Multi-relaxation Time Lattice Boltzmann Model Research Articles

Study on the evolution of heterogeneous double-cavity induced by near-wall and the fluctuation characteristics of load field

It is well known that the collapse of heterogeneous multi-cavity near the wall will induce the fluctuation of the load field. To address this problem, the Lattice Boltzmann Method (LBM) is applied to model the three-phase coupling between gas-liquid-solid. The objective is to investigate the evolution of heterogeneous double bubbles and the spatial-temporal distribution characteristics of wall loads induced near the wall. In this study, the pseudopotential Multi-Relaxation-Time Lattice Boltzmann Model (MRT-LBM) and the Carnahan-Starling Equation of State (C-S-EOS) with an extended format for the external force term are used. The effects of the distance of the bubble to the wall, the pressure differences between the inside and outside of the bubble, and the relative size of the bubble on the dynamic evolution and the load distribution characteristics of heterogeneous multi-bubbles near the wall are investigated in order to determine the influence of these factors. Under a two-dimensional pressure field, the collapse process of double cavitation bubbles is visualized. Through the flow field, the morphological changes of the cavitation bubble collapse near the wall are also described. Various parameters are found to have an influence on the evolution of double cavitation bubbles near the wall and the resulting load field. The study employs the Lattice Boltzmann Method and the Potential Model for the analysis of the heterogeneous bubble collapses in the near wall region.

Investigation of oil/water two-phase flow behavior in laminated shale porous media considering heterogeneous structure and fluid-solid interaction

The laminated structure of continental shale oil reservoirs introduces significant macro and micro heterogeneity, posing challenges for efficient shale oil extraction. Existing microscopic experimental and simulation methods are insufficient to accurately simulate the fluid flow behavior in mud–lime interactive laminated shale reservoirs. This study delves into the complexities of laminated shale reservoirs with a focus on their heterogeneous structure and wettability. Using scanning electron microscopy, we extracted the structural features of laminated shale reservoirs and established a Multicomponent and multiphase -multi relaxation time-Lattice Boltzmann model(MCMP-MRT-LBM) that considers nanoscale effects such as wall adsorption, liquid–solid slippage, and liquid–liquid slippage. We investigated the occurrence state, the flow behavior, and the phase seepage characteristics of crude oil in laminated shale at different water saturation stages and explored the reasons behind interlayer channeling and the conditions under which crude oil is mobile within limestone and mudstone layers. Then, we examined the impact of varying factors, including heterogeneous wettability, displacement pressure gradients, and pore size, on relative permeability, water injection capacity, sweep efficiency, and crude oil recovery in laminated reservoirs. The results indicate that wettability and pore size distribution, driven by capillary and viscous forces, dictate the occurrence state of remaining oil. Wettability primarily influences fluid distribution, whereas pore size distribution substantially impacts fluid morphology. It also highlights the pivotal role of flow velocity differences between layers in causing interlayer channeling. Increasing the capillary number promotes crude oil mobility within mudstone layers, with the initiation pressure gradient in mudstone layers being 2.5 times that of the limestone layer. The examination of the oil–water relative permeability reveals the dominance of pressure gradients in affecting oil flow capabilities, while pore size significantly influences water flow capacity. By optimizing various factors, it is possible to enhance water injection capacity and sweep efficiency, resulting in a substantial 5%–10% increase in crude oil recovery from laminated shale reservoirs.

A two-dimensional transient study on the impact of pore space connectivity on the immiscible two-phase flow in a water-wet, water–oil system

A multi-relaxation time lattice-Boltzmann model is employed to investigate the dynamic evolution of two immiscible phases through an artificial, randomly generated, porous structure. The flow is driven by a constant pressure gradient, in the absence of gravitational effects. Constraining attention to two dimensions, the impact of the morphological properties of the porous structure, generated using constant radius circular solid grains, on a water-wet, oil–water two-phase flow is studied. Variations in the pore space connectivity and topology are quantified by the Euler characteristic. It is found that the wetting phase saturation and the degree of pore network homogeneity have a significant impact on the dynamic evolution of the non-wetting phase topology, which is governed by a series of coalescence and snap-off events. It is also observed that the phenomenal macro-scale steady-state based on the velocity field does not also imply a temporal topological invariance of the displaced phases. The impact of the pore space morphology on the transient dynamics of the two-phase flow is monitored and quantified through a series of hydrodynamic and topological parameters that signify the underlying flow transport processes.

A two-dimensional study on the impact of pore space connectivity on the immiscible two-phase flow in a water-wet, water–oil system under steady state conditions

Immiscible displacements in porous media are unquestionably of great significance in numerous natural and industrial processes. It has been well established and accepted that in addition to the immiscible fluid properties, the morphology of the porous medium also plays a significant role in the final volumetric throughput of a particular fluid. Topological features of the porous medium have been found to exert a strong influence on the hydrodynamic behaviour of single and two-phase flows as they express a measure of pore space and consequently flow path connectivity and availability. The current study investigates the effect of the pore space connectivity, expressed through the Euler characteristic, on the hydrodynamic behaviour of a water-wet, oil–water two-phase system at steady state. Two-dimensional simulations are conducted in artificially generated porous media with constant diameter circular solid grains using a multi-relaxation time lattice-Boltzmann model. It is shown that topological features of the porous medium can significantly affect the macro-scale capillary pressure and relative permeability curves for drainage and imbibition but in different ways. It is also demonstrated that pore space connectivity has a strong influence on the fluid phase distribution and fragmentation patterns in the porous structure depending on the displacement process.

Pore-scale conjugate heat transfer of nanofluids within fibrous medium with a double MRT lattice Boltzmann model

The conjugate heat transfer of nanofluids within fibrous medium is explored at pore scales. To handle the heat flux discontinuities neighboring the complex interfaces, the correction terms are projected into the thermal multi-relaxation-time (MRT) lattice Boltzmann (LB) scheme which offer an effective and reliable approach to explore conjugate heat transfer dynamics. A random-walk-based stochastic model is presented to generate the fibrous medium made up of interconnected bending fibers. For conjugate heat transfer without convective flow, the steady-state temperature profiles are found independent to the fiber-to-fluid thermal conductivity ratio. Whereas for conjugate heat transfer with convective flow, heat transfer is enhanced with large fiber-to-fluid thermal conductivity ratios. In addition, with the convective flow with high Reynolds numbers, the resulting temperatures for varied fiber-to-fluid thermal conductivity ratios are considerable decreased which indicate high Reynolds numbers dominate the heat transfer process. The 3D pore-scale temperature distributions with varied thermal parameters are provided which demonstrate the capability of present conjugate thermal LB model.

Enhanced multi-relaxation-time lattice Boltzmann model by entropic stabilizers.

The difficulty of choice of relaxation rates in multi-relaxation-time lattice Boltzmann model (MRT-LBM) is surmounted by solution of least-square problem of entropic stabilizer equations. Relaxation rates in the enhanced MRT-LBM are evolving with time rather than remain constants. To derive entropic stabilizer equations, nonequilibrium population is split into different modes in terms of column vectors in the inverse transform matrix. The entropic stabilizer equations are achieved by minimization of H-function. Different moment representations in MRT-LBM, such as Gram-Schmidt orthogonal moment, natural moment, and central moment, are tested for double periodic shear flow, shock tube problem, and lid-driven cavity flow, which demonstrates the potential of enhanced MRT-LBM.

Lattice Boltzmann model for shallow water in curvilinear coordinate grid

In this study, a multi-relaxation time lattice Boltzmann model for shallow water in a curvilinear coordinate grid is developed using the generalized form of the interpolation supplemented lattice Boltzmann method. The Taylor-Colette flow tests show that the proposed model enjoys a second order accuracy in space. The proposed model is applied to three types of meandering channels with, and consecutive bends. The numerical results demonstrate that the simulated results agree well with previous computational and experimental data. In addition, the model can achieve the acceptable accuracy in terms of the water depth and the depth-averaged velocities for shallow water flows in curved and meandering channels over a wide range of bend angles.

Entropic multi-relaxation time lattice Boltzmann model for complex flows

Entropic lattice Boltzmann methods were introduced to overcome the stability issues of lattice Boltzmann models for high Reynolds number turbulent flows. However, to date their validity has been investigated only for simple flows due to the lack of appropriate boundary conditions. We present here an extension of these models to complex flows involving curved and moving boundaries in three dimensions. Apart from a thorough investigation of resolved and under-resolved simulations for periodic flow and turbulent flow in a round pipe, we study in detail the set-up of a simplified internal combustion engine with a valve/piston arrangement. This arrangement allows us to probe the non-trivial interactions between various flow features such as jet breakup, jet–wall interaction, and formation and breakup of large vortical structures, among others. Besides an order of magnitude reduction in computational costs, when compared to state-of-the-art direct numerical simulations (DNS), these methods come with the additional advantage of using static Cartesian meshes also for moving objects, which reduces the complexity of the scheme. Going beyond first-order statistics, a detailed comparison of mean and root-mean-square velocity profiles with high-order spectral element DNS simulations and experimental data shows excellent agreement, highlighting the accuracy and reliability of the method for resolved simulations. Moreover, we show that the implicit subgrid features of the entropic lattice Boltzmann method can be utilized to further reduce the grid sizes and the computational costs, providing an alternative to modern modelling approaches such as large-eddy simulations for complex flows.

Simulation of micro flow in the transition regime using effective-viscosity-based multi-relaxation-time lattice Boltzmann model

With the rapid development of micro-electro-mechanical systems (MEMS), microscale rarefied gas flows have received considerable attention in the past decades. Recently, the lattice Boltzmann method (LBM) emerges as a promising way to study the flow in MEMS for its kinetic nature and distinctive computational features. Various LBM models have been used to simulate the microscale and nanoscale flow, among which the two-dimensional and nine-velocities (D2Q9)-based LBM is most widely accepted due to its extremely simplicity and high efficiency. However, the D2Q9-based LBM encounters great difficulties in the transition regime due to the rarefaction effects on mean free path and gas viscosity. An effective way to improve the capability of the existing LBM model is to incorporate an effective viscosity into the relaxation time, which can improve the accuracy of LBM model while keeping the simplicity and efficiency of LBM. However, the existing D2Q9-based LBM models with effective viscosity cannot give satisfactory predictions of the none-equilibrium phenomenon at moderate or high Knudsen (Kn) number both in accuracy and efficiency. To solve the above problem, in this study, an effective mean free path function proposed by Dongari et al. (Dongari N, Zhang Y H, Reese J M 2011 J. Fluids Eng. 133 071101) via modular dynamics mean is introduced into the D2Q9 multi-relaxation-time lattice Boltzmann model (MRT-LBM) to account for the effect of Knudsen layer in transition flow regime, and the viscosity in the MRT-LBM model is modified correspondingly. The combination of the bounce-back and specular reflection boundary condition is used to deal with the velocity slip, and the relaxation time and the reflection coefficient are properly set to eliminate the numerical artifact on the boundaries as the kinetic boundary condition is used. Micro Couette flow at Kn=0.1-6.77, and periodic Poiseuille flow at Kn=0.1128-2.2568, respectively, are numerically investigated by using the proposed MRT-LBM model, and the numerical results, including the non-dimensional velocity profile and the mass flow rate, are verified by the direct simulation Monte~Carlo (DSMC) data, the linearized Boltzmann solutions and the existing LBM model. The calculation results demonstrate that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases. It is shown that the velocity profiles predicted by the present MRT-LBM model agree well with the DSMC data and linearized Boltzmann solutions up to Kn=4.5 in Couette flow, which is much more accurate than that obtained from the existing LBM model. And the present LBM model gives at least the same order of accuracy in the prediction of velocity profile and mass flow rate as the existing LBM model in periodic Poiseuille flow. What is more, the Knudsen minimum phenomenon of flow in the microchannel is successfully captured at around Kn=1. The results demonstrate that the proposed model can enhance the ability of LBM in capturing the non-equilibrium phenomenon in micro flow in the transition regime both in accuracy and efficiency.

Simulation of Acoustic Behavior of Bubbly Liquids with Hybrid Lattice Boltzmann and Homogeneous Equilibrium Models

AbstractHomogeneous equilibrium model (HEM) has been widely used in cavitating flow simulations. The major feature of this model is that a single equation of state (EOS) is proposed to describe the thermal behavior of bubbly liquid, where both kinematic and thermal equilibrium is assumed between two phases. In this paper, the HEM was coupled with multi-relaxation-time lattice Boltzmann model (MRT-LBM) and the acoustic behavior was simulated. Two approaches were applied alternatively: adjusting speed of sound (Buick, J. Phys. A, 2006, 39:13807-13815) and setting real gas EOS. Both approaches result in high accuracy in acoustic speed predictions for different void (gas) volume of fractions. It is demonstrated that LBM could be successfully applied as a Navier-Stokes equation solver for industrial applications. However, further dissipation and dispersion analysis shows that Shan-Chen type approaches of LBM are deficient, especially in large wave-number region.

Investigations on the Droplet Impact onto a Spherical Surface with a High Density Ratio Multi-Relaxation Time Lattice-Boltzmann Model

AbstractIn the current study, a two-dimensional multi-relaxation time (MRT) lattice Boltzmann model which can tolerate high density ratios and low viscosity is employed to simulate the liquid droplet impact onto a curved target. The temporal variation of the film thickness at the north pole of the target surface is investigated. Three different temporal phases of the dynamics behavior, namely, the initial drop deformation phase, the inertia dominated phase and the viscosity dominated phase are reproduced and studied. The effect of the Reynolds number, Weber number and Galilei number on the film flow dynamics is investigated. In addition, the dynamic behavior of the droplet impact onto the side of the curved target is shown, and the effect of the contact angle, the Reynolds number and the Weber number are investigated.

Three-dimensional multi-relaxation time lattice-Boltzmann model for the drop impact on a dry surface at large density ratio

Extensive application of the multiphase lattice Boltzmann model to realistic fluid flows is often restricted by the numerical instabilities induced at high liquid-to-gas density ratios, and at low viscosities. In this paper, a three-dimensional multi-relaxation time (MRT) lattice Boltzmann model with an improved forcing scheme is reported for simulating multiphase flows at high liquid-to-gas density ratios and relatively high Reynolds numbers. The model is based on a recently presented model in the literature. Firstly, the MRT multiphase model is evaluated by verifying Laplace’s law and achieving thermodynamic consistency for a static droplet. Then, a relationship between the fluid–solid interaction potential parameter and contact angle is investigated. Finally, the improved three-dimensional MRT Lattice Boltzmann model is employed in the simulation of the impingement of a liquid droplet onto a flat surface for a range of Weber and Reynolds numbers. The dynamics of the droplet spreading is reproduced and the predicted maximum spread factor is in good agreement with experimental data published in the literature.