Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

三维可压缩Boltzmann模型及其在低Mach数湍流中的应用

改进了有限差分格子Boltzmann方法(FDLBM),以直接数值模拟气动噪声.基于LB求解器特性,采用动力学方程中的恒定对流速度以实施高阶迎风差分,提高了声波和湍流的分辨率.通过建立一个新的三维粒子模型,计算得到了任意比热容的三维可压缩Navier-Stokes系统.此外,利用Bhatnagar-Gross-Krook (BGK)碰撞算子,通过引入热流量修正,实现了Prandtl数的可变性.在激波管内弱声波以及伴随有温度梯度的Taylor-Couette层流的验证计算中,提出的新方法结果良好.此外也对NACA0012翼型绕流进行了三维模拟.其中,Reynolds数、Mach数和攻角分别取2× 105,8.75×10-2以及9°.计算发现,在机翼前缘附近的分离气流位置,以及表面压力波动强度的Maeh数依赖性方面,数值计算结果与实验结果相吻合.     

Complex fluid simulations with the parallel tree-based Lattice Boltzmann solver Musubi

We present the open source Lattice Boltzmann solver Musubi. It is part of the parallel simulation framework APES, which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi. Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos.     

Lattice Boltzmann 3D flow simulations on a metallic foam

In this paper a lattice Boltzmann method (LBM) is used to simulate isothermal incompressible flow in a RCM-NCX-1116 metallic foam. The computational technique is a multiple relaxation time (MRT) lattice Boltzmann equation model. Computer aided X-ray micro-tomography is used to obtain 3D images of the metallic foam, providing the geometry and information required for LB simulations of a single phase flow.Pressure drops are computed and successfully compared to experimental measures and correlated with Ergun’s equation. Invariance of Ergun’s parameters A and B with the sampling rate of the images is observed.     

Lattice Boltzmann simulation for the spiral waves in the excitable medium

We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov reactions with scratching mark, i. e. using a scratching mark pacemaker, obtained one classical spiral waves.     

前后排列旋转圆柱体对流热交换的格子Boltzmann方法解

用格子Boltzmann方法,数值研究流过前后排列两旋转圆柱体的二维层流．用二阶精度的速度场和温度场,数值化涉及运动的曲线边界．在Reynolds数为100,Prandtl数为0.71时,研究旋转速度比的变化和不同间距的影响．在4种不同间距(3, 1.5, 0.7, 0.2)下,研究旋转速度比的不同范围．结果表明,当间距取大数值时,第1个圆柱体的升力和阻力系数,与单个圆柱体相类似;对所有间距(除间距3以外),第2个圆柱体的升力系数,随着角速度的增加而减小,而阻力系数反而增加．圆柱体表面平均周期Nusselt数的结果表明,当两圆柱体间距小且角速度又低时,热传导是主要的传热机理,而当间距大且角速度又高时,对流是主要的传热机理．     

多孔介质中两相驱离的格子Boltzmann模型新研究

利用粒子之间相互作用,即同种物质粒子相互吸引,异种物质粒子相互排斥这一物理化的原理研究并提出了一个新型的模拟多孔介质中二相驱离的格子玻耳兹曼模型,结果表明它能有效地模拟多孔介质中的二相驱离问题,且节省机时,分界面上涨落也小,不必采取任何平均措施.     

Lattice Boltzmann methods for solving partial differential equations of exotic option pricing

This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.     

基于格子Boltzmann方法的液滴撞击具有不同润湿性孔板的研究

基于格子Boltzmann方法,对液滴撞击不同湿润性节流孔板表面进行了数值模拟.主要研究了在液滴撞击过程中,Weber数(We)、孔板表面湿润性和孔板尺寸对液滴通过孔板时不同状态的影响.数值模拟结果表明:孔板为亲水特性时,在较低We下,液滴不会与孔板表面脱离,而是附着在孔板下表面,并且在毛细作用下液滴会在孔道中上升一段...     

充满多孔介质的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,对4个壁面均为低温、低浓度,内置高浓度发热圆的充满均匀多孔介质的方腔内双扩散自然对流现象进行了数值模拟研究.分析了Darcy(达西)数Da(10-4≤D_a≤10~(-2))和浮升力比B(-5.0≤B≤5.0)对内部发热圆表面平均Nusselt(努赛尔)数Nuav和平均Sherwood(舍伍德)数Shav的影响.模拟结果表明:除B=-1.0时,Nu_(av)和Sh_(av)随D_a的增加而增大;当-5.0B5.0,在D_a=10~(-4)时,Nu_(av)和Sh_(av)几乎不受B变化的影响;在Da=10~(-3)和Da=10~(-2)时,Nu_(av)和Sh_(av)随B的增加先减小后增大,在B=-1.0时取得最小值.     

一维浅水方程的格子Boltzmann模拟

通过无量纲化变换 ,建立了一个一维浅水方程的LB模型 ,对一维溃坝波进行了模拟计算 ,并分别与文献结果和精确解作了比较 ,说明了此种模型的进步之处和可行性 .     

Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force Using a Lattice Boltzmann Fictitious Domain Method

Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs, which motivates us to model the sedimentation of red blood cell (RBC) under strong external magnetic body force. To model the sedimentation of a RBC in a square duct and a circular pipe, a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods (LBM-DLM/FD) is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow. The flow is simulated by the LBM with a strong magnetic body force, while the network model is used for modeling RBC deformation. The fluid-RBC interactions are enforced by the Lagrange multiplier. The sedimentation of RBC in a square duct and a circular pipe is simulated, which demonstrates the developed method's capability to model the sedimentation of RBCs in various flows. Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force. The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area. The larger the exerted force, the smaller the frontal area and the larger the RBC deformation become. Additionally, the wall effect on the motion and deformation of RBC is also investigated.     

Cahn-Hilliard vs Singular Cahn-Hilliard equations in simulations of immiscible binary fluids

An efficient semi-implicit spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility in this paper. We compared the kinetics of bulk-diffusion-dominated and interface-diffusion-dominated coarsening in two-phase systems. As expected, the interface-diffusion-controlled coarsening evolves much slower. Also we find that the velocity field will be caused different greatly by using Singular Cahn-Hilliard equation and using Cahn-Hilliard in the simulation of immiscible binary fluids.     

Outward melting of ice enhanced by Cu nanoparticles inside cylindrical horizontal annulus: Lattice Boltzmann approach

Heat transfer enhancement of water-(Ice) as a phase change material (PCM) through dispersion of Cu-nanoparticles is the centerpiece of this research study. The nanoparticle-enhanced phase change material (NEPCM) demonstrates increased thermal conductivity and decreased melting time in comparison with the conventional PCM. An enthalpy-based lattice Boltzmann method (LBM) with a double distribution function (DDF) model is implemented to trace phase change front in a cylindrical-horizontal annul. The subcooling case is neglected and Prandtl number, Stefan number and Rayleigh number are fixed to 6.2, 1 and 10⁵, respectively. In addition, the effects of varying the position of heated cylinder and nanoparticle volume fractions on the transient isotherms and liquid fractions are discussed.     

A characterization of complex lattice homomorphisms

In this paper we discuss the problem of how to recognize a complex lattice homomorphism on the complexification of a real vector lattice L from its behavior on a small subset of .      

Affine Completeness and Lexicographic Product Decompositions of Abelian Lattice Ordered Groups

In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product is never affine complete. This work was supported by VEGA grant 2/1131/21.     

Convergent Flows of Molten Polymers Modeled by Generalized Second-Grade Fluids of Power-Law Type

The molding processes of polymer melts involve geometrically complex dies. Such dies are usually tapered or streamlined to achieve a maximum output rate under conditions of laminar flow. The model of a generalized second-grade fluid of power-law type is used and the results obtained are illustrated by examples of convergent flows in conical and wedge-shaped dies.     

Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels

Transient electro-osmotic flow of viscoelastic fluids in rectangular micro-channels is investigated. The general twofold series solution for the velocity distribution of electro-osmotic flow of viscoelastic fluids with generalized fractional Oldroyd-B constitutive model is obtained by using finite Fourier and Laplace transforms. Under three limiting cases, the generalized Oldroyd-B model simplifies to Newtonian model, fractional Maxwell model and generalized second grade model, where all the explicit exact solutions for velocity distribution are found through the discrete Laplace transform of the sequential fractional derivatives. These exact solutions may be able to predict the flow behavior of viscoelastic biological fluids in BioMEMS and Lab-on-a-chip devices and thus could benefit the design of these devices.     

Two-layer flows of generalized immiscible second grade fluids in a rectangular channel

Unsteady one-dimensional flows of two incompressible and immiscible generalized second grade fluids in a rectangular channel are studied. A constant pressure gradient acts in the flow direction, while the channel walls have oscillating translational motions in their planes. The generalization considered in this paper consists into a mathematical model based on constitutive equations of second grade fluid with Caputo time-fractional derivative in which the history of the shear stress influences the velocity gradient. The velocity and shear stress fields in the Laplace transform domain are obtained. Numerical solutions for the real velocity and shear stress have been found by employing the Stehfest numerical algorithm for the inverse Laplace transform. The influence of the fractional parameters on the velocity and shear stress has been studied by numerical simulations and graphical illustrations. It is found that the memory effects are significant only for small values of the time t.