Modified Lattice Boltzmann Model Research Articles

Modified Lattice Boltzmann Model Based on the System Performance Optimization Life Cycle for decaying isotropic turbulence simulations

Modified Lattice Boltzmann Model Based on the System Performance Optimization Life Cycle for decaying isotropic turbulence simulations

A modified lattice Boltzmann model for microcylindrical Couette gas flows

We develop an axisymmetric lattice Boltzmann (LB) model to simulate microcylindrical Couette gas flows (MCGF) in the slip regime and transition regime, respectively. A kinetic boundary scheme in the cylindrical coordinate system is proposed to fulfill the second-order slip boundary condition at the cylindrical wall. To consider the effect of the Knudsen layers for transition flows, local effective Knudsen numbers are introduced into the kinetic boundary scheme and relaxation time. Numerical tests are executed to acquire the velocity distributions of the time-independent and time-dependent MCGF. Comparisons with the analytical solution and direct Monte Carlo data are also implemented. The simulation results demonstrate that the developed LB model can successfully acquire the velocity distribution of the MCGF with an intermediate Knudsen number in the transition regime.

A lattice Boltzmann simulation on the gas flow in fractal organic matter of shale gas reservoirs

The gas flow in the organic matter with multiple flow regimes is critical to the shale gas production from shale gas reservoirs, but simultaneously simulating the full flow regimes of shale gas in the nanopores of the fractal shale organic matter is still unavailable. This paper presents a modified lattice Boltzmann model with effective relaxation time to simulate the shale gas micro-flow behaviors in fractal organic matter for permeability prediction. Firstly, some fractal shale organic matters are reconstructed by the quartet structure generation set (QSGS) algorithm, and the structural parameters such as fractal dimension, lacunarity and average pore diameter are calculated to characterize the complexity of the fractal shale organic matter. Secondly, effective viscosity and Knudsen layer are introduced into the effective relaxation time to formulate a modified lattice Boltzmann model. Thirdly, this modified lattice Boltzmann model is verified by comparing with the theoretical permeability models for the gas flow in the body centered cubic (BCC) arrays. Finally, a series of gas flow simulations in reconstructed fractal shale organic matter are conducted to explore the effects of structure parameters on permeability. Numerical simulations show that the modified lattice Boltzmann model can simulate the full gas flow regimes and predict the permeability of the fractal shale organic matter. The logarithm of permeability is negatively linearly correlated with fractal dimension and positively linearly correlated with lacunarity of the shale organic matter. This permeability exponentially increases with the increase of average pore diameter and a power law is observed between the fractal dimension and average pore diameter of these fractal shale organic matters. The anisotropic structures have great impacts on the directional permeability of shale organic matter. The permeability kx in the horizontal direction increases first and then decreases with the increase of anisotropic ratio (AR) and reaches the peak when AR is about 20. The permeability ky in the vertical direction monotonically decreases with the increase of AR.

Stochastic Effects of 2D Random Arrays of Cylinders on Rarefied Gas Permeability Using the Lattice Boltzmann Method

A large set of 2D random arrays of circular cylinders is generated to perform a statistical study on rarefied gas flow through micro-porous media. The flow regimes in this work lie for Knudsen numbers (Kn) ranging from the continuum to the transition regimes. Arrays are built by randomly placing cylinders with constant diameter with a uniform distribution without overlapping, and are generated for three target porosities. Fluid flow is assumed to be incompressible and isothermal. A modified lattice Boltzmann model is adopted to account for discrete effects, with slip-velocity boundary conditions and a Kn-dependent multi-relaxation time collision operator. The apparent permeability is modeled with Darcy’s law with a Klinkenberg-type relationship and compared with existing correlations. Velocity fields highlight the increasing contribution of fluid flow through small pores with increasing Kn. Numerical results show that porous media randomness leads to an uncertainty on rarefied gas permeability calculation despite the same structural characteristics and may not strictly follow a specific correlation. The influence of a local collision operator based on a local Kn instead of a global one in the numerical model is also studied. Results show that the permeability in rarefied regimes undergoes significant deviation when applying the local collision operator compared to the global one. These differences could result from a more accurate capture of the pore-scale behavior with a local Kn. Thus, it emphasizes the sensitivity of the model and the apparent permeability calculation to the appropriate definition of Kn.

Effects of a centered conducting body on natural convection of a non-Newtonian fluid in a square enclosure with time-periodic temperature distribution

In this paper, a modified lattice Boltzmann model that incorporates the effect of heat capacity is adopted to study the effects of a centered conducting body on the natural convection of a non-Newtonian fluid in a square cavity with time-periodic temperature distribution. The effects of power-law index, Rayleigh number, heat capacity ratio, thermal conductivity ratio, body size, temperature pulsating period, and temperature pulsating amplitude on fluid flow and heat transfer are analyzed in detail. The results showed that the increase of Rayleigh number and thermal conductivity ratio as well as the decrease of power-law index can strengthen both transient and global heat transfer, while the increase of heat capacitance of the fluid to the solid wall can enhance the transient heat transfer and has little effect on the overall heat transfer. Furthermore, the increase of body size will reduce both the transient heat transfer ratio and the overall heat transfer ratio. In addition, the decrease of temperature pulsating period can enhance the transient heat transfer, but will slightly weaken the overall heat transfer. Finally, the results show that both the transient and overall heat transfer ratios increase with the increase of temperature pulsating amplitude.

On the shear viscosity of dilute suspension containing elliptical porous particles at low Reynolds number

In view of the significance of non-spherical and permeable particles in liquid-solid and gas-liquid-solid reactors in industrial processes, it is essential to understand and quantify the rheological properties of multiphase flows in these processes. In this study, we investigate the shear viscosity of dilute suspension containing elliptical porous particles at low Reynolds number Re of O(0) by use of a modified lattice Boltzmann model. The fluid flow around and inside an elliptical porous particle is described by the volume-averaged macroscopic governing equations. The relative viscosity is calculated for an elliptical porous particle rotating in a two-dimensional (2D) simple shear flow, based on the relation between the shear stress and the second order moments of non-equilibrium particle distribution function. The effects of porous structure of the elliptical particle on the viscosity and flow field are investigated with different axis ratios in detail. Our results demonstrate that the relative viscosities of dilute suspension containing elliptical porous particles increase linearly with solid volume fraction at various Darcy number for particles with varying axis ratios. Moreover, a simple empirical expression for intrinsic viscosity is proposed as a function of Darcy number.

Permeability calculation of rarefied gas flows through 2D porous structures using the lattice Boltzmann method

In the perspective of understanding the flow behavior of atmosphere gases through porous thermal protection systems (TPS) for spacecrafts, permeability calculation has been performed by implementing a modified lattice Boltzmann model. This realization allows the simulation of rarefied gas flows through the TPS micro-porous media. Rarefaction, characterized by the Knudsen number (Kn) is taken into account in the Multi-Relaxation Time (MRT) collision operator. In order to capture slippage effects encountered at solid interfaces in rarefied regimes, a diffuse bounce-back approach has been followed. Numerical simulations have been performed on structured 2D arrays of circular and square cylinders and permeability has been calculated according to Darcy's law. The effects of rarefaction, porous media geometry and porosity on permeability have been investigated.Computed results show that permeability increases as the gas becomes more rarefied. In the frame of the current study, it was also found that the rate of increase in permeability caused by rarefied effects appears to be independent of any geometric parameter. Finally, numerical results have shown to be well suited within the range of permeability values given by the correlations used for comparison.

Pore-scale prediction of the effective mass diffusivity of heterogeneous shale structure using the lattice Boltzmann method

Shale is a kind of heterogeneous porous medium consisting of organic matter (OM), inorganic matter (IM), and interparticle pores. A modified lattice Boltzmann model is developed at the pore-scale to accurately predict the effective mass diffusivity of the heterogeneous shale structure by fully considering the multicomponent and irregular morphological features. The model is validated by the classic empirical formulas and numerical results of the shale with regular IM and OM skeletons. The effects of average gain diameter, irregular structural morphology, porosity, OM volume fraction, and OM diffusivity on the effective mass diffusivity are investigated. The effect of average gain diameter can be ignored. The Nield formula is capable of predicting the effective mass diffusivity of a random OM structure. The formula of Comiti and Renaud can be extended to predict the effective mass diffusivity of a random IM structure by modifying the empirical coefficient to 1.6. The effective mass diffusivity of the heterogeneous shale structure with random OM and IM is between that of pure IM and OM. This effective mass diffusivity increases with the increment of porosity, OM volume fraction, and OM diffusivity. A general empirical formula is proposed to calculate the effective mass diffusivity effectively and conveniently.

A modified lattice Boltzmann model for conjugate heat transfer in porous media

A modified lattice Boltzmann model for conjugate heat transfer in a system containing simultaneously a porous medium and other media is proposed. In this model, the volumetric heat capacity and a new parameter are introduced to the equilibrium temperature distribution function for satisfying the temperature and heat flux continuities at the interface between two phases with different thermal properties (thermal conductivity and volumetric heat capacity), as well as avoiding any correction of distribution functions neighboring the interface. The macroscopic temperature equations are correctly recovered from the corresponding lattice Boltzmann equations by the Chapman–Enskog procedure. Detailed numerical tests of the proposed model are carried out for several benchmark problems including steady-state conjugate heat conduction within two-layer solid medium, transient conjugate heat conduction in infinite composite solid, conjugate natural convection in a cavity partially filled with porous medium and conjugate heat transfer in porous media with a conducting wall. The present numerical results are in excellent agreement with analytical and numerical solutions reported in previous studies. Therefore, it is verified that the present model can be served as a feasible tool for conjugate heat transfer problems in porous media.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles.

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100. The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

A modified lattice Boltzmann model for shallow water flows over complex topography

SummaryA modified lattice Boltzmann model is proposed to describe shallow water flows over complex topography. In the proposed model, the quadratic depth term is excluded from the equilibrium distribution functions (EDFs), and the hydrostatic pressure term is combined with the bed slope term to be treated as a part of the sourcing term in the lattice Boltzmann equation (LBE). Therefore, it is unnecessary to match the coefficients of the quadratic depth term in the EDFs with those of the bed slope term in the sourcing terms in the LBE. This would bring more flexibility to the treatment of the sourcing terms in the LBE. In order to recover the shallow water equations (SWEs), the basic constraints are redefined, and under these constraints, the coefficients of the EDFs are derived afterwards. Several benchmark problems are used to validate the proposed model, including stationary case, steady flows over a two‐dimensional bump and tidal wave flows over irregular bed elevation. The computed results are in excellent agreement with the results of the other numerical methods and the analytical solutions, indicating that the proposed model is capable of simulating shallow water flows over complex bathymetry. It also proves that the proposed model has potential to produce competitive solutions to shallow water flows over complex bed topography. Copyright © 2014 John Wiley & Sons, Ltd.

The fractal roughness effect of micro Poiseuille flows using the lattice Boltzmann method

The fractal roughness effect of the two-dimensional micro Poiseuille gas flows is studied by a modified lattice Boltzmann model at high Knudsen numbers. A simple expression of the relaxation time as a function of dynamical viscosity and density is re-deduced from the gas dynamics theory. The rough wall of the microchannel is described by a self-affine fractal, and then the effect of the accommodation coefficient on the slip velocity of rough boundary is discussed. Numerical simulations of nitrogen and helium show that surface roughness influences not only velocity distribution but also pressure distribution. Reverse flow or eddy appears in the vicinity of the tips of the roughness surface. The mass flow rate decreases greatly and the resistance coefficient rises at an increasing rate as the relative roughness is enhanced. These phenomena different from macroscopic flows are of great importance in understanding the characteristics of micro Poiseuille flows.

Erratum: Modified lattice Boltzmann model for axisymmetric flows [Phys. Rev. E75, 056703 (2007)

Erratum: Modified lattice Boltzmann model for axisymmetric flows [Phys. Rev. E75, 056703 (2007)

Modified lattice Boltzmann model for axisymmetric flows

A modified lattice Boltzmann model based on the two-dimensional, nine-velocity lattice-Bhatnagar-Gross-Krook fluid is presented for axisymmetric flows. A spatially and temporally varying source term is incorporated into the evolution equation for the momentum distribution function on a two-dimensional Cartesian lattice. The precise form of the source term is derived through a Chapman-Enskog analysis, so that the additional axisymmetric contributions in the Navier-Stokes equations are furnished when written in the cylindrical polar coordinate system.

A lattice Boltzmann model with random dynamical constraints

In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime moving obstacles. Fluid motion is described by a lattice Boltzmann equation and obstacles are randomly distributed semi-permeable barriers which constrain the motion of the fluid particles. After a lifetime delay, obstacles move to new random positions. It is found that the non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous patterns in fluid density and non-exponential relaxation of two-time autocorrelation function.