Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method

A numerical investigation of the two-dimensional laminar flow around side-by-side rotating circular cylinders using Lattice Boltzmann method is conducted. The effects of variation of rotational speed ratio β and different gap spacings g* at Reynolds number of 100 are studied. A various range of rotational speed ratio 0 ≤ β ≤ 2 for four different gap spacings of 3, 1.5, 0.7 and 0.2 are investigated. Flow conditions and its characteristics, such as lift and drag coefficients and Strouhal number, is studied. The results indicated that as β increases, the flow changes its condition from periodic to steady after a critical rotational speed. Results also indicated that variation of the gap spacing and rotational speed has significant effect on wake pattern. Wake pattern in turn has significant effect on the Strouhal number. Finally, the result is compared with experimental and other numerical data.     

Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders

A second-order lattice Boltzmann algorithm is used for Power-Law non-Newtonian flow simulation. The shear dependent behavior of the fluid is implemented through calculating the shear locally from the lattice distribution functions. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The flow past a series of tandem arrangement of two cylinders is computed in a confined domain. The effects of Reynolds number, the Power-Law index, and the distance between two cylinders on both the flow field and the drag coefficients of the cylinders are examined in detail.     

Lattice Boltzmann simulation of heat transfer and fluid flow in a microchannel with nanofluids

Mathematical modeling is performed to simulate forced convection flow of 47 nm- Al₂O₃/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Single channel flow and conjugate heat transfer problem are taken into consideration and the heat transfer rate using a nanofluid is examined. Simulations are conducted at low Reynolds numbers (2 ≤ Re ≤ 16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range of 0.6 ￡ [`(Nu)] ￡ 13 0.6 \le \overline{Nu} \le 13 . Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for practical applications.     

棱柱绕流流动的数值模拟

利用数值方法对长宽比为1／3, 1和3的棱柱绕流在雷诺数为100的非稳态流动特性进行了分析和研究。采用有限体积法对棱柱绕流的二维流动N-S方程进行离散求解,分析和研究了非稳态的棱柱绕流流场,升力系数,阻力系数和涡动特性,数值模拟的结果与相关文献的数据比较吻合。通过上述研究能够为了解棱柱绕流的非稳态流动特性提供有力的帮助。而对棱柱三维流动的模拟分析和对雷诺数的变化对棱柱流动特性的影响进行研究,将为掌握棱柱绕流的工程特性打下基础。     

Lattice Boltzmann simulation of two-sided lid-driven flow in a staggered cavity

In this article, the lattice Boltzmann method is employed in order to explore incompressible fluid flow inside a two-sided lid-driven staggered cavity. Results of the lattice Boltzmann simulation for antiparallel motion of lids are compared with the data from existing literature. For parallel motion of lids, the characteristics of flow pattern for a variety of Re numbers (50–3200) are presented. An asymmetric steady-state flow pattern for parallel motion of lids is obtained.     

Numerical simulation of viscous flow around unrestrained cylinders

A 2-D analysis is made for the dynamic interactions between viscous flow and one or more circular cylinders. The cylinder is free to respond to the fluid excitation and its motions are part of the solution. The numerical procedure is based on the finite volume discretization of the Navier–Stokes equations on adaptive tri-tree grids which are unstructured and nonorthogonal. Both a fully implicit scheme and a semi-implicit scheme in the time domain have been used for the momentum equations, while the pressure correction method based on the SIMPLE technique is adopted to satisfy the continuity equation. A new upwind method is developed for the triangular and unstructured mesh, which requires information only from two neighbouring cells but is of order of accuracy higher than linear. A new procedure is also introduced to deal with the nonorthogonal term. The pressure on the body surface required in solving the momentum equation is obtained through the Poisson equation in the local cell. Results including flow field, pressure distribution and force are provided for fixed single and multiple cylinders and for an unrestrained cylinder in steady incoming flow with Reynolds numbers at 200 and 500 and in unsteady flow with Keulegan–Carpenter numbers at 5 and 10.     

Lattice Boltzmann method for the simulation of viscoelastic fluid flows

The simulation of viscoelastic fluids is a challenging task from the theoretical and numerical points of view. This class of fluids has been extensively studied with the help of classical numerical methods. In this paper we propose a new approach based on the lattice Boltzmann method in order to simulate linear and non-linear viscoelastic fluids and in particular those described by the Oldroyd-B and FENE-P constitutive equations. We study the accuracy and stability of our model on three different benchmarks: the 3D Taylor–Green vortex decay, the simplified 2D four-rolls mill, and the 2D Poiseuille flow. To our knowledge, the methodology described in this work is a first attempt for the simulation of non-trivial flows of viscoelastic fluids using the lattice Boltzmann method to discretize the constitutive and conservation equations.     

Lattice Boltzmann simulation of flow past a circular cylinder near a moving wall

The two‐dimensional flows past a circular cylinder near a moving wall are simulated by lattice Boltzmann method. The wall moves at the inlet velocity and the Reynolds number ranges from 300 to 500. The influence of the moving wall on the flow patterns is demonstrated and the corresponding mechanism is illustrated by using instability theory. The correlations among flow features based on gap ratio are interpreted. Force coefficients, velocity profile and vortex structure are analyzed to determine the critical gap ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

复杂微通道气体流动的格子Boltzmann模拟

构建了一个模拟复杂微通道内气体流动的多松弛格子Boltzmann模型。该模型采用动力学曲面滑移边界,考虑了微尺度效应和努森层影响。此外,为了更准确地描述微通道内气体的滑移速度,在模型中引入孔隙局部Kn数来代替平均Kn数。之后采用Poiseuille流对模型进行验证,模拟结果与用直接模拟蒙特卡洛方法和分子模拟结果吻合较好,证明了该模型模拟微通道内处于滑移区和过渡区气体流动的有效性。最后,采用该模型模拟多孔介质内气体渗流过程。结果表明,随着孔隙平均Kn数的增加,多孔介质内的高渗区域增加,且优先从小孔隙中开始增加,这是由于小孔隙中微尺度效应更加明显,相对大孔隙流动阻力更小所致。     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

Viscous dissipation of a power law fluid in axial flow between isothermal eccentric cylinders

We study the temperature distribution of a power law fluid in a pressure-driven axial flow between isothermal eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible and fully developed flow [Eq. (64)]. We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power law exponent n. The temperature is a strong function of the gap between the cylinders. The temperature profiles are flat in the middle of the gap and then, near the wall, suddenly drop to the wall temperature.     

不同壁面绕流特性的格子Boltzmann模拟研究

为了探讨不同壁面的绕流特性,针对粘性流场中,不同壁面诱导的涡脱落现象以及升阻力系数等流场特性进行了格子Boltzmann数值研究。利用基于分子动理论的格子Boltzmann方法(LBM)求解Navier-Stokes方程,实现对流体运动的描述,针对不同的壁面条件,分别采用不同的格子Boltzmann流-固壁面处理方法。采用Half-way反弹边界条件来处理平直壁面,而曲壁面则采用LBM与有限差分法相结合的形式进行处理,计入了壁面与标准网格不重合对结果造成的影响。开发相应的计算程序,计算结果与已发表文献结果吻合良好,验证了数值模型的正确性。同时,探讨了进出口边界与钝体中心的距离对结果的影响。对比分析了不同壁面的绕流模型中升阻力系数、斯托罗哈数和涡量云图等,并进一步研究了雷诺数条件的影响。结果表明,不同壁面的绕流特性具有明显差异,且同时受雷诺数的显著影响;一般地,平直壁面对于来流作出的响应更迅速。     

基于格子Boltzmann方法的粘弹性流体圆柱绕流分析

将光滑界面法引入到格子Boltzmann方法中分析粘弹性流体绕流问题,分别采用单松弛模型和对流扩散模型求解运动方程和Oldroyd-B本构方程,针对圆形和椭圆内部边界条件,给出连续界面插值函数,在此基础上,运用光滑界面法将内部边界转换为作用力项施加到演化方程中。首先分析圆柱绕流问题,给出不同材料参数情况下的流场分布和阻力系数计算结果,比较发现与宏观数值模拟结果相吻合。将模型拓展到绕椭圆流动中,分析椭圆形状和材料参数对粘弹性流体绕柱流的影响,发现随着椭圆长轴与短轴比值的增加和维森伯格数的增加,阻力系数逐渐下降,并且长短轴比对迭代收敛有较大影响。     

二维水平通道内流动沸腾换热的格子Boltzmann模拟

利用格子Boltzmann方法模拟二维水平通道内水的流动沸腾过程,获得不同壁面过热度下流型特点和不同因素对换热过程的影响规律。结果表明,随着壁面过热度升高,流道内流型依次经历从泡状流、弹状流到反环流的转变,平均热流密度和平均换热系数先增大后减小。入口流速降低会使流道内出现受限气泡流,核态沸腾受到抑制。提高入口流速能够有效促进气泡脱离,壁面平均换热系数随入口流速增大而增大,但增长速率有所减小。减小通道宽度有利于汽化现象发生,核态沸腾得到强化,壁面平均换热系数有所提高。     

Lattice Boltzmann modeling of pore‐scale fluid flow through idealized porous media

In order to capture the hydro‐mechanical impacts on the solid skeleton imposed by the fluid flowing through porous media at the pore‐scale, the flow in the pore space has to be modeled at a resolution finer than the pores, and the no‐slip condition needs to be enforced at the grain–fluid interface. In this paper, the lattice Boltzmann method (LBM), a mesoscopic Navier–Stokes solver, is shown to be an appropriate pore‐scale fluid flow model. The accuracy and lattice sensitivity of LBM as a fluid dynamics solver is demonstrated in the Poiseuille channel flow problem (2‐D) and duct flow problem (3‐D). Well‐studied problems of fluid creeping through idealized 2‐D and 3‐D porous media (J. Fluid Mech. 1959; 5 (2):317–328, J. Fluid Mech. 1982; 115 :13–26, Int. J. Multiphase Flow 1982; 8 (4):343–360, Phys. Fluids A 1989; 1 (1):38–46, Int. J. Numer. Anal. Meth. Geomech. 1999; 23 :881–904, Int. J. Numer. Anal. Meth. Geomech. 2010; DOI: 10.1002/nag.898, Int. J. Multiphase Flow 1982; 8 (3):193–206) are then simulated using LBM to measure the friction coefficient for various pore throats. The simulation results agree well with the data reported in the literature. The lattice sensitivity of the frictional coefficient is also investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

Intercomparison of boundary schemes in Lattice Boltzmann method for flow simulation in porous media

The Lattice Boltzmann method has been widely adopted to simulate flow in porous media. The choice of appropriate boundary schemes is essential to achieve simulation accuracy; however, the criteria for the most suitable boundary treatment in the simulation of flow in porous media flow remain unresolved. Here, three types of the most commonly used boundary conditions are tested: interpolation bounce back (IBB), partial saturated method (PSM), and immersed boundary method (IBM). The dimensionless drag of face-centered cubic (FCC) sphere array and the dimensionless permeability of a random closely packed (RCP) sphere array are calculated and compared at different viscosities and resolutions. In the FCC sphere array case where spheres are not contacted, the IBB and PSM exhibit the same accuracy and both are of the second-order convergence rate. The IBM is less accurate and is of the first-order convergence rate. In the RCP sphere array case where the spheres are contacted, the IBB shows finer results and a second-order convergence rate. PSM underestimates the dimensionless permeability and increases resolution only slightly improved the results of PSM. The IBM overestimates the dimensionless permeability. These results indicate that among the three methods, the IBB is the most accurate. The PSM has the same accuracy as the IBB when sediments are not contacted; however, it loses its accuracy in the simulation of flow in closely packed porous media. This work could serve as a benchmark for further research in choosing the most appropriate method in the simulation of flow in porous media.