Analysis of collimated radiation in participating media using the discrete transfer method

A general formulation of the discrete transfer method is provided to analyze radiative heat transfer problems in a participating medium subjected to collimated radiation. The formulation is validated by considering 1-D planar absorbing, emitting and anisotropically scattering gray medium in radiative equilibrium. Anisotropy of the medium is approximated by linear anisotropic phase function. For the purpose of comparison, the problem is also solved analytically. Results are obtained for different angles of incidence of the collimated radiation. At a given angle of incidence, results are obtained for forward, isotropic and backward scattering situations. Heat flux results are compared over a wide range of values of the extinction coefficient. Emissive power distributions in the medium are also obtained for some cases. The discrete transfer method results are found to compare very well with the analytic results.     

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media

In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction-radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction-radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.     

用格子Boltzmann方法数值模拟三维空化现象

空化是一种微观、瞬时、随机、多相的复杂现象,其过程中所产生的极端条件以及伴随的一系列空化效应,将对液流系统产生破坏性和建设性两方面的作用.采用基于Shan-Chen模型的单组分多相流格子Boltzmann方法对水体中的三维空化现象进行了数值模拟,研究了低压下水体中气核半径与空化现象的相互关系,成功再现了低压下水体中微小气核发展成气泡的过程,并进一步研究了水体依次流经低压区、高压区时空化产生、发展、溃灭的全过程.数值模拟结果和理论预测结果符合良好. 关键词： 单组分多相流 格子Boltzmann方法 三维空化     

Simulation of microchannel flow using the lattice Boltzmann method

For microchannel flow simulation, the slip boundary model is very important to guarantee the accuracy of the solution. In this paper, a new slip model, the Langmuir slip model, instead of the popularly used Maxwell slip model, is incorporated into the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the rarefied gas flow. Its feasibility and accuracy are examined by simulations of microchannel flow. Although, for simplicity, in this paper our recently developed LB model is used to solve the flow field, this does not prevent the present boundary scheme from easily incorporating other LB models, for example the more advanced collision model with multiple relaxation times. In addition, the existing non-equilibrium extrapolation LB boundary scheme for macroscopic flows can be recovered naturally from the present scheme when the Knudsen number .     

Factorization symmetry in the lattice Boltzmann method

A non-perturbative algebraic theory of the lattice Boltzmann method is developed based on the symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) A special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves the factorization of quasi-equilibrium moments, and (iii) An algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. The present theory includes previously known limiting and special cases of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding the roots of one polynomial and solving a few linear systems.     

Dynamic simulation of multi-component viscoelastic fluids using the lattice Boltzmann method

We develop a discrete model for multi-component viscoelastic fluids based on the lattice Boltzmann method. The model newly introduces the kinetics of polymers so that viscoelasticity is included. We perform three-dimensional simulations of a Newtonian drop in shear flow of a viscoelastic fluid in order to investigate the validity of the current model. In the investigation, effects of viscoelasticity on deformation and orientation of drops are evaluated. The simulation results are compared with experimental measurements quantitatively, and they show good agreement with each other.     

气泡成核过程的格子Boltzmann方法模拟

利用精确差分格子Boltzmann模型探讨水在特定温度下的亚稳态及不稳定平衡态, 获得等温相变过程中形成气泡和液滴的条件, 模型预测结果与理论解符合良好. 在该等温模型的基础上耦合能量方程, 通过调节流体-壁面相互作用力获得不同的气泡与固壁间接触角, 从而建立了一种新的描述气液相变的格子Boltzmann理论模型. 利用该新模型模拟不同流体-壁面相互作用力下凹坑气泡成核过程, 再现了气泡成核过程中的三阶段特性; 探讨了接触角、曲率半径及气泡体积随气泡成核过程的变化关系, 获得了与文献结果定性符合的曲率-气泡体积关系曲线. 关键词： 格子Boltzmann方法 气泡成核过程 气液相变 接触角     

Modeling and simulation of thermocapillary flows using lattice Boltzmann method

To understand how thermocapillary forces manipulate droplet motion in microfluidic channels, we develop a lattice Boltzmann (LB) multiphase model to simulate thermocapillary flows. The complex hydrodynamic interactions are described by an improved color-fluid LB model, in which the interfacial tension forces and the Marangoni stresses are modeled in a consistent manner using the concept of a continuum surface force. An additional convection–diffusion equation is solved in the LB framework to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. A stress-free boundary condition is also introduced to treat outflow boundary, which can conserve the total mass of an incompressible system, thus improving the numerical stability for creeping flows.The model is firstly validated against the analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of three-dimensional deformable droplet at various Marangoni numbers, and its accuracy is once again verified against the theoretical prediction in the limit of zero Marangoni number. Finally, we numerically investigate how the localized heating from a laser can block the microfluidic droplet motion through the induced thermocapillary forces. The droplet motion can be completely blocked provided that the intensity of laser exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and constant velocity. When the droplet motion is completely blocked, four steady vortices are clearly visible, and the droplet is fully filled by two internal vortices. The external vortices diminish when the intensity of laser increases.     

三维方腔温盐双扩散的格子Boltzmann方法数值模拟

研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟，检验了方法的可行性及有效性，所得到的结果与差分法结果符合良好，继而将此方法推广到三维，建立了三维温盐双扩散系统的格子Boltzmann方法，对三维方腔双扩散问题进行了模拟和分析，并与差分法模拟的结果进行了比较，结果令人满意.最后，分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性. 关键词： 格子Boltzmann方法 温盐双扩散 Boussinesq近似 数值模拟     

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young–Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.     

Numerical modeling of condensate droplet on superhydrophobic nanoarrays using the lattice Boltzmann method

In the present study,the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multicomponent multi-phase lattice Boltzmann model.The results indicate that three typical nucleation modes of condensate droplets are produced by changing the geometrical parameters of nanoarrays.Droplets nucleated at the top(top-nucleation mode),or in the upside interpillar space of nanoarrays(side-nucleation mode),generate the non-wetting Cassie state,whereas the ones nucleated at the bottom corners between the nanoarrays(bottom-nucleation mode) present the wetting Wenzel state.Time evolutions of droplet pressures at the upside and downside of the liquid phase are analyzed to understand the wetting behaviors of the droplets condensed from different nucleation modes.The phenomena of droplet condensation on nanoarrays patterned with different hydrophilic and hydrophobic regions are simulated,indicating that the nucleation mode of condensate droplets can also be manipulated by modifying the local intrinsic wettability of nanoarray surface.The simulation results are compared well with the experimental observations reported in the literature.     

The stochastic collocation method for radiation transport in random media

Stochastic spectral expansions are used to represent random input parameters and the random unknown solution to describe radiation transport in random media. The total macroscopic cross section is taken to be a spatially continuous log-normal random process with known covariance function and expressed as a memoryless transformation of a Gaussian random process. The Karhunen-Loève expansion is applied to represent the spatially continuous random cross section in terms of a finite number of discrete Gaussian random variables. The angular flux is then expanded in terms of Hermite polynomials and, using a quadrature-based stochastic collocation method, the expansion coefficients are shown to satisfy uncoupled deterministic transport equations. Sparse grid Gauss quadrature rules are investigated to establish the efficacy of the polynomial chaos-collocation scheme. Numerical results for the mean and standard deviation of the scalar flux as well as probability density functions of the scalar flux and transmission function are obtained for a deterministic incident source, contrasting between absorbing and diffusive media.     

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.     

Simulation of two-phase flow and heat transfer phenomena in a boiling water reactor using the lattice Boltzmann method

The paper describes a new computational tool based on lattice Boltzmann methods for the simulation of two-phase flow and heat transfer phenomena in boiling water reactor fuel bundles.     

用格子Boltzmann模型模拟垂直平板间的热对流

引入一个新的能量分布函数，利用该能量分布函数与粒子速度分布函数耦合来求解一个热流场. 因而，这一能量分布函数与粒子速度分布函数和Boltzmann方程构成了一个新的格子Boltzmann模型. 这一模型满足质量、动量和能量守恒的准则. 用该模型对垂直平板间的狭缝热对流进行了数值模拟，数值结果表明，在Prandtl数为1，Grashof数在1.3×10²—1×10⁶之间时，流场将出现多个旋涡结构的流型. 得出了与Lee相一致的结论. 关键词： 能量分布函数 Boltzmann方程 热对流     

Simulation of the piston effect by the lattice Boltzmann method

A new lattice Boltzmann model is presented for the simulation of heat transfer in near-critical fluids. Fluid layer between two horizontal plates heated below near the thermodynamic critical point is simulated by the model. The spatial and temporal evolution of the temperature field is analyzed. It is demonstrated that the model can describe accurately the piston effect induced heat transfer at the piston effect timescale.     

Rotational invariance in the three-dimensional lattice Boltzmann method is dependent on the choice of lattice

The lattice Boltzmann method has recently gained popularity as a tool for simulating complex fluid flows. It uses discrete sets of velocity vectors, or lattices, to create a reduced model of the molecular dynamics of a continuum fluid. While several lattices are believed to behave isotropically, there are reports of qualitatively incorrect results. However, thus far, the reason as to why a lack of isotropy occurs is not known. Based on the hypothesis that lower order lattices may not display rotational invariance, this study tests the isotropy of the D3Q15, D3Q19 and D3Q27 lattices by performing simulations at intermediate Reynolds numbers (50–500) and low Knudsen number (<0.0005) in an axisymmetrical geometry with a nozzle leading to a throat followed by a sudden expansion. The symmetry properties of the results were examined. It was found that at Re ? 250 the D3Q15 and D3Q19 lattices produced different results depending on the plane of the lattice with which the flow was aligned. Lattice planes with fewer than six velocity vectors consistently produced results which were qualitatively different from the planes with six or more velocity vectors. These errors were not observed at Re = 50 or when a D3Q27 lattice was used. They appeared to be independent of grid density, collision operator and Ma. This suggests that the lattices which contain these planes are not fully isotropic and therefore do not properly replicate the behavior of a real fluid in this particular situation, notably downstream from the expansion. Predictions made using these models in more complex geometries may therefore be affected by the orientation of the lattice. When using LBM in CFD simulation (including validation) this study highlights the need for caution to ensure that the solution obtained is independent of the lattice orientation throughout the domain.