用格子Boltzmann模型模拟激波现象

根据微观和宏观之间的质量、动量、能量守恒准则,建立了一个两维的D2Q13格子Boltzmann模型,可从该D2Q13模型出发推导出宏观的流体力学方程,所得动量方程和Navier-Stokes方程相比,在黏性输运项上有明显的改进,用该模型对冲击波在障碍物表面上的折射和反射现象的数值模拟都得到了比较满意的结果,而且数值稳定性也很好.证明了D2Q13模型的适宜性 关键词： Boltzmann模型 分布函数 冲击波 流体力学方程     

热声热机声场的格子气分析

从格子气自动机演化方程恢复了宏观热声方程,采用D2Q9热格子气模型模拟热声热机系统的压力场、温度场和速度场,获得压力驻波的传播和反射过程。模拟结果显示,在所给模拟条件下压力波具有非线性的特征,变截面附近的流场区域会产生引起非线性耗散的涡流。本文也分析了谐振管几何尺寸及格子气粒子密度对系统频率和压力的影响,验证了热声热机格子气模型的有效性。     

一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法

建立格子Boltzmann方法（LBM）的D1Q3演化模型,研究一类Riesz空间分数阶对流扩散方程的数值求解问题。对分数阶微积分算子中的积分项离散化处理,得到逼近的标准对流扩散方程。结合Taylor展式和Chapman-Enskog多尺度展开技术得到模型的各个方向上的平衡态分布函数,通过D1Q3演化模型正确恢复所要求解的宏观方程。数值算例验证该方法的有效性。     

非正交多松弛系数轴对称热格子Boltzmann方法

提出了一种模拟轴对称热流动的非正交多松弛系数格子Boltzmann(MRT-LB)模型.通过采用非正交转换矩阵,建立了基于D2Q9离散速度的求解流场的MRT-LB模型和基于D2Q5离散速度的求解温度场的MRT-LB模型.Chapman-Enskog分析表明,该模型可以恢复对应的柱坐标下的宏观连续方程、动量方程和能量方程.与现有的轴对称MRT-LB模型相比,本文采用的非正交转换矩阵中含有更多的零元素,因而具有更高的计算效率.采用本文模型对几种典型的轴对称热流动问题,包括热Womersley流动、竖直圆柱体内的Rayleigh-Bénard对流和环形柱体内的自然对流进行了数值模拟,通过等温线图和流线图以及定量数据的对比,验证了本文模型的可行性和可靠性.并且数值模拟结果表明,相对现有模型,本文模型具有更好的数值稳定性和计算效率.     

鼓泡床内气固两相流的变尺度格子气模拟

基于格子气自动机的建模思想,建立气固两相流的变尺度格子气模型,用微观层次的气固作用规则描述两相流的宏观行为.二维流场空间被离散成两层不同尺度的正六边形网格,固体颗粒和气体粒子分别在各自的网格上运动;在格子气自动机基本规则基础上设计气固相作用规则和附加演化规则;确定模型宏观物理量的统计计算方法,并根据相似原理建立模型物理量与真实物理量之间的转换关系.用建立的模型对鼓泡床内气固流动行为进行模拟,通过比较发现,变尺度格子气模型的模拟结果与文献中的实验结果和双流体模型的模拟结果吻合较好,且平均相对误差更小,表明建模方法的正确性和模型的有效性.     

活性炭吸附甲醛的格子Boltzmann模拟

基于孔隙尺度,结合活性炭与甲醛的真实物性参数,利用格子Boltzmann方法,选取热质耦合的LBGK模型对填充有球形活性炭的方腔内部双扩散混合对流、流固共轭传热及吸附特性进行数值模拟.分别采用二维D2Q9模型描述速度温度场,D2Q5模型描述浓度场,研究活性炭颗粒直径、孔隙率以及颗粒的排列方式对整个动态吸附性能的影响.结...     

三维双气泡融合的格子Boltzmann模拟

针对基于自由能模型的格子Boltzmann方法,推导D3Q15格子模型对应的平衡态分布函数;采用该模型模拟双气泡的融合过程.结果表明,气泡的融合不仅与它们之间的初始间距有关,还与表面张力有关.表面张力越大,气泡融合的临界距离也越大.此外,研究气泡融合速度与初始间距、表面张力及粘性系数的关系.     

基于格子Boltzmann方法的超声速非平衡流模拟

基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法.     

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟（英文）

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项uxxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟

针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项u_xxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.     

A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus

Absorption and extinction properties of the finite hexagonal ice column and hexagonal ice plate in random and preferred orientation are studied at the wavelength of 80 μm using a new implementation of exact T-matrix theory. For the case of random orientation at size parameters around two, it is shown that the hexagonal ice column and hexagonal ice plate absorption resonances are diminished relative to Mie theory, and the same behaviour is also noted for an aggregate particle consisting of eight hexagonal elements. The absorption properties of the aggregate particle have been calculated using the finite-difference time-domain method. It is also shown that extinction and absorption solutions for the hexagonal ice column and hexagonal ice plate can differ significantly if incidence occurs perpendicular or parallel to the cylindrical axis of the hexagon. For the case of perpendicular incidence on the edge of the hexagon, absorption solutions can exceed those of Mie theory, and for the case of parallel incidence, behaviour of the extinction solutions for hexagonal ice columns and hexagonal ice plates is shown to be similar to previously published work based on the prolate and oblate spheroid. Interference structure, associated with surface waves, is resolved on the hexagonal column extinction solution and the hexagonal plate absorption solution, thereby demonstrating that surface waves can exist on a non-axisymmetric geometry. The usefulness of assuming the hexagonal ice column in retrieval of ice crystal effective size is also investigated using aircraft based radiometric observations of semi-transparent cirrus at the wavelengths of 8.5 and 11 μm.     

Light scattering with swollen hexagonal phases

We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio. Received 7 July 1999     

Optical Properties of Zinc Oxide Nano-particles Embedded in Dielectric Medium for UV region: Numerical Simulation

Zinc oxide nano-particles have been used by cosmetic industry for many years because they are extensively used as agents to attenuate (absorb and/or scatter) the ultraviolet radiation. In the most UV-attenuating agent is formulated in which the metal oxide nano-particles are incorporated into liquid media or polymer media are manufactured, such as sunscreens and skin care cosmetics. In this paper we study the wavelength dependence on the particle size (r _eff = 10–100 nm) by solving the scattering problem of hexagonal ZnO particle for different shapes (plate, equal ratio, column) using the discrete dipole approximation method to find the absorption, scattering, and extinction efficiencies for the UV region (30–400 nm). A new modified hexagonal shape is introduced to determine the scattering problem and it is assumed in this study that the wavelength is comparable to the particle size. From these results, we conclude that the optimum particle radius to block the UV radiation is between r _eff = 40–80 nm.     

Nucleation,Growth, and Aggregation of Au Nanocrystals on Liquid Surfaces

We report the formation of gold ramified aggregates after deposition of Au on an ionic liquid surface by thermal evaporation method at room temperature.It is observed that the aggregates are composed of both granules and nanocrystals with hexagonal or triangular appearances.The most probable size of the nanocrystals is much larger than that of the granules and it increases with the nominal deposition thickness.The formation mechanism of the granules,nanocrystals and aggregates is presented.     

等效球模型模拟冰晶云反射的误差分析

用射线光学理论计算了具有一定尺度分布的六角冰晶粒子在可见和近红外光谱区一系列波长上(0.2～5μm)的单次散射特性.利用米氏(Mie)理论,计算了与六角冰晶具有相同截面积的球形粒子的单次散射特性.根据辐射传输理论,应用累加法,分别计算了由冰晶粒子和等效球形粒子构成的卷层云的多次散射特性,计算结果表明当入射波长λ≈3.0 μm时,等效球Mie理论可以很好地用于计算卷层云的反射特性,但是当λ＜2.8μm时,尤其在可见光区,将引起显著的误差.最后提出了计算冰云光学特性的两种方案.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.     

CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.^[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.^[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.     

A 3D implementation of ray tracing combined with diffraction on facets: Verification and a potential application

A 3D implementation of a new model of light scattering applicable to dielectric faceted objects is introduced. The model combines standard geometric optics with diffraction on individual facets. It can be applied to any faceted geometry. The model adds no significant computational overheads to classical geometric optics yet provides much improved results. Initial results for long hexagonal columns are compared to SVM and appear favourable. 2D scattering patterns are calculated for a hexagonal column in a fixed orientation and compared to those created by ice analogue crystals in the laboratory with close agreement. The comparison includes the observation of a guided wave propagating along the length of the column. The new model is then applied to a selection of geometries to illustrate how it could be used to aid particle characterization, particularly in the case of cirrus ice.     

Numerical simulation of a tribo-aero-electrostatic separation of a ternary plastic granular mixture

Granular materials, when fluidized by air or other gaseous medium, acquire electrostatic charge by particle-particle and particle-wall collisions. The effectiveness of particle tribocharging achieved with such fluidization process is crucial for establishing the feasibility of electrostatic separation of mixed granular solid wastes in the recycling industry. The aim of the present work is to introduce a simple mathematical model for simulating the outcome of a novel tribo-aero-electrostatic separation process involving mixture of three granular materials. The process is characterized by the fact that the charging of the granules is produced in a fluidized bed device, in the presence of an electric field. The mathematical model in this case assumed that the probability of a granule to be separated can be expressed using the normal distribution law, as a function of the number of impacts with granules belonging to the other classes of materials. The effect of the presence of a third species of particles was taken into account. Thus, it was possible to calculate the evolution over time of the mass of granules separated at the electrodes for different compositions of the granular mixture. The calculated results are in good agreement with the experiments.     

用格子Boltzmann模型模拟可压缩完全气体流动

采用一种新的格子Boltzmann模型模拟超音速流动。在这种模型中,粒子的速度不受限制,可以取得很广。而平衡分布函数的支集却相对集中,使模型得以简化。粒子速度的这种自适应特性允许流体以较高的马赫数流动。通过引入粒子的势能使得该模型适用于具有任意比热比的完全气体。利用Chapman-Enskog方法,从BGK型Boltzmann方程推导出Navier-Stokes方程。在六边形网格上模拟了马赫数为3的前台阶绕流,得到了合理的结果。