Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Simple lattice Boltzmann approach for turbulent buoyant flow simulation

In the present work, a simple large eddy simulation （LES）-based lattice Boltz- mann model （LBM） is developed for thermal turbulence research. This model is validated by some benchmark tests. The numerical results demonstrate the good performance of the present model for turbulent buoyant flow simulation.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method （LBM） with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

基于格子-波尔兹曼法的流体能耗求解

格子-波尔兹曼法是近年来新兴的一种计算流体力学数值方法。随着这种方法的不断发展,人们将它用于流体的仿真、优化等不同场合。与此同时,一些与流场流速和压强相关的物理量(如能耗)的求解也成为关注的焦点。本文介绍了能耗这一流体宏观量的格子-波尔兹曼法求解及其实现。与传统的有限差分法不同,本文在求解有关的速度梯度时使用了格子-波尔兹曼-矩法,这种方法不但能够避免有限差分法在边界处失效的缺点,而且计算简单,算法局部性好,适合大规模并行计算。本文在分析其数值解精度的基础上,使用这种方法进行了以能耗极小为目标的直通道内椭圆挡块的参数优化。这些分析和算例分别定量和定性地说明了本文算法的准确性。     

Parallel computation of turbulent flows using moment base lattice Boltzmann method

This paper describes parallel computing approach for simulating turbulent flows using a moment base lattice Boltzmann method. The distribution functions of the lattice Boltzmann method are expressed by corresponding moments. Choosing proper relaxation times for higher order moments, a minimum numerical dissipation is implicitly added to stabilise the method at high Reynolds numbers. Validation of the method is made by computing free decaying periodic turbulent flows and fully developed turbulent channel flows on a GPU platform. Though the present method requires additional work to calculate the higher order moments, it is shown that additional computational cost is negligible in the GPU computing. The numerical results stably obtained for the turbulent flows are in good agreement with those of a pseudo-spectral method and corresponding DNS database.     

Large eddy simulation in a turbulent channel flow using exit boundary conditions

The influence of the exit boundary conditions on the vanishing first derivative of the velocity components and constant pressure on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbances that are mostly damped by the grid stretching. The difference of rms values between the fully developed turbulent channel flow with periodicity conditions and the fully developed channel flow using inlet and the exit boundary conditions is less than 10% for the equidistant grids and less than 5% for the stretched grids. The chosen boundary conditions are of interest because they may be used in complex problems with back flow at the exit. Copyright © 1999 John Wiley & Sons, Ltd.     

Large eddy simulation of turbulent shallow water flows using multi‐relaxation‐time lattice Boltzmann model

In this paper, the standard Smagorinsky's algorithm is embedded into the multiple relaxation time (MRT) lattice Boltzmann model (LBM) for large eddy simulation (LES) of turbulent shallow water flows (MRT‐LABSWE^TM). The model is based on the two‐dimensional nonlinear shallow water equations, giving the depth‐averaged features. It is verified by applying the model in three typical cases in engineering with turbulence: (i) the flow around a square cylinder, (ii) plane cavity flow, and (iii) flows in a junction of 90°. The results obtained by the MRT‐LABSWE^TM are compared with BGK‐LABSWE^TM results and experimental data. The objectives of this study are to validate the MRT‐LABSWE^TM in a turbulence simulation and perform a comparative analysis between the results of BGK‐LABSWE^TM and MRT‐LABSWE^TM. Copyright © 2012 John Wiley & Sons, Ltd.     

Three‐dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model

Turbulent flow in a compound meandering open channel with seminatural cross sections is one of the most complicated turbulent flows as the flow pattern is influenced by the combined action of various forces, such as centrifugal force, pressure, and shear stresses. In this paper, a three‐dimensional (3D) Reynolds stress model (RSM) is adopted to simulate the compound meandering channel flows. Governing equations of the flow are solved numerically with finite‐volume method. The velocity fields, wall shear stresses, and Reynolds stresses are calculated for a range of input conditions. Good agreement between the simulated results and measurements indicates that RSM can successfully predict the complicated flow phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of incompressible flow within ½ circular cavity using lattice Boltzmann method

A wall‐driven incompressible viscous flow in a ½ circular cavity is simulated, based on the lattice Boltzmann method (LBM). The treatment of curved boundary with second‐order accuracy is used. The force evaluation is based on the momentum‐exchange method. The streamlines and vorticity contours and the velocity component along the central line of a semi‐circular cavity are obtained for different Reynolds numbers. The numerical results show that the LBM can capture the formation of primary, secondary and tertiary vortices exactly as the Reynolds number increases and has a great agreement with those of current literatures. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation (DNS) with a lattice Boltzmann (LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow, the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.     

用格子Boltzmann方法数值模拟混合层中旋涡的合并过程

用格子Boltzmann方法计算混合层中的流动问题。在流场的入口处加不同频率、振幅和相位的小扰动,观察混合层中旋涡的演进机理,模拟二维混合层中旋涡合并现象。在基本扰动波的基础上,又加入频率为基本波频率一半的亚谐波,得到了两个涡合并的计算结果,当加入的亚谐波频率为基本波频率的三分之一时,得到了三个涡合并的计算结果。这些计算结果与已有文献的结果基本一致,显示用格子Boltzmann方法模拟混合层问题是可行的。     

Numerical simulation of turbulent flows in trapezoidal meandering compound open channels

Three‐dimensional (3D) numerical study is presented to investigate the turbulent flow in meandering compound open channels with trapezoidal cross‐sections. The flow simulation is carried out by solving the 3D Reynolds‐averaged continuity and Navier–Stokes equations with Reynolds stress equation model (RSM) for steady‐state flow. Finite volume method (FVM) is applied to numerically solve the governing equations of fluid flow. The velocity magnitude, tangential velocity, transverse velocity and Reynolds stresses are calculated for various flow conditions. Good agreement between the simulated and available laboratory measurements was obtained, indicating that the RSM can accurately predict the complicated flow phenomenon. Comparison of the calculated secondary currents of four cases (one being inbank flow and other three being overbank flow) with different water depths reveals that (i) the inbank flow exhibits different flow behaviors from that of the overbank flow does and (ii) the water depth has significant effects on the magnitude and direction of secondary currents. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical study of the properties of the central moment lattice Boltzmann method

Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify the collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Because the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as the accuracy, grid convergence, and stability for well‐defined canonical problems is lacking, and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor–Green vortex flow, and lid‐driven cavity flow. We first establish its grid convergence and demonstrate second‐order accuracy under diffusive scaling for both the velocity field and its derivatives, that is, the components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. The cascaded MRT LBM based on the central moments is found to be of similar accuracy when compared with the standard MRT LBM based on the raw moments, when a detailed comparison of the flow fields are made, with both reproducing even the small scale vortical features well. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost. Copyright © 2015 John Wiley & Sons, Ltd.     

Theoretical and numerical study of Couette-Taylor flow with an axial flow using lattice Boltzmann method

In this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette-Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette-Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette-Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Re_c (total disappearance of instabilities) with both protocols and both manners.     

Efficient viscosity contrast calculation for blood flow simulations using the lattice Boltzmann method

The lattice Boltzmann method (LBM) combined with the immersed boundary method is a common tool to simulate the movement of red blood cel ls (RBCs) through blood vessels. With very few exceptions, such simulations neglect the difference in viscosities between the hemoglobin solution inside the cells and the blood plasma outside, although it is well known that this viscosity contrast can severely affect cell deformation. While it is easy to change the local viscosity in LBM, the challenge is to distinguish whether a given lattice point is inside or outside the RBC at each time step. Here, we present a fast algorithm to solve this issue by tracking the membrane motion and computing the scalar product between the local surface normal and the distance vector between the closest LBM lattice point and the surface. This approach is much faster than, for example, the ray-casting method. With the domain tracking applied, we investigate the shape transition of a RBC in a microchannel for different viscosity contrast and validate our method by comparing with boundary-integral simulations.     

Simulation of gravity currents using the thermal lattice Boltzmann method

The lattice Boltzmann method (LBM) is becoming an effective numerical technique of computational fluid dynamics (CFD). In this study, with some new thermal LBM schemes being proposed, the LBM is used to simulate the gravity current prior to backdraft (a particular and hazardous phenomenon in compartment fire) within laminar restrictions. The dimensionless time for gravity current traveling from the opening to the rear wall of a bench‐scale compartment is calculated under different opening geometries, respectively, including: full end opening, upside‐slot end opening, middle‐slot end opening, downside‐slot end opening, and slot ceiling opening. The application is very successful and the results show that the dimensionless time under the slot ceiling opening is the longest. Among the slot end openings, similar dimensionless time has been obtained for the upside‐slot and middle‐slot end openings, which is shorter than the downside‐slot end opening. For the full end opening, the shortest dimensionless time is obtained. Finally, some valuable advices are given for fire protection engineering. Copyright © 2010 John Wiley & Sons, Ltd.