MRT-LBM-based numerical simulation of seepage flow through fractal fracture networks

Fan, Huo; Zheng, Hong

doi:10.1007/s11431-013-5402-3

Cited by 25 publications

(10 citation statements)

References 18 publications

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“…The fracture aperture was first used as the control condition to construct an indoor physical model, and head loss and velocity were observed to analyze the characteristics of the fluid in the single fissure. Following the verification of the computational fluid dynamics (CFD) model in simulation of characteristics of the fluid in the single fissure with parameters most used [24][25][26][27][28], the relationship between the shape of the fracture (corner θ) and head loss was studied using it.…”

Section: Experiments and Methodologymentioning

confidence: 99%

A Fast Calculation Model for Local Head Loss of Non-Darcian Flow in Flexural Crack

Liu

Mou

Song

et al. 2020

Water

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Local head loss caused by fracture intersection is often ignored because there has not been a simple method to calculate it until now. Relevant research shows that neglecting the local flow resistance leads to inaccurate results, especially when the velocity and cross angle are large. Therefore, it is necessary to find a portable method for calculation. Physical experiments of single fracture with different apertures (e = 0.77, 1.18, 1.97, 2.73 mm) were set up first to study the flow characteristics, showing obvious non-Darcian flow, which can be depicted by the Forchheimer equation when the flow velocity is sufficiently large. The computational fluid dynamics (CFD) software ANSYS FLUENT was used to build numeric simulation models. A good correlation between CFD simulation results and physical experiment results was found (Pearson's correlation coefficient > 0.99). Then, the CFD models of flexural crack with different angles from 30 • to 150 • were established to compute the pressure drop of flexural crack at different velocity. It was found that the local head loss of the flexural crack varied with the bending angle, and its coefficient was expressed by the deformation of the logistic equation. By using this model, as well as a frictional head loss equation fitted by Forchheimer equation, the head loss of crossed fissures with fixed fracture aperture could be easily calculated. Water 2020, 12, 232 2 of 15 applications, a quadratic equation (J = Av + Bv 2 ) and an exponential equation (J = Cv −m ) are used to under limited conditions [8-11]. The Forchheimer equation can express the characteristics of non-Darcian flow in fracture [12-15]: − ∇P = aQ + bQ 2 (1) where Q is volumetric flow velocity, a and b are model coefficients, and −∇P is the pressure gradient. The factors affecting the flow of fissure fluid are complex and include the shape of the fissure, degree of contact, roughness, fluid viscosity, and external pressure [16-19]. Liu et al. [20] studied the law of fluid movement in a fracture network and found that the coefficient (a, b) of the Forchheimer equation decreases with an increase in the fracture aperture, and the error in model fitting can be reduced by expressing the coefficients of the Forchheimer equation as a power equation of fracture aperture [14]. Olson et al. [21] studied the effect of the ratio of the fracture opening to its height on the flow pattern, and Shu et al. [22] studied the variation in head loss with the width of the fissure and the velocity of flow when water flows through L-shaped fissures. Li et al. [23] studied the correlation between the head loss of a fluid in cross fissures and the width as well as roughness of the fissures.This study proposes a portable calculation model where the aperture and the shape of flexural crack are considered to predict head loss directly. It is difficult to consider all factors when studying the characteristics of flow in fractures. In order to investigate the influence of each one, the synergistic effects of each condition need to be reduced, ...

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Section: Experiments and Methodologymentioning

confidence: 99%

A Fast Calculation Model for Local Head Loss of Non-Darcian Flow in Flexural Crack

Liu

Mou

Song

et al. 2020

Water

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“…where is a magic parameter [18]; it affects the stability and the accuracy of the calculation and this magic parameter is assigned 1/6 in this study [23]. ( ⃗, ) is the heat flux vector and � ��⃗ is the discrete velocity of the ℎ direction and is given in Equation (14).…”

Section: Lbm Algorithmmentioning

confidence: 99%

“…Due to the complex geometries in the realistic structure, it would be difficult to solve the heat and mass transfer by the normally used finite volume or finite element methods. Lattice Boltzmann method (LBM) is a promising mesoscopic method to deal with complex boundaries and has been successfully applied in numerous studies [12][13][14][15] of heat and mass transfer in soil-like materials.…”

Section: Introductionmentioning

confidence: 99%

Randomly fractal approach to calculate the thermal conductivity of moist soil

Cai¹,

Zhang²,

Cui³

et al. 2018

Proceedings of the IGSHPA Research Track 2018

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Ground coupled heat pump (GCHP) is an energy saving technology that uses the shallow geothermal energy for the building heating and refrigerationsystems. An optimized design of ground heat exchangers (GHEs) is the key to minimize the installation fee of GCHP systems. The effective thermal conductivity of soil is an important input parameter in the design of GHEs. This paper proposed a randomly fractal approach to predict the effective thermal conductivity of soil-like materials (quartz sand). The fractal Monte-Carlo method combined with the Quartet Structure Generation Set (QSGS) method was used to reconstruct the random structure of the soil-like materials. Lattice Boltzmann method (LBM) was further applied to the complicated porous structure and compute the effective thermal conductivity. The simulation results were compared to the findings from experiments and other similar models. The impacts of porosity, fractal dimension, size ratio and accumulation structure on the effective thermal conductivity were also analyzed in detail.

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“…For example, the molecular dynamics method [1][2][3][4][5][6] has been proposed to model the physical movements and interactions of atoms and molecules. The lattice Boltzmann method [7][8][9][10][11] has been widely employed to simulate the evolution of a fluid system through modeling the collisions and propagations of fictive particles over a discrete lattice mesh. Meanwhile, the discrete element method (DEM) [12][13][14][15][16] has been particularly popular in simulating engineering materials such as granular sands.…”

Section: Introductionmentioning

confidence: 99%

Variational inequality‐based framework of discontinuous deformation analysis

Fan

Zhao

Zheng

2018

Numerical Meth Engineering

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Summary For modeling discrete particle‐block systems, a new framework of discontinuous deformation analysis is established on the basis of finite‐dimensional variational inequality. The presented method takes into account the contacts, the rolling resistance, and the tensile resistance of cemented interface among particles and blocks using the corresponding variational or quasivariational inequalities. The new formulation avoids using the artificial springs that are usually indispensable in many conventional methods dealing with similar discrete problems and conveniently integrates the rigid circle particles, the nonrigid ring particles, and the arbitrary shape blocks into a uniform framework. The proposed discontinuous deformation analysis approach is further coupled with the finite element method using a node‐based composite contact matrix and several simple transformation matrices to solve practical problems. A particle/block‐based composite contact matrix is constructed to further broaden the application of the proposed method. The accuracy, robustness, and capability of the presented method are demonstrated with examples.

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MRT-LBM-based numerical simulation of seepage flow through fractal fracture networks

Cited by 25 publications

References 18 publications

A Fast Calculation Model for Local Head Loss of Non-Darcian Flow in Flexural Crack

A Fast Calculation Model for Local Head Loss of Non-Darcian Flow in Flexural Crack

Randomly fractal approach to calculate the thermal conductivity of moist soil

Variational inequality‐based framework of discontinuous deformation analysis

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