Aeroelastic study of flexible flapping wings by a coupled lattice Boltzmann-finite element approach with immersed boundary method

In this paper, the behavior of two-dimensional symmetric flapping wings moving in a viscous fluid is investigated. Harmonic motion is applied to idealize flying organisms with flexible wings and extensive testing is carried out to investigate the resultant flight behavior related to the ability to take-off or accelerate the flapping wing system away from a starting location. Special attention is paid to analyze the effect of the main mechanical parameters, as well as the effect of lateral wind on flight performances. Moreover, aiming to investigate the possible benefits of flying in flocks, a couple of synchronously flapping wings is considered in addition to the single arrangement. The numerical simulations are performed by solving the fluid–structure interaction problem through a strongly coupled partitioned approach. Fluid dynamics are modeled at the mesoscopic scale by the lattice Boltzmann method. The resulting macroscopic quantities are derived, as usual, based on the statistical molecular-level interpretation.Wings are modeled by geometrically nonlinear, elastic beam finite elements and structure dynamics is solved by the time discontinuous Galerkin method. Fluid–structure interface conditions are handled using the immersed boundary method. The resultant numerical approach combines simplicity and high computational efficiency. A Monte Carlo simulation strategy is employed to characterize the flight behavior subjected to lateral wind. Various scenarios are discussed.     

Direct-forcing immersed boundary lattice Boltzmann simulation of particle/fluid interactions for spherical and non-spherical particles

The lattice Boltzmann method (LBM) is a useful technique for simulating multiphase flows and modeling complex physics. Specifically, we use LBM combined with a direct-forcing (DF) immersed boundary (IB) method to simulate fluid–particle interactions in two-phase particulate flows. Two grids are used in the simulation: a fixed uniform Eulerian grid for the fluid phase and a Lagrangian grid that is attached to and moves with the immersed particles. Forces are calculated at each Lagrangian point. To exchange numerical information between the two grids, discrete delta functions are used. The resulting DF IB-LBM approach is then successfully applied to a variety of reference flows, namely the sedimentation of one and two circular particles in a vertical channel, the sedimentation of one or two spheres in an enclosure, and a neutrally buoyant prolate spheroid in a Couette flow. This last application proves that the developed approach can be used also for non-spherical particles. The three forcing schemes and the different factors affecting the simulation (added mass effect, corrected radius) are also discussed.     

A method for direct simulation of flexible fiber suspensions using lattice Boltzmann equation with external boundary force

The computational method presented here can be used to study the effect of volume fraction and particle deformation on the rheology and microstructure of deformable fibers suspended in Newtonian fluid. In this method, the flow is computed on a fixed regular ‘lattice’ using the lattice Boltzmann method, where each solid particle is mapped onto a Lagrangian frame moving continuously through the domain. Instead of the standard bounce-back method, an external boundary force is used to impose the no-slip boundary condition at the fluid–solid interface for stationary or moving boundaries. The motion and orientation of the fiber are obtained from Newtonian dynamics equations. Although the external boundary force method is general, in this application it is used in conjunction with a flexible fiber model, which calculates the flexible fiber deformation by the real material properties. The methodology is validated by comparing with experimental and theoretical results.     

Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method

Based on the lattice Boltzmann (LB) approach, a novel hybrid method has been proposed for getting insight into the microscale characteristics of the multicomponent flow of nanofluid. In this method, the whole computational domain is divided into two regions in which different-sized meshes are involved for simulation (fine mesh and coarse mesh). The multicomponent LB method is adopted in the fine mesh region, and the single-component LB approach is applied to the coarse mesh region where the nanofluid is treated as a mixed single-component fluid. The conservation principles of mass, momentum and energy are used to derive a hybrid scheme across the different scaled regions. Numerical simulation is carried out for the Couette flow and convective heat transfer in a parallel plate channel to validate the hybrid method. The computational results indicate that by means of the present method, not only the microscopic characteristics of the nanofluid flow can be simulated, but also the computational efficiency can be remarkably improved compared with the pure multicomponent LB method.     

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。     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

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.     

A comparative study of lattice Boltzmann methods using bounce‐back schemes and immersed boundary ones for flow acoustic problems

In order to find applicable treatments of moving boundary conditions based on the lattice Boltzmann method in flow acoustic problems, three bounce‐back (BB) methods and four kinds of immersed boundary (IB) methods are compared. We focused on fluid–solid boundary conditions for flow acoustic problems especially the simulations of sound waves from moving boundaries. BB methods include link bounce‐back, interpolation bounce‐back and unified interpolation bounce‐back methods. Five IB methods are explicit and implicit direct‐forcing (Explicit‐IB and Implicit‐IB), two kinds of partially saturated computational methods and ghost fluid method. In order to reduce the spurious pressure generated by the fresh grid node changing from solid domain to fluid domain for BB methods and sharp IB methods, we proposed two new kinds of treatments and compared them with two existing ones. Simulations of the benchmark problems prove that the local evolutionary iteration (LI) is the best one in treatments of the fresh nodes. In addition, for standing boundary problems, although BB methods have a little higher accuracy, all the methods have similar accuracy. However, for moving boundary problems, IB methods are more appropriate than BB methods, because IB methods' smooth interpolation of pressure eld produces less disturbing spurious pressure waves. With improved treatments of fresh nodes, BB methods are also acceptable for moving boundary acoustic problems. In comparative tests in respective type, unified interpolation bounce‐back with LI, Implicit‐IB, and ghost fluid with LI are the best choices. Copyright © 2013 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.     

Validation of EMMS-based drag model using lattice Boltzmann simulations on GPUs

Interphase momentum transport in heterogeneous gas–solid systems with multi-scale structure is of great importance in process engineering. In this article, lattice Boltzmann simulations are performed on graphics processing units (GPUs), the computational power of which exceeds that of CPUs by more than one order of magnitude, to investigate incompressible Newtonian flow in idealized multi-scale particle–fluid systems. The structure consists of a periodic array of clusters, each constructed by a bundle of cylinders. Fixed pressure boundary condition is implemented by applying a constant body force to the flow through the medium. The bounce-back scheme is adopted on the fluid–solid interfaces, which ensures the no-slip boundary condition. The structure is studied under a wide range of particle diameters and packing fractions, and the drag coefficient of the structure is found to be a function of voidages and fractions of the clusters, besides the traditional Reynolds number and the solid volume fractions. Parameters reflecting multi-scale characters are, therefore, demonstrated to be necessary in quantifying the drag force of heterogeneous gas–solid system. The numerical results in the range 0.1 ≤ Re ≤ 10 and 0 < ? < 0.25 are compared with Wen and Yu's correlation, Gibilaro equation, EMMS-based drag model, the Beetstra correlation and the Benyahia correlation, and good agreement is found between the simulations and the EMMS-based drag model for heterogeneous systems.     

Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation

Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying turbulent flow simulation. We determined that a decrease in the number of velocities, in particular, 13-velocities, which can be used in the quasi-equilibrium lattice Boltzmann and in the multiple-relaxation time models (MRT), could considerably decrease the computational effort. However, decreasing the number of velocities deteriorates the stability and the accuracy of the results. By comparing the collision models, we also determined that the stability of the entropic lattice Boltzmann model (ELBM), and 19- and 27- velocity MRT is much higher than in other models. However, the numerical viscosity introduced by the ELBM underestimates the enstrophy, and the computational effort increases because of the calculation overhead required to solve the additional equations if special care is not given to the calculation.     

Analytical and numerical studies of the boundary slip in the immersed boundary‐thermal lattice Boltzmann method

We analytically and numerically investigate the boundary slip, including the velocity slip and the temperature jump, in immersed boundary‐thermal lattice Boltzmann methods (IB‐TLBMs) with the two‐relaxation‐time collision operator. We derive the theoretical equation for the relaxation parameters considering the effect of the advection velocity on the temperature jump of the IB‐TLBMs. The analytical and numerical solutions demonstrate that the proposed iterative correction methods without the computational cost of the sparse matrix solver reduce the boundary slip and boundary‐value deviation as effectively as the implicit correction method for any relaxation time. Because the commonly used multi‐direct forcing method does not consider the contributions of the body force to the momentum flux, it cannot completely eliminate the boundary slip because of the numerical instability for a long relaxation time. Both types of proposed iterative correction methods are more numerically stable than the implicit correction method. In simulations of flow past a circular cylinder and of natural convection, the present iterative correction methods yield adequate results without the errors of the velocity slip, the temperature jump, and the boundary‐value deviation for any relaxation time parameters and for any number of Lagrangian points per length. The combination of the present methods and the two‐relaxation‐time collision operator is suitable for simulating fluid flow with thermal convection in the multiblock method in which the relaxation time increases in inverse proportion to the grid size.     

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.     

Simulation of shockwave propagation with a thermal lattice Boltzmann model

A two‐dimensional 19‐velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u⁴) rather than the usual O(u³) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher‐order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13‐velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 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.     

Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

The flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWE^TM) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, D_r (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWE^TM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering. Copyright © 2008 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.     

Free convection of nanofluid filled enclosure using lattice Boltzmann method （LBM）

The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles: TiO₂, Ag, Cu, and Al₂O₃. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical methods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ = 2.5 when Ra = 10⁶ while at λ = 1.5 for other Rayleigh numbers.     

A coupled immersed boundary‐lattice Boltzmann method with smoothed point interpolation method for fluid‐structure interaction problems

The immersed boundary‐lattice Boltzmann method has been verified to be an effective tool for fluid‐structure interaction simulation associated with thin and flexible bodies. The newly developed smoothed point interpolation method (S‐PIM) can handle the largely deformable solids owing to its softened model stiffness and insensitivity to mesh distortion. In this work, a novel coupled method has been proposed by combining the immersed boundary‐lattice Boltzmann method with the S‐PIM for fluid‐structure interaction problems with large‐displacement solids. The proposed method preserves the simplicity of the lattice Boltzmann method for fluid solvers, utilizes the S‐PIM to establish the realistic constitutive laws for nonlinear solids, and avoids mesh regeneration based on the frame of the immersed boundary method. Both two‐ and three‐dimensional numerical examples have been carried out to validate the accuracy, convergence, and stability of the proposed method in consideration of comparative results with referenced solutions.