二维空腔黏性流的格子Boltzmann方法模拟

用13速六方格子BhatnagarGrossKrook(缩写为BGK)模型模拟二维空腔黏性流.给出了上边界流体作匀速运动时,具有不同雷诺数的空腔黏性流的流场速度分布情况,模拟了在雷诺数Re=3000时,流场中的涡旋形成过程及流场稳定后,腔内密度、压力和温度的分布情况 关键词：     

基于格子Boltzmann方法的幂律流体二维顶盖驱动流转捩研究

研究非牛顿流体转捩问题,可为调控非牛顿流体动力特性提供理论基础.相对于牛顿流体转捩问题,非牛顿流体转捩研究较少,缺乏转捩雷诺数精细预报方法.论文以格子Boltzmann方法为核心求解器,以典型非牛顿流体幂律模型为例,开展了幂律流体二维顶盖驱动流转捩模拟,给出剪切变稀和剪切增稠流体的第一转捩雷诺数,并分析了转捩雷诺数附近流场时频域特性及模态分布.结果表明,剪切变稀流体和剪切增稠流体的第一转捩雷诺数与牛顿流体差异显著,且在转捩临界雷诺数附近监控点处速度分量均呈现周期性变化趋势.通过对流场速度和涡量的本征正交分解发现,不同类型的流体在转捩临界雷诺数附近,前两阶模态均为流场的主模态,能量占比超过95%,且同类型流体不同雷诺数的主模态间具有相似的结构.     

流体惯性对弹性界面液滴吸附行为的影响

弹性膜包裹黏性流体组成的液滴(弹性界面液滴)可与功能性壁面形成化学吸附键,产生吸附力,与黏性力和惯性力共同控制流场中液滴的吸附动力学行为。本文基于前期发展的界面追踪(Front tracking method)-界面有限元方法,结合吸附反应动力学模型,发展了可同时考虑流体惯性、界面弹性和流体黏性的弹性界面液滴吸附动力学三维模拟方法。重点分析了流体惯性对弹性界面液滴吸附行为的影响规律。结果表明:雷诺数增大导致流场作用于弹性界面液滴的阻力和升力都增大,因此流体惯性作用导致弹性界面液滴更容易从壁面脱附。     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

哈密顿量宇称-时间对称性的刻画

宇称-时间(PT)对称性理论描述了具有实能级的非厄密特哈密顿量,在量子物理学和量子信息科学中起着重要作用,是量子力学中活跃且重要的主题.研究者们对如何描述哈密顿量的PT对称性的问题给予了高度关注.本文基于PT对称理论和哈密顿量归一化特征函数,提出了算子F的定义.然后,在找到算子CPT和算子F的对易子和反对易子的特性后,给出了刻画了无量纲情况下哈密顿量的PT对称性的第一种方法.进一步研究发现,该方法还可以量化哈密顿量在无量纲情况下的PT对称性.此外,提出了另一种基于哈密顿量特征值实部和虚部来描述哈密顿量PT对称性的方法,该方法仅用于判断哈密顿量是否具有PT对称性.     

考虑双向耦合效应的格子Boltzmann气固两相湍流模型

在流体粒子概率密度函数输运方程中考虑颗粒对流体的反作用力,发展了考虑双向耦合效应的LB气固两相流模型,引入Smagorinsky亚格子模型模拟高雷诺数气相流场.对经典后台阶气固两相流动进行模拟,气相和颗粒相速度分布与实验结果进行比较,发现考虑双向耦合效应的LB气固两相流模型结果明显优于单向耦合结果.进一步研究不同惯性颗粒在流场中的弥散特性,小颗粒(St~O(0.1))对流体的跟随性较好,在流场中分布较为均匀;而St~O(1)的颗粒难被流场涡卷吸进入涡内,呈现倾向性弥散现象;大颗粒(St~O(10))由于自身惯性进入流场涡,在流场中分布较为均匀.     

声表面波驱动的非接触式转动马达

在研究摩擦力驱动的接触式转动马达的基础上,本文研制了一种由声表面波驱动的非接触式转动马达.这种马达的定子选用128°YX-LiNbO3晶体,在晶体表面光刻两对叉指换能器,由叉指换能器在定子表面激发两列平行而反向传播的声表面波.定子表面铺一层流体,转子就浮在流体表面.当定子表面有两列平行而反向的声表面波传播时,流体层中就会产生平行而反向的声流,这种黏性流体的声流运动就会驱动转子运动.实验上测定了马达的角速度随驱动电压,流体层厚度以及流体运动黏性系数变化的结果.同时,我们也发现,在相同工作频率下,非接触式转动马达的阈值电压远小于接触式.     

通道中串列旋转圆柱的格子Boltzmann-虚拟区域方法的模拟

通过结合格子Boltzmann方法(LBM)和虚拟区域(Fictitiou sDomain)思想,建立格子Boltzmann-虚拟区域(LB-DF/FD)方法.采用两套网格系统,欧拉网格用于流体,拉格朗日网格用于固体.原有的LBM在计算运动固体的受力方面存在数据振荡,LB-DF/FD方法改进了此缺陷.为验证该方法,模拟圆柱绕流、圆形颗粒在无限长通道中平动及在无限大流场中转动三种情况,结果与其他数值解及理论解符合得很好.利用该方法模拟低雷诺数下通道中串列旋转圆柱周围的流场,分析圆柱间距(g)及雷诺数(Re)对流场结构的影响.给出Re=0.001,0.1和10下,0.2≤g≤8.0的流线结构、圆柱升力、阻力以及力矩等数值结果.结果表明,g对流场的结构及圆柱的受力有显著影响,Re对圆柱阻力及Stokes单元数目的影响较大.     

溶解与热对流对固体颗粒运动影响的直接数值模拟

对牛顿流体内溶解与热对流对单颗粒在垂直管道中的沉降运动进行了直接数值模拟.流体运动由守恒方程计算,密度和黏性的变化考虑流场温度变化的影响,通过积分黏性应力和压力获得颗粒的受力跟踪颗粒运动,溶解引起的相变及其形状的变化由溶解潜热、溶解质量与分散相边界处的温度梯度的关系建立的方程决定.通过颗粒和流体间相互的作用力和力矩及边界条件的施加实现相间耦合.分别模拟了颗粒在等温流体、热流体、冷流体及颗粒溶解四种情况下的沉降过程.结果表明,在一定雷诺数内,热对流产生的颗粒尾迹处涡的脱落以及溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动,并使颗粒沉降速度发生了变化. 关键词： 溶解 热对流 颗粒两相流 直接数值模拟     

非对称螺旋扭曲管管内流动与传热特性数值模拟研究

本文利用数值模拟方法对一种非对称螺旋扭曲管在雷诺数4000~20000的范围内管内流动阻力和传热特性进行了研究.结果表明,与椭圆扭曲管相比,非对称的螺旋扭曲管的努塞尔数得到了显著的提高.通过流场的对比分析可知,非对称螺旋管横截面上的三叶扭曲,使得三叶区域内的流体流动发生偏向,形成强烈的二次旋流使得传热性能得到提升.低雷诺数时,非对称螺旋扭曲管(顺向扭曲)显示出更好的传热性能和更高的阻力因子.随着雷诺数的增加,非对称螺旋扭曲管与对称性螺旋扭曲管的传热与阻力特性差别不大.此外,通过两种不同综合性能因子对比不同管型传热综合性能。在相同泵功率下,非对称螺旋扭曲管在低雷诺数时显示较优的性能,而在相同质量流率下,传统的椭圆扭曲管显示较好的性能。     

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

A lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.     

基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法

双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略.     

Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.     

格子Boltzmann亚格子模型的研究

为了将格子Boltzmann法应用于大雷诺数流动的模拟,本文将Smagorinsky亚格子模型和LBGK模型相结合,并对该亚格子LBM模型进行了研究。利用该亚格子LBM模型,对二维顶盖驱动流进行了模拟,得到了若干大雷诺数下流线图和方腔中心线上无量纲速度分布。计算结果与基准解进行比较,两者相互吻合。     

Nonextensive statistics in viscous fingering

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power-law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele–Shaw flow as simulated by the lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial q-Gaussian profile and a power-law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcy's law combined with the nonlinear advection–diffusion equation for the concentration field. Power-law and q-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.     

基于速度源修正的浸入边界-晶格玻尔兹曼法研究仿生微流体驱动模型

浸入边界—晶格波尔兹曼法在流固耦合等复杂的流体系统中得到广泛的应用.本文采用基于速度源修正的浸入边界—晶格玻尔兹曼法,建立了仿生微流体驱动模型,创新性地将波动弹性体的速度引入晶格玻尔兹曼方程,避免了传统浸入边界—晶格玻尔兹曼法中浸入边界速度-结构变形-力之间的转换,提高了计算效率和准确率.研究了行波波动细丝对流场内流动速度和压力的影响,重点分析了驱动模型各项参数对微流体的驱动效果.研究结果表明:细丝长度、频率、振幅的增加引起出口处流量的增加;波长、流体粘滞系数以及细丝位置与出口处流量呈复杂的非线性关系.     

Lattice Boltzmann Study of Mixed Convection in aCubic Cavity

The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed
convection in the cubic cavity. The numerical results show that the flow and temperature patterns change greatly with variations of the Reynolds and Richardson numbers.     

Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders

We apply the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model to simulate laminar flows in two-dimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched non-uniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of non-uniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRT-LBE. The MRT-LBE with non-uniform stretched grids is first validated with a number of test cases: the Poiseuille flow, the flow past a cylinder asymmetrically placed in a channel, and the flow past a cylinder in an unbounded domain. We use the LBE method to simulate the flow past two tandem cylinders in an unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRT-LBE method with grid stretching.     

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.     

A lattice Boltzmann method for nonlinear disturbances around an arbitrary base flow

In this paper we address the problem of the time evolution of a perturbation around a steady base flow with the use of the lattice Boltzmann method (LBM). This approach, named base flow lattice Boltzmann method, is of great interest in particular for aeroacoustic fields where the acoustic perturbation, on the one hand, is almost exclusively influenced by the large scale average structures of the underlying flow, and on the other hand, has a low effect on the large structures. The method is implemented for weakly compressible flows and the results of the base flow lattice Boltzmann are compared with the standard single relaxation time LBM. The boundary conditions for the base flow lattice Boltzmann method are discussed, as well as the implementation of outflow conditions for acoustic waves.