Coupled Lattice Boltzmann Method Research Articles

Coupled LBM-FVM-CA simulation of particle deposition and removal processes on tubes

A numerical model was proposed to simulate the fouling processes on the tubes, which contained the evolution of the fouling shape and the particle deposition/removal mechanisms. Firstly, the coupled lattice Boltzmann method (LBM) and finite volume method (FVM) was established to simulate the air flow. The flow around the tubes was simulated by the LBM due to its convenience in complex boundary conditions. The downstream flow was simulated by the FVM to save the computational source. A reconstruction operator was derived for the information transfer from macroscopic parameters to multiple-relaxation-time LBM. The cellular automata model, energy conservation model and moment analysis were included to simulate the particle motion, collision, deposition and removal. Then, because the time step in the simulation was several orders of magnitude shorter than the real fouling time, a time ratio was proposed for the conversion between simulation and real time. Finally, the evolutions of the fouling shapes along with time for different particle diameters and inlet velocities were simulated and analyzed. The results showed that the proposed coupled model can be used to study the particle deposition, removal and the changing of the fouling layers. When the mass concentration was the same, the fouling of small particle grew faster. The fouling area grew exponentially with time. It grew rapidly in the beginning, then grew slower and finally reached an asymptotic balance value. When the particle concentration was specified, the fouling rate first grew with and then decreased with the increasing inlet velocity. Therefore, there was a velocity range in which the fouling rate was high. As for the shape of the fouling layer, the removal was severe on the windward side, but the direct impaction of the particles formed the cone-shaped fouling layers. The cone-shape changed the air flow and stopped the deposition on the windward side. The fouling layers grew on the entire leeward side of the tubes and finally stopped when the removal was equal to the deposition. The simulated fouling shape was compared with the real picture of the fouling on a tube of an economizer and the fouling shapes on the leeward side coincided well with each other. The growth of the fouling mass was also compared with the existing experiment. The simulated mass had the same trend with the experiment. This demonstrated that the time ratio can be used to convert the time scale. The distribution of the particle sizes and the properties of the real particles should be considered in the future works.

Numerical Simulation of the Particle Deposition on a Tube with Coupled Lattice Boltzmann Method and Finite Volume Method

A coupling method between multiple-relaxation-time lattice Boltzmann method and finite volume method is used to simulate the 2D fouling process on a single row of tubes. The particle motion is simulated by the cellular automata model. The fluid flow and particle deposition process around the tubes is simulated by multiple-relaxation-time lattice Boltzmann method, while the downstream fluid flow is simulated by finite volume method to save the computational time. The restitution coefficient calculated by the energy balance and the critical impact angle are used as the criterions for particle deposition. The deposition processes for 5μm, 10μm particles with inlet velocity 5m/s and 10m/s are simulated with the method. The results show that the particle with small diameter and inlet velocity tends to deposit more rapidly. The vortices behind the tubes bring the particles back to the leeward side of the tube, and a concave shape of fouling continues growing on the entire leeward half of the tube. A cone shape fouling layer forms on the windward side of the tube. The cone shape changes the air flow and stops the deposition on the windward side. The proposed coupling method is suitable for the study of the fouling process on the tubes.

Modeling of electrokinetic reactive transport in micropore using a coupled lattice Boltzmann method

AbstractIt is well known that a solid surface will be charged when it comes into contact with liquid, especially with electrolyte solutions. The surface charge influences ion distribution and transport and, therefore, affects the chemical reaction. Such an effect may become significant in micropores/nanopores when the electrical double layer thickness is comparable to the pore size, but this has never been well studied. This work investigates the coupled electrokinetic and reactive transport in micropores using mesoscopic modeling. We established a numerical framework by coupling multiple lattice Boltzmann models to combine all effects on ion transport from convection, diffusion and electrokinetics, and therefore, on heterogeneous reactions in micropore. After validations, the mechanism of surface charge effects on reactive transport is studied for an ion precipitation case and a solid dissolution case. The results show that two factors, transport and reaction, compete in such complicated processes based on their characteristic rates. When the transport rate, including diffusion and convection, is much lower than the reaction rate, i.e., the transport‐dominated process, the surface charge significantly reduces the reaction. Otherwise for a reaction‐dominated process, the surface charge effect may be negligible.

Coupled LBM–DEM Micro-scale Simulations of Cohesive Particle Erosion Due to Shear Flows

In this paper, the erodibility of cohesive micro-scale particles is investigated for a range of surface shear stresses. Compacted layers of particles, formed by compressing 100 cohesive spheres together, are subjected to shear flow conditions. Fluid–particle interactions are solved using the lattice Boltzmann method (LBM), while the particle–particle interactions are treated by coupling with the distinct element method (DEM). Results reveal a clearly defined critical surface shear stress, beyond which erosion occurs, and a linear relation between the rate of erosion and excess surface shear stress. Further to this, an interesting mechanism by which detached particles gain upward movement is observed. This work also serves to highlight the potential of the coupled LBM–DEM approach for modelling dynamic erosion processes in three dimensions.

Coupled lattice Boltzmann method for generalized Keller–Segel chemotaxis model

In this work, an efficient and stable lattice Boltzmann method (LBM) for generalized Keller–Segel (K–S) chemotaxis model is proposed. Through the Chapman–Enskog analysis, the proposed LBM can correctly recover to the K–S model. The stability of the proposed LBM has been improved through adding correction terms in the evolution equations. Moreover, a local computational scheme for the gradient operator, which is included in the evolution equation, is developed, making the proposed LBM be implemented locally. Hence, both 2D and 3D problems with arbitrary geometries can be processed easily. In the numerical experiments, several representative chemotaxis problems are studied, including the blow up problem in square and circle domains, two-species chemotaxis blow up problem, chemotactic bacteria pattern formation in semi-solid medium in circle domain, 3D pattern formation in liquid medium, and the tumor invasion into surrounding healthy tissue. The numerical results demonstrate the high efficiency, stability and robustness of the proposed LBM. Furthermore, the capability of the proposed LBM in handling both 2D and 3D problems with complex domain is also illustrated.

Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

We present a coupled lattice Boltzmann method (LBM) to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst–Planck equation for the ion concentration, and the Navier–Stokes equation for the flows of the electrolyte solution. In the proposed LBM, the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator, which maintains the locality of the algorithm inherent to the original LBM. Furthermore, the Neumann-type boundary condition at the solid/liquid interface is then correctly imposed. In order to validate the present LBM, we consider an electro-osmotic flow in a slit between two charged infinite parallel plates, and the results of LBM computation are compared to the analytical solutions. Good agreement is obtained in the parameter range considered herein, including the case in which the nonlinearity of the Poisson equation due to the large potential variation manifests itself. We also apply the method to a two-dimensional problem of a finite-length microchannel with an entry and an exit. The steady state, as well as the transient behavior, of the electro-osmotic flow induced in the microchannel is investigated. It is shown that, although no external pressure difference is imposed, the presence of the entry and exit results in the occurrence of the local pressure gradient that causes a flow resistance reducing the magnitude of the electro-osmotic flow.

A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows

In this paper, we focus on the nonlinear coupling mechanism of the Nernst---Planck model and propose a coupled lattice Boltzmann method (LBM) to solve it. In this method, a new LBM for the Nernst---Planck equation is developed, a multi-relaxation-time (MRT)-LBM for flow field and an LBM for the Poisson equation are used. And then, we discuss the choice of the model and found that the MRT-LBM is much more stable and accurate than the LBGK model. A reasonable iterative sequence and evolution number for each LBM are proposed by considering the properties of the coupled LBM. The accuracy and stability of the presented coupled LBM are also discussed through simulating electro-osmotic flows (EOF) in micro-channels. Furthermore, to test the applicability of it, the EOF with non-uniform surface potential in micro-channels based on the Nernst---Planck model is simulated. And we investigate the effects of non-uniform surface potential on the pattern of the EOF at different external applied electric fields. Finally, a comparison of the difference between the Nernst---Planck model and the Poisson---Boltzmann model is presented.

Numerical simulation of solid particle behaviors in fluid flow by using a numerical method coupling technique

In rock engineering, the behavior of solid particles in a fluid flow has become an important topic. This paper demonstrates the effectiveness of a numerical simulation method based on the micro-mechanics of the fluid-solid interaction that couples the lattice-Boltzmann method (LBM) and the discrete element method (DEM). LBM is known to be a suitable technique for simulating fluid flow in complex and time-varying geometries with boundaries. DEM has attracted much attention among rock engineers as a useful simulation technique for large deformation problems. With the coupling of both methods, the complex motions of solid particles in a fluid flow can be simulated. To verify this, the sedimentation behavior of a single circular particle is simulated in a fluid with different Reynolds numbers, and the results are compared with FEM. In addition, the drafting, kissing, and tumbling (DKT) phenomenon between two particles in a fluid is modeled and reasonable results are obtained. The results of these case studies suggest that the method of coupling LBM and DEM can be an effective technique for simulating many kinds of engineering problems.

Influence of asperities on fluid and thermal flow in a fracture: A coupled lattice Boltzmann study

The characteristics of the hydro‐thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier‐Stokes and advection‐diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three‐dimensional (3‐D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two‐dimensional (integrated over the thickness) advection‐diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic lattices. Beyond some critical slope for the boundaries, the velocity profile is observed to be far from a quadratic profile in the vicinity of the sharp asperity: the fluid within the triangular asperity is quasi‐static. We find that taking account of both the 3‐D effects and the cooling of the rock, are important for the thermal exchange. Neglecting these effects with lubrication approximations results in overestimating the heat exchange efficiency. The evolution of the temperature over time, toward steady state, also shows complex behavior: some sites alternately reheat and cool down several times, making it difficult to forecast the extracted heat.

Analysis of Coupled Lattice Boltzmann Model with Well-Balanced Scheme for Shallow Water Flow

The coupled lattice Boltzmann method (CLBM) is applied in investigating contamination transport in shallow water flows. Shallow water equations and advection-diffusion equation are both solved using lattice Boltzmann method (LBM) on a D2Q9 square lattice and Bhatnagar-Gross-Krook (BGK) term. For extending application of CLBM in shallow water flows, the well-balanced scheme is introduced to replace the source term. Three cases including dam break, 2D pure diffusion and complex tidal flow are calculated and analyzed. Dam break and 2D pure diffusion are prepared to validate the flow module and water quality module, respectively. Both the cases show satisfactory consistency between predicting results and analytical solutions. Since clear reproduction of the shock wave propagation and precise prediction of contamination transport are derived, LBM is proved to be the numerical method naturally conservative with acceptable computing error. Furthermore, complex tidal flow with irregular geometry and sinus-varied bathymetry is simulated by adopting the well-balanced treating on the source term. The velocity fields, water levels, and water quality are compared between the ebb tide and flood tide, the results of which are in excellent accordance with the physical laws during the process. Hence, it may demonstrate that improved by well-balanced scheme CLBM can be widely applicable in shallow water flow.

A coupled lattice Boltzmann model for thermal flows

We present a coupled lattice Boltzmann method (LBM) for thermal viscous flows based on a two relaxation times kinetic model. The method is directly derived by projecting the coupled kinetic model equations for the distribution functions onto the tensor Hermite polynomials following Grad’s moment expansion method. By choosing a proper reference velocity, the coupling of lattice velocities and the local temperature is avoided and the resultant method is consistent with the original kinetic model. The intrinsic discrete nodes of the Gauss–Hermite quadrature provide the natural lattice velocities for the thermal LBM. Simulations of 2D natural convection flows are shown. The numerical results agree well with the previous benchmark data.

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

AbstractThis paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.