改进的浸入边界-晶格Boltzmann法的蠕动流分析

基于改进的浸入边界-晶格Boltzmann方法研究蠕动流问题,采用晶格Boltzmann法描述流场,用改进的浸入边界法实现管壁运动-流体流动之间的相互作用,将变形管壁的运动速度作为速度源引入晶格Boltzmann方程,代替了传统浸入边界-晶格Boltzmann法中固态变形力与流体速度之间的转换。分析了管道内蠕动流场的分布情况,研究了各相关参数如振幅比、频率、液体黏度以及波数对流量的影响,数值结果与已有的结果进行了对比,证实了本研究方法的合理性与有效性。     

格子Boltzmann方法三种边界格式的对比分析

采用格子Boltzmann方法(Lattice Boltzmann Method-LBM)对二维顶盖驱动方腔流动进行数值模拟。在计算中分别使用半步长反弹、非平衡反弹、以及非平衡外推三种边界处理格式,并得到了不同格式对应的流线分布,流函数最小值、涡心坐标、几何中心线速度分布等。通过将所得结果与基准解进行比较,就三种边界格式的计算效率,计算精度、以及计算稳定性等方面进行了讨论和分析,为LBM计算中边界格式的选择提供了有益的参考。     

Flow around a flexible plate in a free stream

This paper presents a numerical scheme for fluid-structure interaction, especially for flexible structures. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used for the fluid, and a finite element method with Euler beam elements is used for the flexible plate. The direct forcing scheme of the lattice Boltzmann method was improved for the immersed boundary scheme by introducing the occupation ratio of fluid lattices among the interpolated lattices. We compared the results of our proposed scheme with the known results of conventional schemes. Using the proposed numerical scheme, the flow around the flexible plate in a free stream is simulated for the effect of flexibility. Our results show that the major role of the flexibility of the flexible plate is the reduction of the resistance from flow. From the unsteady flow around a flexible plate, we found that the St of the flexible plate up to Re < 80 increased regardless of plate flexibility, but the St in the range of Re > 120 was dependent on plate flexibility. In the range of Re > 120, the St of very flexible plate increased with increasing Re, while the St of rigid plate decreased with increasing Re.     

Numerical simulation of fish motion by using lattice Boltzmann-Immersed Boundary Velocity Correction Method

Numerical simulation of a flow past an undulating two-dimensional fish-like body is carried out by using Lattice Boltzmann Method (LBM) and our newly-proposed immersed Boundary Velocity Correction Method (IBVCM). The fish body used in the simulation is constructed from the NACA0012 airfoil. Based on the kinematics for undulatory swimming fish, the midline of the fish-like body oscillates transversally in the form of traveling wave. The current study is focused on the effects of Reynolds number and the character of midline oscillation on the generation of propulsion force. The investigation indicates that the higher Reynolds number, or higher frequency, or higher amplitude of midline oscillation produces a higher propulsion force. Among the parameters affecting the generation of propulsion force, the amplitude of midline oscillation is the most noticeable factor.     

An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries

An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the Cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylin-ders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method.     

基于格子Boltzmann方法模拟方腔顶盖驱动流

格子Boltzmann方法是使用时间和空间完全离散的细观模型来模拟流体宏观行为的一种新方法，模型的平均行为符合宏观的Navier-Stokes方程。给出了格子Boltzmann方法详细的求解过程，提出了一种简化的固壁边界条件处理方法。用格子Boltzmann方法对方腔顶盖驱动流进行了数值模拟，并对模拟结果进行了分析和讨论。通过与前人已有的试验及数值研究结果对比，验证了格子Boltzmann方法的正确性。     

利用三维格子Boltzmann法研究化学机械抛光中压力分布

利用三维格子Boltzmann法(LSM),对化学机械抛光(CMP)的润滑过程做了数值模拟,得到了不同晶片和抛光垫转速下的压力分布,并讨论了抛光液黏度对高压涡中压力最大值的影响.数值模拟结果表明,晶片自转是产生"双涡图"的主要原因,抛光垫旋转则主要产生"单涡图",抛光垫和晶片旋转的综合作用一起影响抛光效果,其中抛光垫的转速的改变对去除率影响较大.利用格子Bohzmann法模拟润滑问题,所得结果与求解Reynolds方程的结果一致,并具有计算效率高、几何直观等特性,能实现CMP过程的三维模型,且较容易实现对多相流的模拟.     

Second order bounce back boundary condition for the latice Boltzmann fluid simulation

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.     

Mesoscopic investigation of frost crystal nucleation on cold surface based on the lattice-Boltzmann method

Journal of Mechanical Science and Technology - A lattice Boltzmann method (LBM) two-dimensional (2D) mesoscopic model is presented for studying the frost crystal nucleation process involved in...     

Numerical analysis of a weak shock wave propagating in a medium using lattice boltzmann method (LBM)

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method,a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles θ_w. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.     

Parallel computation of two-phase flow in a microchannel using the lattice Boltzmann method

We present a numerical simulation of two-phase flow in a three-dimensional cross-junction microchannel by using the lattice Boltzmann method (LBM). At first, we validated our LBM code with the velocity profile in a 3-dimensional rectangular channel. Then, we developed a lattice Boltzmann code based on the free energy model to simulate the immiscible binary fluid flow. The parallelization of the developed code is implemented on a PC cluster using the MPI program. The numerical results of two-phase flow in the microchannel reveal droplet formation process, which compares well with corresponding experimental results. The size of droplet decreases with increase of the flow-rate ratio and the capillary number. The movement of a droplet through the microchannel induces three-dimensional circulating flow inside the droplet. This complex flow is thought to enhance the mixing and reaction of reagents.     

A review of spurious currents in the lattice Boltzmann method for multiphase flows

A spurious current is a small-amplitude artificial velocity field which arises from an imbalance between discretized forces in multiphase/multi-component flows. If it occurs, the velocity field may persist indefinitely, preventing the achievement of a true equilibrium state. Spurious velocities can sometimes be as large as the characteristic velocities of the problem, causing severe instability and ambiguity between physical and spurious velocities. They are typically exacerbated by large values of numerical surface tension or when the two fluids being simulated have large density ratios. The resulting instability can restrict what parameters may be simulated. To varying degrees, spurious currents are found in all multiphase flow models of the lattice Boltzmann method (LBM). There have been many studies of the occurrence of the phenomenon, and many suggestions on how to eliminate it. This paper reviews the three main models of simulating multiphase/multi-component flow in the lattice Boltzmann method, as well as the subsequent modifications made in order to reduce or eliminate spurious currents.     

Numerical simulation of droplet formation in a micro-channel using the lattice Boltzmann method

This study investigates droplet formation in a micro-channel using the lattice Boltzmann (LB) method. A cross-junction micro-channel and two immiscible, water and oil phase fluids, were used to form the micro-droplets. Droplets are formed by the hydrodynamic instability on the interface between two immiscible fluids when two immiscible fluids are imported simultaneously in a cross-junction micro-channel. The Shan & Chen model, which is a lattice Boltzmann model of two-phase flows, is used to treat the interaction between immiscible fluids. The detailed process of the droplet formation in the cross-junction micro-channel was illustrated. The results of the droplet formation by the LBM predicted well the experimental data by PIV (particle image velocimetry). The effect of the surface tension and the flow rate of water phase fluid on the droplet length and the interval between droplets was also investigated. As the surface tension increased, the droplet length and the interval between droplets were increased. On the other hand, when we increased the flow rate of the water phase fluid under the condition of the fixed oil-phase fluid flow rate, the droplet size was increased while the interval between droplets was decreased.     

Application of Immersed Boundary Method for flow over stationary and oscillating cylinders

IBM (Immersed Boundary Method) with feedback momentum forcing was applied to stationary and moving bodies. The capability of IBM to treat the obstacle surfaces, especially with moving effect has been tested for two dimensional problems. Stationary and oscillating cylinders were simulated by using IBM based on finite volume method with Cartesian coordinates. For oscillating cylinder, lateral and vertical motions are considered, respectively. Present results such as time histories of drag and lift coefficients for both stationary and oscillating cases are in good agreement with previous numerical and experimental results. Also, the instantaneous wake patterns of oscillating cylinder with different oscillating frequency ratios well represented those of previous researches. More feasibility study for IBM has been carried out to two oscillating cylinders. Drag and lift coefficients are presented for two cylinders oscillating sinusoidally with phase difference of 180°.     

Numerical simulation of the droplet formation in a cross-junction microchannel using the Lattice Boltzmann Method

This study describes the numerical simulation of two-dimensional droplet formation and the following motion by using the Lattice Boltzmann Method (LBM) with the phase field equation. The free energy model is used to treat the interfacial force and the deformation of a binary fluid system, drawn into a cross-junction microchannel. While one fluid is introduced through the central inlet channel, the other fluid is drawn into the main channel through the two vertical inlet channels. Due to the effect of surface tension on the interface between the two fluids, the droplets of the first fluid are formed near the cross-junction. The aim in this investigation is to examine the applicability of LBM to the numerical analysis of the droplet formation and its motion in the microchannel. It was found from comparison with the experimentally visualized patterns that LBM with the free energy model can reproduce the droplet formation successfully. However because of the stability problem which is intrinsic for high surface-tension cases, it requires a very long computational time. This issue is to be resolved in the future.     

格子波尔兹曼方法及其应用

格子波尔兹曼方法为研究非线性复杂系统提供了一种新的手段。本文详细叙述了格子气自动机和格子波尔兹曼方法的基本原理以及其在流体力学中的应用     

Numerical simulation of fluid-structure interaction of a moving flexible foil

The hybrid Cartesian/immersed boundary method is applied to fluid-structure interaction of a moving flexible foil. A new algorithm is suggested to classify immersed boundary nodes based on edges crossing a boundary. Velocity vectors are reconstructed at the immersed boundary nodes by using the interpolation along a local normal line to the boundary. For eliminating pressure reconstruction, the hybrid staggered/non-staggered grid method is adapted. The deformation of an elastic body is modeled based on dynamic thin-plate theory. To validate the developed code first, free rotation of a foil in a channel flow is simulated and the computed angular motion is compared with other computational results. The code is then applied to the fluid-structure interaction of a moving flexible foil which undergoes large deformation due to the fluid loading caused by horizontal sinusoidal motion. It has been shown that the moving flexible foil can generate much larger vertical force than the corresponding rigid foil and the vertical force can be attributed to the downward fluid jet due to the alternating tail deflection. This paper was recommended for publication in revised form by Associate Editor Haecheon Choi Sangmook Shin received his B.S. and M.S. degrees in Naval Architecture from Seoul National University, Korea in 1989 and 1991, respectively. He received his Ph.D. degree in Aerospace Engineering from Virginia Tech, USA in 2001. He is currently an Assistant Professor at Department of Naval Architecture and Marine Systems Engineering at Pukyong National University in Busan, Korea. His research interests include fluid-structure interaction, unstructured grid method, internal wave, and two-phase flow. Hyoung Tae Kim received the B.S. and M.S. degrees in Naval Architecture from Seoul National University in 1979 and 1981, respectively and the Ph.D. degree in Mechanical Engineering from University of Iowa, U.S.A. in 1989. Dr. Kim is currently a Professor at the Department of Naval Architecture & Ocean Engineering at Chungnam National University, Korea. His research interests are in the area of Ship Hydrodynamics, CFD calculations of turbulent flows around ships and propellers, and human-powered and solar boat design.     

Shape optimization of flow channels based on lattice Boltzmann method

A new optimality criterion algorithm is presented for producing modified shape designs for fluid flow inside channels. To compute the fluid motion in a channel, the lattice Boltzmann method (LBM) was used based on D2Q9 and D3Q15 lattice spaces associated with the Bhatnagar-Gross-Krook (BGK) collision term. An experiential optimality method to design channels with the lowest pressure drop along the passage is introduced. The positions of solid cells and fluid cells are exchanged based on the strain rate tensor at the solid-fluid interface. To obtain the optimized shape, the cells are changed until the optimality condition is obtained with the restriction of constant fluid volume. Examples are presented to validate the algorithm, including an elbow tube as well as symmetrical and nonsymmetrical Tjunction channels. The validation exercises demonstrate that the algorithm is suitable for optimal channel design.     

Numerical simulation of the flow around two fixed circular airfoils positioned in tandem using the LS-STAG method

In recent years the popularity of immersed boundary methods has been increasing in computational hydrodynamics. One of the most effective methods of this class is the LS-STAG method developed in 2010, which allows computations on sufficiently coarse grids. A software package was developed to solve a number of hydrodynamics and hydroelasticity problems by the LS-STAG method. We present the results of the testing the developed software package by simulating a flow around two fixed circular airfoils positioned in tandem at different distances between the airfoils. We simulate the flow modes for which two symmetric vortices, two asymmetrical vortices, and a vortex wake form behind the front airfoil. For each mode, the typical time dependences of the drag force and lift coefficients are presented. The results agree well with the experimental data in the literature and numerical results of other authors.     

Analysis of wave reflection of a stenotic vessel blood pressure wave using the lattice Boltzmann method and impedance boundary condition

Pressure wave produced by a stenotic vessel was analyzed in terms of the stiffness index, augmentation index and reflection index. An understanding of blood pressure wave reflection is key to developing non-invasive and easy-to-use diagnostic methods. The purpose of this study was to use computational fluid dynamics to analyze blood pressure waves and understand blood pressure wave reflections in stenotic vessels. The lattice Boltzmann method was used with the impedance boundary condition for the blood pressure waves. Variations in blood pressure wave parameters according to different degrees of stenosis were analyzed, in addition to fluid dynamic properties, including flow energy loss. We found that blood pressure wave reflection is related to flow energy loss from stenosis.