Representative Elementary Volume Scale Research Articles

Pore-scale study of miscible density-driven mixing flow in porous media

Two-dimensional density-driven convective mixing processes in synthetic porous media are simulated at pore-scale using lattice Boltzmann method with a rescaled version of the nonequilibrium extrapolation method in the present work. Numerical results demonstrate that the density-driven convective mixing process varies with the Rayleigh number (Ra). For low values of Ra, the numerical results at pore-scale are consistent with those at representative elementary volume (REV) scale. With the increase in Ra, the convective mixing process becomes different, which can be reflected by the time evolution of the dissolution flux and onset time of convection at different Rayleigh numbers. On the one hand, the flux growth regime in the time evolution of the dissolution flux can be divided into two sub-regimes, which are named early and late flux growth regimes in this study. In addition, for the shutdown regime, the dissolution flux can be scaled as J∼t−1 rather than t−2 for high Ra cases, which is consistent with our theoretical analysis. On the other hand, the existence of the early flux growth regime consumes the mass at the top diffusive layer, leading to a delay of convective onset time. Therefore, the onset time of the convection calculated at pore-scale is much higher than that predicted by the existing theory and REV scale studies. The present study shows practical implications for CO2 capture and storage.

Micromechanical approach to effective viscoelastic behavior of jointed rocks

Assessing the overall instantaneous behavior and strength properties of jointed materials have been the subject of important investigations in the last decades, including phenomenological or micromechanics-based contributions. However, less attention has been dedicated to delayed component of deformation in such media. This issue is addressed in this paper, which is devoted to the formulation of a micromechanical approach to effective viscoelastic properties of jointed rocks with consideration of constituents aging. At the scale of representative elementary volume (REV), the joints are modeled as planar interfaces whose behavior is described by means of generalized viscoelastic state equations under normal and shear loading conditions. Closed-form expressions for the homogenized creep tensor are derived from solving an appropriate viscoelastic concentration problem stated on the REV. The local strain and displacement jump fields are analyzed by extending the concept of strain concentration to relate the components of joint displacement jump to macroscopic strain. Main features of the theoretical overall creep behavior, such as the anisotropy associated with the privileged joint orientations, are highlighted through explicit formulations in some particular configurations of the jointed medium. Finally, the ability of the approach to accurately reproduce the creep behavior of jointed media is assessed by comparison with experimental data as well as with finite element solutions derived in the context of multilayered stratified composite modeling.

Advanced thermal lattice Boltzmann method for the simulation of latent heat thermal energy in a porous storage unit

The current research expounds numerical investigation of key parameters effects, namely porosity ( ε= 0.4, 0.6, 0.7 and 0.8), Reynolds number (Re = 100, 200, 400 and 600) and Eckert number (Ec= 0, 1, 5 and 10) on the forced convective laminar flow and heat transfer through a horizontal porous channel filled with a metal foam structure impregnated with paraffin as a phase change material (PCM). The Darcy-Brinkman-Forchheimer model under the local thermal non-equilibrium (LTNE) condition is deemed at the representative elementary volume (REV) scale. The fully coupled equations of Navier-Stokes, Poisson’s equation, energy equations, and continuity equation were handled numerically via a thermal single relaxation time lattice Boltzmann method (TSRT-LBM). To facilitate implementation, all LB equations are based on the same speed discretization scheme (D2Q9). Three-population distribution functions were applied to simulate the fluid flow, and temperatures of the fluid and solid phases. Previously, the numerical model was validated by available cases. Then, a comprehensive investigation has been performed to investigate the influence of the aforementioned dimensionless numbers. All LBM results are found to be highly consistent with other numerical works. The outcomes reported that at lower porosities, the energy and exergy efficiencies increased with increasing Re and Ec. However, for large porosity values, the efficiencies were optimum for a critical Re ~ 400. To sum up, it can be stated that the implemented thermal lattice Boltzmann method has been demonstrated as a suitable approach study the thermal sensible energy storage.

Generalized effective stress concept for saturated active clays

Experimental evidence shows that changes in pore-water chemistry can significantly affect the mechanical behavior of saturated active clays. Despite this evidence, how the chemical composition of the pore water can be considered in effective stress definition is questionable. This paper develops the concept of generalized effective stress for active clays. To this end, physicochemical studies on water–clay mineral interactions are used to clearly define the different types of ions and water present in an active clay. In particular, the presence of both movable and non-movable ions within the liquid water is highlighted. Taking this into account, thermodynamic and geochemistry principles are applied to the representative elementary volume scale for determining the pore-water pressure and redefine the effective stress accordingly. The theoretical development results in the dependence of the effective stress on the pore-water chemistry through the effective solute suction variable. Equations for the determination of this chemical variable are developed. The implications of the use of the proposed effective stress concept are investigated using experimental results taken from the literature. The results show advantages both in the interpretation of shear strength and volumetric data, and all support the theoretical explanation underlying the proposed concept.

A general multi-scale topology optimisation method for lightweight lattice structures obtained through additive manufacturing technology

A general framework for the multi-scale topology optimisation (TO) of lattice structures (LSs) is presented in this work. The proposed method involves: Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the LS representative volume element (RVE) topology, the Solid Isotropic Material with Penalisation (SIMP) approach and the strain energy-based homogenisation method (SEHM) to perform the scale transition. The main contributions of this work are essentially three. Firstly, physical responses are defined at different scales and their gradient is evaluated by exploiting the NURBS local support property and the Dirichlet’s problem properties at the RVE scale. Secondly, the computational efficiency of the SEHM based on elements strain energy over that of the SEHM based on elements averaged stresses is rigorously proven. Finally, to show the effectiveness of the method, numerical analyses are conducted on 2D and 3D problems. A sensitivity analysis of the optimised topology to the integer parameters of the NURBS hyper-surface is carried out. Moreover, the influence of the initial guess and of the macroscopic loading condition on the RVE optimised topology is investigated. The minimum length-scale requirement is also integrated into the problem formulation as a manufacturing constraint.

Random pore structure and REV scale flow analysis of engine particulate filter based on LBM

Abstract In this article, lattice Boltzmann method (LBM) is used to simulate the multi-scale flow characteristics of the engine particulate filter at the pore scale and the representative elementary volume (REV) scale, respectively. Four kinds of random wall-pore structures are considered, which are circular random structure, square random structure, isotropic quartet structure generation set (QSGS), and anisotropic QSGS, with difference analysis done. In terms of the REV scale, the influence of different inlet flow velocities and wall permeabilities on the flow in single channel is analyzed. The result indicates that the internal seepage laws of random structures constructed in this article and single channel are in accordance with Darcy’s law. Circular random structure has better permeability than square random structure. Isotropic QSGS has better fluidity than anisotropic one. The flow in single channel is similar to Poiseuille flow. The flow lines in the channel are complicated and a large number of vortices appear at the ends of channel with high inlet flow rate. With the increase of inlet velocity, the static pressure in channel gradually increases along the axial direction as well as the seepage velocity. The temperature field in the channel becomes more uniform as the flow velocity increases, and the higher temperature distribution appears on the wall of the porous media.

The Complexity of Porous Media Flow Characterized in a Microfluidic Model Based on Confocal Laser Scanning Microscopy and Micro-PIV

In this study, the complexity of a steady-state flow through porous media is revealed using confocal laser scanning microscopy (CLSM). Micro-particle image velocimetry (micro-PIV) is applied to construct movies of colloidal particles. The calculated velocity vector fields from images are further utilized to obtain laminar flow streamlines. Fluid flow through a single straight channel is used to confirm that quantitative CLSM measurements can be conducted. Next, the coupling between the flow in a channel and the movement within an intersecting dead-end region is studied. Quantitative CLSM measurements confirm the numerically determined coupling parameter from earlier work of the authors. The fluid flow complexity is demonstrated using a porous medium consisting of a regular grid of pores in contact with a flowing fluid channel. The porous media structure was further used as the simulation domain for numerical modeling. Both the simulation, based on solving Stokes equations, and the experimental data show presence of non-trivial streamline trajectories across the pore structures. In view of the results, we argue that the hydrodynamic mixing is a combination of non-trivial streamline routing and Brownian motion by pore-scale diffusion. The results provide insight into challenges in upscaling hydrodynamic dispersion from pore scale to representative elementary volume (REV) scale. Furthermore, the successful quantitative validation of CLSM-based data from a microfluidic model fed by an electrical syringe pump provided a valuable benchmark for qualitative validation of computer simulation results.Graphic

Estimation of REV for Danba schist based on 3D synthetic rock mass technique

This paper aims to provide a case study of determining the structure and mechanical Representative Elementary Volume (REV) simultaneously for a specific jointed rock mass. The schist of Danba HPP project is taken as the study case here. A Synthetic Rock Mass model (SRM) is firstly constructed based on sophisticated geological loggings. With which the number of joint centers per unit volume (P30), the area of joint per unit volume (P32), and the Young’s modulus (E) are examined for various sample sizes. It is found that the SRM is a powerful tool to address those problems. The P30 reduces gradually with the increase of rock mass scale. As for P32 and E, maximum and minimum value and the variance decrease rapidly with the increase of rock mass size. A comprehensive REV size of 50~60m is then estimated based on the above 3 indexes. According to the SRM simulation, young’s modulus of the REV scale is around 6.8GPa, which is a little bit higher than the recommended value by geologists. This difference is believed to be reasonable as the recommended value usually been significantly undervalued. The procedures and findings of this paper may provide a certain reference for further studies on rock mass scale effects.

Insight into Foam Pore Effect on Phase Change Process in a Plane Channel under Forced Convection Using the Thermal Lattice Boltzmann Method

In this work, the two-dimensional laminar flow and the heat transfer in an open-ended rectangular porous channel (metal foam) including a phase change material (PCM; paraffin) under forced convection were numerically investigated. To gain further insight into the foam pore effect on charging/discharging processes, the Darcy–Brinkmann–Forchheimer (DBF) unsteady flow model and that with two temperature equations based on the local thermal non-equilibrium (LTNE) were solved at the representative elementary volume (REV) scale. The enthalpy-based thermal lattice Boltzmann method (TLBM) with triple distribution function (TDF) was employed at the REV scale to perform simulations for different porosities (0.7≤ε≤0.9) and pore per inch (PPI) density (10≤PPI≤60) at Reynolds numbers (Re) of 200 and 400. It turned out that increasing Re with high porosity and PPI (0.9 and 60) speeds up the melting process, while, at low PPI and porosity (10 and 0.7), the complete melting time increases. In addition, during the charging process, increasing the PPI with a small porosity (0.7) weakens the forced convection in the first two-thirds of the channel. However, the increase in PPI with large porosity and high Re number limits the forced convection while improving the heat transfer. To sum up, the study findings clearly evidence the foam pore effect on the phase change process under unsteady forced convection in a PCM-saturated porous channel under local thermal non-equilibrium (LTNE).

Modeling of salt finger convection through a fluid-saturated porous interface: Representative elementary volume scale simulation and effect of initial buoyancy ratio

Simultaneous existence of solute gradients along with temperature gradients in a double diffusive system is favorable to the onset of salt finger convection and this phenomenon has been investigated for several decades due to its efficient mixing mechanism. However, relatively few works were focused on the double diffusive process through a fluid-saturated porous interface (FPI), which could be applied in a variety of scenarios such as the directional solidification of concentrated alloys or mixing zones in coastal freshwater aquifers. In this paper, we consider the evolution of double-diffusive salt finger through FPI with a single-domain approach adopted for the solution of flow in a composite region made up of a fluid layer overlying a porous layer. Comparisons with existing numerical results show great agreement and demonstrate that flows through a fluid–porous system can be predicted with good accuracy by the proposed method. Several cases spanning a range of initial buoyancy ratio N0 from 2 to 7 are conducted to study the structure and behavior of salt finger together with key issues being focused on the effect of initial buoyancy ratio on flux variations. Differing from in stratified fluid layers, salt finger through FPI shows an asymmetric structure in which the growth rate in the fluid layer is much greater and the finger column in the porous layer presents a squarer shape. It is found that under the condition of low initial buoyancy ratios, the potential energy stored in the unstable stratification of salinity converted more into kinetic energy, which enhances the mixture of heat and masses in the vertical direction.

Pore-scale simulation of heat and mass transfer in deformable porous media

Most porous media are susceptible to deformation during the heat and mass transfer process. In this paper, the bi-dispersed porous media model, which was generated through digitized image reconstruction, was used to effectively and conveniently simulate the real porous media. The thermal-hydro-mechanics model, which was established based on the Navier-Stokes equations and stress differential equations, was solved according to the finite element method. Meanwhile, the arbitrary Lagrange-Euler theory was applied to deal with the fluid-solid boundary. The results suggested favorable agreement between the numerical results and the experimental data. Moreover, the detailed distributions of velocity, temperature and water content in the porous media were obtained, which varied depending on the structural properties of porous media. Further, the stress and deformation were comparatively analyzed in the open and closed pore regions, and it was found that the wall of closed pore was prone to stress concentration. The deformation of the bi-dispersed porous sample resulted in an increase in pore area fractal dimension and a decrease in tortuosity fractal dimension. In addition, the effective transport properties and volume shrinkage of the deformable porous media at the representative elementary volume (REV) scale were also computed based on the obtained pore scale results, which confirmed that it was necessary to consider the effects of deformation on the real flexible porous media.

A Multiple-Relaxation-Time Lattice Boltzmann Model for Natural Convection in a Hydrodynamically and Thermally Anisotropic Porous Medium under Local Thermal Non-Equilibrium Conditions

To investigate the natural convective process in a hydrodynamically and thermally anisotropic porous medium at the representative elementary volume (REV) scale, the present work presented a multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on the assumption of local thermal non-equilibrium conditions (LTNE). Three sets of distribution function were used to solve the coupled momentum and heat transfer equations. One set was used to compute the flow field based on the generalized non-Darcy model; the other two sets were used to solve the temperature fields of fluid and solid under the LTNE. To describe the anisotropy of flow field of the porous media, a permeability tensor and a Forchheimer coefficient tensor were introduced into the model. Additionally, a heat conductivity tensor and a special relaxation matrix with some off-diagonal elements were selected for the thermal anisotropy. Furthermore, by selecting an appropriate equilibrium moments and discrete source terms accounting for the local thermal non-equilibrium effect, as well as choosing an off-diagonal relaxation matrix with some specific elements, the presented model can recover the exact governing equations for natural convection under LTNE with anisotropic permeability and thermal conductivity with no deviation terms through the Chapman-Enskog procedure. Finally, the proposed model was adopted to simulate several benchmark problems. Good agreements with results in the available literatures can be achieved, which indicate the wide practicability and the good accuracy of the present model.

Lattice Boltzmann simulation of forced convection melting of a composite phase change material with heat dissipation through an open-ended channel

This paper performs a numerical analysis of time-dependent forced convection heat transfer in an open-ended straight channel filled with a metal structure and paraffin as a phase change material (PCM). The unsteady two-dimensional governing equations, based on the Darcy-Brinkmann-Forchheimer (DBF) model and the two-energy transport equations (i.e. local thermal non-equilibrium, LTNE) at the representative elementary volume (REV) scale in their dimensionless forms, have been simulated using the thermal single relaxation time (T-SRT) Lattice Boltzmann Method (LBM) with three distribution functions to handle the fluid, and temperatures of the fluid and solid phases. Effects of Reynolds number (100 ≤ Re ≤ 600), Eckert number (0 ≤ Ec ≤ 10), porosity (0.1 ≤ ɛ ≤ 0.8) on dynamic and thermal fields, entropy generation, and energy and exergy efficiencies of the considered system are examined. The relevance of these parameters is highlighted and discussed during the charging (melting) and discharging (solidifying) processes. Interestingly, it can be stated that small porosities promptly accelerate these two processes due to high thermal conductivity of the metal foam/PCM composite, and improve energy and exergy efficiencies of the system, whatever Re for the very low porosity values (0.4 and 0.6). In addition, streamlines, isotherms and melt front (phase field) are exhibited for this parameters range. Based on the findings obtained, it is concluded that, in the context of laminar forced convection melting of a composite PCM with heat dissipation in a porous PCM-filled channel, 1) there is a critical Reynolds number for which the storage energy is optimal and whose quality is improved using both the porosity and the effects of viscous dissipation, and 2) the proposed approach's potential and the in-house code flexibility implemented are demonstrated.

Numerical simulations of convection heat transfer in porous media using a cascaded lattice Boltzmann method

Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in porous media requires efficient and powerful numerical tools. In this paper, a cascaded lattice Boltzmann (CLB) method for convection heat transfer in porous media at the representative elementary volume (REV) scale is presented. In the CLB method, the flow field is solved by an isothermal CLB model with the D2Q9 lattice based on the generalized non-Darcy model, while the temperature field is solved by a temperature-based CLB model with the D2Q5 lattice. The key point is to incorporate the influence of the porous media into the CLB method by introducing the porosity and heat capacity ratio into the shift matrices. The effectiveness and practicability of the present method are validated by numerical simulations of several heat transfer problems in porous media at the REV scale. It is shown that the present method for convection heat transfer in porous media is second-order accurate in space. Moreover, in comparison with the Bhatnagar-Gross-Krook lattice Boltzmann method, the present method has sufficient tunable parameters and possesses better numerical stability.

Lattice Boltzmann simulation of double diffusive natural convection in heterogeneously porous media of a fluid with temperature-dependent viscosity

Double diffusive natural convection inside a porous cavity with non-uniform porosity has been numerically studied. The cavity was filled with two parallel porous layers with different porosity. Considering the effects of temperature-dependent viscosity, simulations have been done via the Lattice Boltzmann method (LBM) at representative elementary volume (REV) scale. In this study, the effect of porosity, buoyancy ratio, the viscosity-variation number and thermal Rayleigh number on heat and mass transfer rates was investigated. The streamlines, isotherms, isoconcentrations, average Nusselt number and average Sherwood number curves of different parameters were discussed in detail. It was observed that the governing parameters has significant impact on the fluid flow, temperature and concentration distributions. In addition, the average Nusselt and Sherwood numbers are increase with an reduce in the viscosity-variation number. Further, as the absolute value of buoyancy ratio and thermal Rayleigh number increases, the effect of porosity and viscosity changes on the heat and mass transfer enhancement was augmented.

A void evolution model accounting for stress triaxiality, Lode parameter and effective strain for hot metal forming

Large numbers of voids inevitably exist in the metal ingot due to non-equilibrium solidification. Forging is an important technique to eliminate such internal defects and obtain sound products. However, the research regarding void evolution mechanisms are currently not sufficient to direct the technological design in practical engineering because of the lack of suitable void evolution model, especially in terms of complex stress states. On the basis of a large number of numerical computations, the effect of Lode parameter on the void volume evolution rate is firstly investigated, and then incorporated together with the stress triaxiality T, effective strain Ee and Norton exponent n into a newly proposed void evolution model. At the scale of representative volume element (RVE), the prediction of void evolution calculated from the new model has achieved better accuracy than other analytical models comparing with the simulation results. Radial forging test for rectangular cross-section billet is carried out to verify the accuracy of the proposed void evolution model. Paired screw threads are used to introduce pre-fabricated voids and then embedded into the billet for measuring void volume variation and the distribution of strain around void during forging. The comparison of void evolution between the experimental and analytical solutions also shows that the prediction of void relative volume change by the proposed model is more accurate than those by other models.

The role of rheological parameters on drying behaviour of a water-based cast tape

In this paper we studied the migration of secondary particles in tape casting of a non-Newtonian ceramic slurry through a generalised local viscosity function in order to obtain the particle distribution along tape thickness. The particle distribution was then used to calculate porosity and permeability of the tapes. We, moreover, linked the aforementioned results to a coupled free-flow-porous-media model on the representative elementary volume (REV) scale for simulating room-temperature drying of the tapes with flow of a relatively dry air (relative humidity of 25%). Finally, we investigated the influence of rheological parameters, i.e. the power-law index, η, and the consistency factor, m, of a typical Ostwald–de Waele power-law fluid on the resultant drying behaviour of the tapes. The results showed that the low consistency and low power-law index values reduce the drying rate (slightly) as well as the final drying time, that favours the manufacturing of tapes by reducing the risk of crack initiation/growth in ceramics.

Analytical Solution of Gas Flow in Rough‐Walled Microfracture at In Situ Conditions

AbstractThe development of the unconventional gas and CO2 sequestration is moving to deep formations. Because of the small flow pathways in the matrix, the Knudsen number might be high even though the gas is dense. In fact, due to the relatively high pressure at in situ conditions, gas flow in microfractures usually manifests a strong slip and nonideal gas effects. Therefore, understanding the coupling mechanism of these two on gas flow in rough‐walled microfractures is required to accurately model subsurface flow behavior. In this study, pressure‐driven gas flow in rough‐walled microfracture is analyzed in depth. Starting from the local governing equations for gas flow, a local flow model that includes gas slip and nonideal gas effects is derived by solving the Stokes equation with a first‐order slip boundary condition. Focusing at the representative elementary volume scale, the upscaled solutions to gas flow in a fracture with sinusoidal surface are derived to obtain the apparent permeability. The impact of nonideal gas effects, fracture roughness and aperture, and the tangential momentum accommodation coefficient on CH4 and CO2 flow is analyzed. The results show that fracture roughness introduces a high degree of heterogeneity in gas flow. At in situ conditions effects of gas slip, fracture roughness and tangential momentum accommodation coefficient on gas flow are reduced. The ideal gas law is capable of estimating CH4 flow to some extent. However, it fails to estimate CO2 flow in microfractures.

How Hydraulic Properties of Organic Matter Control Effective Liquid Permeability of Mudrocks

In organic-rich Mudrocks, porous organic matter embedded within mineral matrix along with inorganic pores forms a dual porosity–permeability (ϕ–k) system. How hydraulic properties of organic matter embedded in the mineral matrix contribute to bulk liquid flow however is not well understood. Using computational methods, Navier–Stokes equations are coupled with Brinkman equations for dual (ϕ–k) mineral matrix–organic matter domains obtained from a focused ion beam–scanning electron microscope (FIB-SEM) image set of an organic-rich Murdock and a series of idealized two-dimensional (2D) pore–organic matrix domains. Results of sensitivity analysis show that variations in organic matter permeability cause variations in effective permeability, which follow ‘S-shaped’ characteristics curve on log–log scale. Hydraulic coupling between the dual (ϕ–k) domains shows magnification of the coupled flow behavior when permeability of organic matter is on the same order as the permeability of the connected inorganic pores. The effect of coupled flow becomes negligible when the permeability of organic matter is 102 higher or lower than the permeability of the connected inorganic pores. The fraction of maximum change in magnitude of effective permeability (Im) is found to be exponentially dependent on organic matter–pore channel fraction (f), i.e., Im ∝ e0.77f, for 0 < f < 5. The maximum contribution of organic matter on bulk liquid flow and a large variation in fluid flow velocities are found to be dependent on both the proportion of organic matter and length scale of investigation, indicating that the µm-scale FIB-SEM domains are far from the scale of representative elementary volume (REV). This study, however, describes how the hydrodynamic coupling of dual ϕ–k porous media contributes to emergent bulk liquid flow in organic-rich Mudrocks, and likely in similar dual ϕ–k porous media encountered within engineered systems to the ones found in nature.

Generalized lattice Boltzmann model for frosting.

Frosting is a multiscale and multiphysics problem, which presents a significant challenge for numerical methods. In this study, a generalized lattice Boltzmann (LB) model is developed to simulate the frosting of humid air at representative elementary volume scale. In this model, three LB equations are introduced to describe the evolution of distribution functions for velocity, temperature, and humidity (i.e., mass fraction of water vapor in the humid air) fields, respectively. The frost layer is regarded as a porous medium, while the humid air is treated as a plain one. This unified LB model can be applied to describe the phase change and transport processes in these two subdomains seamlessly. Through the Chapman-Enskog analysis, the macroscopic equations for the frosting process can be recovered from the present LB model. Benchmark problems in conduction solidification, convection melting and frosting are simulated, and the numerical results match well with analytical or experimental solutions. Finally, this model is applied to simulate frost formation between two parallel plates, and the influences of air velocity, humidity, temperature, and cold wall temperature are evaluated.