liquid phase separation caused by seawater boiling on the carbonate crack dissolution process was investigated using the lattice Boltzmann (LB) method at the pore scale. The gas-liquid two-phase flow with phase change, heat transfer, and solute transport is described by a single-component multiphase LB model, thermal LB model, and mass transport LB model, respectively. In addition, the dissolved solid mass is calculated via the Volume of Pixel method. The main conclusions are as follows: the phase separation negatively affects dissolution, especially in the upper boundary of the crack. Moreover, the negative effect is strengthened with the increase in inlet velocity and the decrease in crack width while the influence of wettability on dissolution is non-linear and its degree depends on the phase distribution of the two phases. In addition, slug flow greatly hinders solute transport but may accelerate the dissolution reaction near the inlet.

Pore-scale conjugate heat transfer of nanofluids within fibrous medium with a double MRT lattice Boltzmann model

The conjugate heat transfer of nanofluids within fibrous medium is explored at pore scales. To handle the heat flux discontinuities neighboring the complex interfaces, the correction terms are projected into the thermal multi-relaxation-time (MRT) lattice Boltzmann (LB) scheme which offer an effective and reliable approach to explore conjugate heat transfer dynamics. A random-walk-based stochastic model is presented to generate the fibrous medium made up of interconnected bending fibers. For conjugate heat transfer without convective flow, the steady-state temperature profiles are found independent to the fiber-to-fluid thermal conductivity ratio. Whereas for conjugate heat transfer with convective flow, heat transfer is enhanced with large fiber-to-fluid thermal conductivity ratios. In addition, with the convective flow with high Reynolds numbers, the resulting temperatures for varied fiber-to-fluid thermal conductivity ratios are considerable decreased which indicate high Reynolds numbers dominate the heat transfer process. The 3D pore-scale temperature distributions with varied thermal parameters are provided which demonstrate the capability of present conjugate thermal LB model.

Modeling coupled temperature and transport effects on biofilm growth using thermal lattice Boltzmann model

AbstractThis paper aims to develop an integrated thermal lattice Boltzmann model and cellular automata to investigate the effects of different temperatures and velocities on biofilm growth in a microbioreactor. Compared with previous studies this model accounted for direct effects of transient temperature on biofilm growth and indirect effects caused by changes of fluid properties. In addition, the algorithms have been improved on variations in solid boundary conditions, detachment and extra mass transport. Results showed that temperature affected both maximum biofilm concentration and growth rate. An increase of 10–75% in biofilm concentration was observed roughly due to increases in temperature. The time required to reach maximum concentration decreased from 30 days at a low temperature to 5 days at a high temperature. This demonstrates the capability of the present model to simulate biofilm behavior in the microbioreactor and its potential industrial and clinical applications.

Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows

Based on recent work by Guo et al. [“An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice,” J. Comput. Phys. 418, 109570 (2020)], an improved thermal hybrid recursive regularized lattice Boltzmann model (iHRR-ρ) on a regular lattice is developed for two- and three-dimensional compressible laminar and turbulent flows. To enhance the numerical stability in a broad range of Courant–Friedrichs–Lewy numbers and in under-resolved simulations, a new equilibrium density distribution function is proposed to enlarge its positivity region in the Mach–temperature plane. An embedded hybridizing procedure is introduced in the quasi-symmetry correction terms, which allow for a decoupled treatment of unphysical modes and physical under-resolved turbulent scales on coarse grids. To handle compressible turbulent flows, the under-resolved scales are modeled using the original hybrid recursive regularized collision model given by Jacob et al. [“A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann method-based large eddy simulation,” J. Turbul. 19, 1051–1076 (2018)] equipped with Vreman’s subgrid model for the large-eddy simulation. The validity and accuracy of the present method for laminar and turbulent compressible flows are assessed by considering six test cases: (I) viscous shock wave internal structure, (II) isentropic vortex convection in a supersonic regime, (III) non-isothermal acoustic pulse, (IV) vortex–shock wave interaction, (V) supersonic flow over NACA airfoil at Re = 10 000 and Ma = 1.5, and (VI) compressible Taylor–Green vortex at Ma = 0.29.

Numerical study of droplet evaporation on heated flat and micro-pillared hydrophobic surfaces by using the lattice Boltzmann method

The evaporation processes of sessile droplets on both heated flat and structured hydrophobic surfaces are numerically studied by using a thermal multi-phase lattice Boltzmann model. The contact-line dynamics and heat transfer regarding the evaporation of droplets are simulated and the effects of the heat conductivity, wettability, and roughness of the substrate on the droplet evaporation are investigated. The results indicate that the different evaporation modes of the droplets on the rough surfaces are attributed to the microscopic “stick–slip” motion of the contact line. The constant contact angle (CCA) mode of droplet evaporation on the rough hydrophobic surface can be regarded as a macroscopic average of the microscopic “stick–slip” processes with a short stick period and small change in apparent contact angle. The weaker stick effect of the surface with a higher hydrophobicity and smaller solid fraction makes the droplet evaporation more likely to occur in the CCA manner.

Pore-scale investigation on the thermochemical process in uniform and gradient porous media considering immiscible phase

In the present study, the complex thermochemical process in uniform and gradient porous media is investigated by the thermochemical dissolution model based on the lattice Boltzmann method considering immiscible phase. The two immiscible phase flow, solute transport and heat transfer are solved by Shan-Chen multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model and multicomponent thermal lattice Boltzmann model, respectively. The immiscible phase, undissolved solid component and porosity gradient effects on the thermochemical process are investigated. For the solid, the dissolvable component is considered and updated by Volume of Pixel method. The results show that the immiscible phase and its initial distribution considerably affect the solid dissolution, acid transport and the average temperature in porous media. The undissolved solid component and the porosity gradient influence the thermochemical process significantly.

Catalytic flow with a coupled finite difference — Lattice Boltzmann scheme

Many catalyst devices employ flow through porous structures, which leads to a complex macroscopic mass and heat transport. To unravel the detailed dynamics of the reactive gas flow, we present an all-encompassing model, consisting of thermal lattice Boltzmann model by Kang et al., used to solve the heat and mass transport in the gas domain, coupled to a finite differences solver for the heat equation in the solid via thermal reactive boundary conditions for a consistent treatment of the reaction enthalpy. The chemical surface reactions are incorporated in a flexible fashion through flux boundary conditions at the gas–solid interface. We scrutinize the thermal FD-LBM by benchmarking the macroscopic transport in the gas domain as well as conservation of the enthalpy across the solid–gas interface. We exemplify the applicability of our model by simulating the reactive gas flow through a microporous material catalyzing the so-called water-gas-shift reaction.