Coupled Lattice Boltzmann Research Articles

The coupled lattice Boltzmann simulation of free convection in a finned L-shaped cavity filled with nanofluid

PurposeThis paper aims to investigate the free convection, heat transfer and entropy generation numerically and experientially. A numerical/experimental investigation is carried out to investigate the free convection hydrodynamically/thermally and entropy generation.Design/methodology/approachThe coupled lattice Boltzmann method is used as a numerical approach which keeps the significant advantages of standard lattice Boltzmann method with better numerical stability. On the other hand, the thermal conductivity and dynamic viscosity are measured using modern devices in the laboratory.FindingsSome correlations based on the temperature at different nanofluid concentration are derived and used in the numerical simulations. In this regard, the results will be accurate with respect to using theoretical properties of nanofluid, and close agreements will be detected between present results and the previous numerical and experimental works. The numerical investigation is done under the effect of Rayleigh number (103 < Ra < 106), volume concentration of nanofluid (?? = 0.5, 1, 1.5, 2, 2.5 and 3%) and thermal configuration of the cavity (Cases A, B, C and D).Originality/valueThe originality of the present work lies in coupling of the lattice Boltzmann method with experimental observations to analyse the free convection in a cavity.

Modeling the propane combustion process within a micro-catalytic porous combustor by using the lattice Boltzmann method

Understanding the micro-catalytic porous combustion mechanisms is vital importance in improving the energy conversion efficiency of a combustion process. However, the investigation on this issue is still challenging due to the complex multiple physicochemical and thermal coupled transport mechanisms occurring in this process. In this work, a coupled lattice Boltzmann model is developed for modeling propane catalytic combustion process within a micro-catalytic porous combustor, in which the coupled transport mechanisms including multi-component gases flow, mass and heat transfers, as well as the heterogeneous catalytic combustion reaction are fully considered. Then, a systematic analysis regarding operating conditions and pore structure parameters was performed to disclose the micro-catalytic porous combustion mechanisms and dominated factors in determining the conversion efficiency. Results show that the conversion efficiency of propane in the micro-catalytic porous combustor majorly depends on the equivalence ratio, gas temperature and support materials properties. With an increment of the equivalence ratio, the conversion efficiency was improved firstly and then reduced, and an optimal combustion performance can be achieved where the equivalence ratio is equal to the chemical equivalent value. As the gas temperature increases, the conversion efficiency rises tremendously. To achieve a desirable combustion performance, the high gas temperature (> 700 K) should be maintained. Moreover, the support materials change the heat transfer and heat loss of the combustor, and the support materials with a low thermal conductivity or thermal diffusivity can reduce the heat loss and therefore enhance the conversion efficiency.

Coupled Light Capture and Lattice Boltzmann Model of TiO2 Micropillar Array for Water Purification

ABSTRACTTiO2 has been widely studied as a photocatalytic material due to its non-toxicity, chemical inertness, and high photocatalytic activity. Here, we explore the operational behavior of a novel TiO2 micropillars array being developed to use solar radiation to treat recycled wastewater in long-duration space missions. A Light Capture model was developed to model light absorption. The Lattice Boltzmann method was used to simulate water flow, and the finite element method was used to model waste mass transfer.

Characterization of mixing and reaction between chemical species during cycles of drainage and imbibition in porous media

Mixing and reaction between chemical species during cycles of drainage and imbibition in porous media are investigated using a coupled lattice Boltzmann model (LBM). This coupled LBM is able to simulate advection-diffusion processes with homogeneous reactions under dynamic (immiscible) multiphase flow conditions. A feature of the model is that there is no need to track the interface specifically for the transport domain, which improves the computational efficiency significantly. Transport simulations of non-reactive tracers in a natural pore domain show that some tracers can be trapped with the resident wetting fluid, with the tracers in these stagnant regions (defined here as regions where Pé < 1) being released slowly during the imbibition phase. Moreover, it is found that the relative amount of tracer diffusing from these stagnant regions increases as the system approaches steady-state flow conditions. For bimolecular reactive transport, the results demonstrate that most of the reaction product generated during mixing in stagnant regions accumulates and remains within these regions, with only some release of the product to infiltrating wetting fluid that bypasses adjacent to these regions.

Analysis of inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow with a coupled lattice Boltzmann method-discrete element method

In this study, a hybrid numerical framework for modelling solid-liquid multiphase flow is established with a single-relaxation-time lattice Boltzmann method and the discrete element method implemented with the Hertz contact theory. The numerical framework is then employed to systematically explore the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in planar Poiseuille flow. The results show that the influence of particle concentration on the migration is primarily determined by the characteristic channel Reynolds number Re0. For relatively low Re0 (Re0 &amp;lt; 20), the migration behaviour can only be observed at a very low particle concentration (≤5%). However, when Re0 &amp;gt; 20 the migration behaviour can be observed at a high concentration (≥20%). Furthermore, a focusing number Fc is proposed to characterise the degree of inertial migration. It was found that the inertial migration can be classified into three regimes depending on two critical values of the focusing number, Fc+ and Fc−: (i) when Fc &amp;gt; Fc+, a full inertial migration occurs; (ii) when Fc &amp;lt; Fc−, particles are laterally unfocused; and (iii) when Fc− &amp;lt; Fc &amp;lt; Fc+, a partially inertial migration takes place.

A coupled Lattice Boltzmann approach to simulate gas flow and transport in shale reservoirs with dynamic sorption

Gas flow in a shale reservoir is hard to model and simulate as certain complex mechanisms should be included, for example, diffusion and sorption. As a mesoscopic approach, Lattice Boltzmann Methods can capture the flow behavior in both scales: free flow through the conventional pore channels and gas transport with sorption in the tight matrix with very small pores. In this paper, two Lattice Boltzmann (LB) schemes are presented to recover the Navier-Stokes equations and advection diffusion equation respectively, to model the flow and transport in the two scales. The Navier-Stokes type LB scheme is constructed to model the free flow in fractures and conventional pore channels in matrix, and the convection diffusion type LB scheme is constructed to model the transport in tight matrix with very small pores. Chapman-Enskog expansions are derived to show the equivalence of the two LB schemes with the two macroscopic equations. Dynamic sorption is included in the advection diffusion with the dependance of gas concentration and free flow velocities, and the absorbed amount can affect the free flow velocity as well. In our simulation of gas flow and transport in shale reservoirs, the media is generated through two methods, reading a realistic media image and generating using a pore-network model. The rock characteristics are preserved in our generated porous media, with the method we proposed to link the LB scheme with the pore network modeling method. The simulation results are reasonable to prove that our schemes are robust and efficient, and the effect of porosity and sorption parameters are presented. Furthermore, the interaction of the two-scale gas flow and transport is analyzed, and we show that the increasing adsorbed gas amount in matrix may not slow down the free flow velocity as this increase may be resulted from changes in the rock characteristics. The scheme is simple to understand and implement, because only a few modifications are needed to construct the LB schemes on the two scales.

Coupled lattice Boltzmann simulation method for bidomain type models in cardiac electrophysiology with multiple time-delays

In this work, we propose a mathematical model of the cardiac electrophysiology which take into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart by using a developed coupling Lattice Boltzmann Method (LBM). The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction-diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. Due to delays, dynamic and geometry complexity, numerical simulation and implementation of this type of coupled systems are very ambitious mathematical and computational problems but are crucial in several biomedical applications. We introduce a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems with multiple time delays. Numerical tests to confirm effectiveness and accuracy of our approach are provided and, the influence and impact of delays to restore normal heart rhythm are analyzed.

Mathematical modeling and analysis of dynamic effects of multiple time-varying delays on electrophysiological wave propagation in the heart

In this work, we propose a mathematical model of the cardiac electrophysiology which takes into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart. The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction–diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. First, the mathematical models are introduced. Afterward the existence and uniqueness of solution of the state equation are proved as well as stability result. A numerical calculation is performed by using a coupling Lattice Boltzmann Method.

Study on frequency patterns of 2D square Rayleigh–Bénard convection filled with air

Abstract In this paper, the coupled lattice Boltzmann BGK method (CLBGK) is applied to simulate the 2D enclosure Rayleigh–Benardconvection (RBC) filled with air at Rayleigh number Ra =7.5 × 104 ∼ 10 9. Based on these results, the pair of character frequencies with their corresponding oscillatory structures is achieved. The present study indicates that the time–dimensionless frequency (f*) of a specific oscillatory structure has a regular change with the increase of Ra. Three f* ∼ Ra trends are clearly confirmed respectively in laminar states, transitional states, and turbulent states, which can be summarized as f* ∼ Ra −1/6 in laminar and transitional states, and f* ∼ Ra 2∕7 in turbulent states, where the former one corresponds to the natural property of RBC and the latter one well matches the scale law of Nu ∼ Ra 2∕7 . With the guidance of these conclusions, a set of auxiliary RBC experiments are performed and obtain the similar f* ∼ Ra trends, which proves the reliability of LBM in the spectral research of RBC.

A novel two-dimensional coupled lattice Boltzmann model for thermal incompressible flows

A novel two-dimensional coupled lattice Boltzmann model is developed for thermal incompressible fluid flows. A modified equilibrium distribution function is proposed in the present model. A mesoscopic discrete force is coupled into the modified equilibrium distribution function based on the Boussinesq approximation. The outstanding advantages of the standard lattice Boltzmann method are retained in present model besides better numerical stability. The present model is validated by the numerical simulation of the natural and Rayleigh–Benard convection at a wide range of Rayleigh numbers. Excellent agreement between the present results and previous lattice Boltzmann method or theoretical prediction demonstrates that present model is an efficient numerical method for natural and Rayleigh–Bénard convection. Further, present model is also successfully assessed considering Rayleigh–Taylor instability. It is also easier and convenient to be implemented as compared with the previous thermal models.

A coupled lattice Boltzmann and fractal geometry method for laminar liquid flows

A coupled lattice Boltzmann and fractal geometry method is introduced to simulate laminar channel flow. The coupled method is divided into two cases. If the height difference between adjacent grids is less than the grid width, the linear interpolation between two points is taken to replace the curve line with the Weierstrass-Mandelbrot (WM) function. If not, the zig-zag line is applied to replace the fractal wall. With a fractal dimension to characterize the shape of the wall, fractal geometry with WM function is adopted to reveal the rough wall. The coupled method overcomes the error of roughness height when adopting fractal function to lattice Boltzmann method. Then, it is concluded that WM function should be used at every grid to ensure the numerical wall is fractal. The coupled method shows its advantage of accuracy with simulations of 2-D laminar channel liquid flows. In addition, the effects of roughness and the boundary slip are taken into consideration. Compared with the experiment data, the proposed method can simulate the real flow accurately. The slip velocity of liquid flow is reduced by the irregular roughness of WM function. Moreover, a comparison between the fractal wall and regular grooves wall indicates that fractal geometry with the WM function is a better way to reveal the real rough wall for laminar flows.

Pore-scale modelling of the coupled thermal and reactive flow at the combustion front during crude oil in-situ combustion

A stable combustion front is important to achieve a successful in-situ combustion process for the crude oil recovery. The understanding of the multiple physicochemical and thermal processes at the combustion front is fundamental to reduce the potential risks, such as high burning temperature and low oxygen utilization. In the present study, a pore-scale modelling of the combustion front was employed based on the Lattice Boltzmann method to couple the fluid flow, heat and mass transfer and chemical reactions with the geometrical evolution. A thermal counter-slip algorithm was developed to solve the coupled interface conditions between conjugated heat transfer and heterogeneous reactions. The accuracy of the coupled lattice Boltzmann numerical models was validated by the finite element method. Pore-scale simulation was then performed to model the thermal and reacting flows through a two-dimensional model porous medium. The numerical simulation distinguished four characteristic regimes corresponding to different control mechanisms for the reacting flow. The study showed that the diffusion-limited mechanism is most desirable for the stable combustion in terms of the ideal burning temperature and full oxygen utilization. The control regime diagram was mapped on the Péclet-Damköhler plane for the specified computational domain. The effects of the Péclet and Damköhler numbers on the burning temperature, combustion front propagation velocity and oxygen utilization were then analyzed to obtain some insights about the control of the combustion front in the ISC process.

Numerical simulation of electroosmotic flow in rough microchannels using the lattice Poisson-Nernst-Planck methods

In this study, coupled Lattice Boltzmann method is applied to solve the dynamic model for an electroosmotic flow and investigate the effects of roughness in a 2-D flat microchannel. In the present model, the Poisson equation is solved for the electrical potential, the Nernst– Planck equation is solved for the ion concentration. In the analysis of electroosmotic flows, when the electric double layers fully overlap or the convective effects are not negligible, the Nernst-Planck equation must be used to find the ionic distribution throughout the microchannel. The effects of surface roughness height, roughness interval spacing and roughness surface potential on flow conditions are investigated for two different configurations of the roughness, when the EDL layers fully overlap through the microchannel. The results show that in both arrangements of roughness in homogeneously charged rough channels, the flow rate decreases by increasing the roughness height. A discrepancy in the mass flow rate is observed when the roughness height is about 0.15 of the channel width, which its average is higher for the asymmetric configuration and this difference grows by increasing the roughness height. In the symmetric roughness arrangement, the mass flow rate increases until the roughness interval space is almost 1.5 times the roughness width and it decreases for higher values of the roughness interval space. For the heterogeneously charged rough channel, when the roughness surface potential ψr is less than channel surface potential ψs, the net charge density increases by getting far from the roughness surface, while in the opposite situation, when ψs is more than ψr, the net charge density decreases from roughness surface to the microchannel middle center. Increasing the roughness surface potential induces stronger electric driving force on the fluid which results in larger velocities in the flow.

A numerical analysis of pressure drop and particle capture efficiency by rectangular fibers using LB-DE methods

In this work, a coupled lattice Boltzmann method (LBM) and discrete element method (DEM) are used to simulate the particle transport and deposition on rectangular fibers of a clean filter. The LBM is employed to describe the fluid flow around the fibers, whereas the DEM is used to deal with the particle dynamics. The effects of the Reynolds number, the fiber aspect ratio and the arrangement of fibers (i.e., orientation angle of a fiber) on the pressure drop and capture efficiency are investigated at the initial stage of the filtration process. The quality factor, commonly used to determine the filtration performance, is also studied. The simulation results illustrate that both pressure drop and capture efficiency are dependent on the orientation angle and aspect ratio. The Reynolds number has only a slight influence on the capture efficiency but has a significant effect on the pressure drop for high aspect ratio. A good filter performance can be obtained for a square fiber when the orientation angle is $$\pi /4$$ from the quality factor standpoint.

Transport and Mixing Induced by Beating Cilia in Human Airways.

The fluid transport and mixing induced by beating cilia, present in the bronchial airways, are studied using a coupled lattice Boltzmann—Immersed Boundary solver. This solver allows the simulation of both single and multi-component fluid flows around moving solid boundaries. The cilia are modeled by a set of Lagrangian points, and Immersed Boundary forces are computed onto these points in order to ensure the no-slip velocity conditions between the cilia and the fluids. The cilia are immersed in a two-layer environment: the periciliary layer (PCL) and the mucus above it. The motion of the cilia is prescribed, as well as the phase lag between two cilia in order to obtain a typical collective motion of cilia, known as metachronal waves. The results obtained from a parametric study show that antiplectic metachronal waves are the most efficient regarding the fluid transport. A specific value of phase lag, which generates the larger mucus transport, is identified. The mixing is studied using several populations of tracers initially seeded into the pericilary liquid, in the mucus just above the PCL-mucus interface, and in the mucus far away from the interface. We observe that each zone exhibits different chaotic mixing properties. The larger mixing is obtained in the PCL layer where only a few beating cycles of the cilia are required to obtain a full mixing, while above the interface, the mixing is weaker and takes more time. Almost no mixing is observed within the mucus, and almost all the tracers do not penetrate the PCL layer. Lyapunov exponents are also computed for specific locations to assess how the mixing is performed locally. Two time scales are introduced to allow a comparison between mixing induced by fluid advection and by molecular diffusion. These results are relevant in the context of respiratory flows to investigate the transport of drugs for patients suffering from chronic respiratory diseases.

Coupled lattice Boltzmann finite volume method for conjugate heat transfer in porous media

ABSTRACTThis work presents a coupled lattice Boltzmann finite volume method for dealing with conjugate heat transfer problems. Lattice Boltzmann scheme is used for fluid-dynamics, while high-order finite volume method is implemented for temperature reconstruction. After a first validation with literature test cases, the method is applied to a heat exchanger with an insert made of porous medium, representative of an open-cell metal foam, innovative material largely used for its thermomechanical properties. This allows maximizing heat exchange processes with advantages in terms of efficiencies. Thus, the coupled method allows dealing with complex boundaries in multiphysics problems.

A Lattice Boltzmann Method and Asynchronous Model Coupling for Viscoelastic Fluids

The numerical algorithms of viscoelastic flows can appear a tremendous challenge as the Weissenberg number (Wi) enlarged sufficiently. In this study, we present a generalized technique of time-stably advancing based on the coupled lattice Boltzmann method, in order to improve the numerical stability of simulations at a high Wi number. The mathematical models of viscoelastic fluids include both the equation of the solvent and the Oldroyd-B constitutive equation of the polymer. In the two-dimensional (2D) channel flow, the coupled method shows good agreements between the corresponding exact results and the numerical results obtained by our method. In addition, as the Wi number increased, for the viscoelastic flows through contractions, we show that the prediction of our presented method can reproduce the same numerical results that were reported by previous studies. The main advantage of current method is that it can be applied to simulate the complex phenomena of the viscoelastic fluids.

A coupled lattice Boltzmann method and discrete element method for discrete particle simulations of particulate flows

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle–particle and particle–fluid interactions require an adequate representation but the computational cost has to be kept low. In this work, we present a novel coupling approach for such simulations. A lattice Boltzmann formulation of the generalized Navier–Stokes equations is used to describe the fluid motion. This promises efficient simulations suitable for high performance computing and, since volume displacement effects by the solid phase are considered, our approach is also applicable to non-dilute particulate systems. The discrete element method is combined with an explicit evaluation of interparticle lubrication forces to simulate the motion of individual submerged particles. Drag, pressure and added mass forces determine the momentum transfer by fluid–particle interactions. A stable coupling algorithm is presented and discussed in detail. We demonstrate the validity of our approach for dilute as well as for dense systems by predicting the settling velocity of spheres over a broad range of solid volume fractions in good agreement with semi-empirical correlations. Moreover, the accuracy of particle–wall interactions in a viscous fluid is thoroughly tested and established. Finally, simulations of mono- and bi-disperse fluidized beds highlight the capability of our new approach to handle configurations with large particle numbers.

Coupled MRT Lattice Boltzmann Study of Electrokinetic Mixing of Power-Law Fluids in Microchannels with Heterogeneous Surface Potential

Coupled MRT Lattice Boltzmann Study of Electrokinetic Mixing of Power-Law Fluids in Microchannels with Heterogeneous Surface Potential

Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method.

This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.