Representative Elementary Volume Scale Research Articles

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects

Anomalous transport has been commonly observed in the fluid flow through a complex porous medium, where the evolution exhibits a complex memory-like behavior. Classical integer-order models fail to depict anomalous transport phenomena, while fractional calculus has been proved effective in describing such behavior due to its ability to characterize long memory processes. In this paper, the time-fractional generalized Navier-Stokes (N-S) equations are formulated to model anomalous transport in porous media at the representative elementary volume (REV) scale by incorporating the Caputo fractional derivative of time into the widely employed generalized N-S equations. An innovative lattice Boltzmann (LB) model is presented for solving the time-fractional generalized N-S equations. We validate the proposed LB model by conducting a numerical example with analytical solutions, and observe a good agreement between the LB results and the analytical solutions. The proposed LB model is utilized for simulating Poiseuille flow, Couette flow, and cavity flow in porous media. Unlike the previous studies, which focus on the steady state of these flows, the present work focuses on the unsteady process from the initial state to the final steady state. It is found that time-fractional effects play a significant role in the unsteady processes of these flows. As the fractional order decreases, the flows undergo a slower evolution process and the impact of Darcy number on the unsteady process becomes increasingly noticeable. The Reynolds number has a significant impact on the velocity profile in the steady state, but it has relatively little effect on the duration of the unsteady process.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Solid–liquid phase transition simulated by the lattice Boltzmann model: from pore scale to representative elementary volume scale

Purpose This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems. Design/methodology/approach Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given. Findings This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices. Originality/value A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

Experimental study on the size effect and anisotropy in mechanical properties of fractured rock mass based on 3D printing

The size effect and anisotropy of fractured rock mass mechanical parameters are difficult problems to solve in the field of engineering. This study taken full advantage of sand 3D printing technology to batch-reproduce complex structures and prepare rock-like specimens with different sizes and rotation directions. The size effect and anisotropy of the fractured rock mass were investigated. Digital image correlation was used to conduct noncontact full-field observations of the specimen. The results showed that the sand 3D printing specimens have the advantages of high precision and brittleness and can reproduce the deformations and failure processes of natural rock. The compressive strength and failure mode of the fractured rock have significant size effect characteristics. Assessing the size effect on the compressive strength of the specimen, 100 × 100 mm is the mechanical representative elementary volume (mREV) scale. The compressive strength and failure mode of the fractured rock under the mREV scale show obvious anisotropy. Based on the size effect of fracture density, 80 × 80 mm was identified as the geometric representative elementary volume (gREV) scale. The gREV scale was smaller than and close to the mREV scale was found. In addition, the differentiation rate of standard deviation (DRSD) is defined to provide information on the dispersion of the strain field and the precursor information of crack initiation during the deformation and fracture of the rock mass. This study provides a new method for laboratory experimental studies on the size effect and anisotropy of complex fractured rock masses from the perspective of 3D printing.

A two-relaxation-time lattice Boltzmann model for simulating incompressible thermal flows in porous media

In this work, a two-relaxation-time (TRT) lattice Boltzmann (LB) model for simulating incompressible thermal flows in porous media at the representative elementary volume (REV) scale is developed. In the REV-scale TRT-LB model, the framework of the TRT-LB equations with forcing and source terms is described clearly as simply as possible. Specifically, the forcing (or source) term is divided into two parts: the symmetric part and the anti-symmetric part, which is consistent with the philosophy of the TRT model. Through the Chapman-Enskog expansion procedure, the macroscopic governing equations can be derived from the present model. Numerical simulations of several benchmark problems are carried out to validate the present model, and the present results match well with the analytical solutions and/or those numerical results in the literature.

Investigation on latent heat energy storage using phase change material enhanced by gradient-porosity metal foam

Utilizing an optimized gradient porosity can help with the temperature uniformity and alleviate the temperature aggregation. In this paper, a solid–liquid lattice Boltzmann (LB) model at the representative elementary volume scale (REV-scale) is established to investigate the enhancement mechanism of gradient porosity on LTES units. Three gradient porosity including Chinese-fan-shape, vertical and concentric distribution has been investigated. The findings demonstrate that a well-designed gradient porosity can significantly decrease the melting time, with the best performance observed when using a fan-shape arrangement of a certain gradient. In comparison to a homogeneous porosity, the fan-shape arrangement of a specific gradient reduces the melting time by 36.1 % and ensures a more uniform temperature distribution. Increasing the number of layers from two to five has no remarkable improvement on melting, not exceeding 4.4 % in total melting time. Conversely, increasing the porosity gradient leads to an increase in melting time of no less than 36.1 %. Furthermore, an extended dimensionless number Ram in a range of 150 ∼ 600 is investigated. The results suggest that, with the increase of Ram the temperature aggregation is more significant, and the gains in melting rate are unable to offset the increased heating temperature's impact on the melting time.

Reactive transport model for calcite-rich caprocks in the context of ge-ological carbon storage

Increased concentrations of greenhouse gases in the atmosphere are known to be the primary cause of the increase in global surface temperature and, consequently, climate change [6]. In order to limit global warming, several decarbonisation strategies have been proposed: among them, geological CO2 storage represents very likely the only short- to medium-term option for substantially improving CO2 sinks and reducing net carbon emissions into the atmosphere.
 To achieve secure and lasting storage of CO2 in underground spaces, it is necessary to have both a reservoir and a low-permeability caprock (seal), that maintains its integrity. Deep saline aquifers, depleted oil and gas fields and unminable coal seams are thus the primary targets for the underground storage of supercritical CO2 [2]. The occurrence of natural reservoirs implies that certain lithotypes have a certain sealing capacity, which can prevent leakage of gas to the atmosphere over long geological time periods (i.e. million of years); however, in order to assess the risk of CO2 leakage through caprock above storage sites, the potential caprock alterations due to the contact with CO2 must be considered. In fact, although certain caprocks can be suitable for hydrocarbons, CO2 in contact with the seal may pose additional risks. As for natural hydrocarbon accumulation, shales and evaporites are potential seals also for carbon storage. With particular reference to shales, their mechanical and transport properties are controlled by the behaviour of clay minerals. The sealing efficiency of intact shale caprocks is in fact dominated by the high specific surface clays, which are characterized by high capillary entry pressures, but are also susceptible to electro-chemical interaction. From the engineering perspective, capillary and electrical phenomena also have relevant effects at the Representative Elementary Volume scale, causing mechanical couplings which could affect porosity, clay fabric, hydraulic conductivity, compressibility, and shear strength [3]. Besides these electro-chemical effects, CO2 dissolution and diffusion in water also result in acidification of the in situ brine, causing chemical reactions with some caprock minerals and potentially affecting the mechanical and transport properties [4].
 This work presents a reactive transport model to assess the effects of pore water acidification on caprock materials. The model includes the water mass balance equation for the saturated porous medium and the mass balance equation for all the primary species dissolved in water, according to the theoretical approach presented in [7]. The modelling approach proposed accounts for both the aqueous (homogeneous) reactions of the CO2 dissolved in water (assumed to be in equilibrium) and the dissolution kinetics of calcite in the acidic environment induced by CO2 injection (see [1] for details). Calcite dissolution is finally linked to porosity changes via the reactive surface area of the mineral and the reaction rate. Chemo-hydraulic coupling is addressed by considering porosity changes in the storage term of the balance equations and by introducing a suitable link between hydraulic conductivity and current porosity. The model requires the solution of an initial chemical speciation problem, which has been performed with the software PHREEQ-C, and then the integration of a set of partial differential equations (the mass balance equations of water and of the master primary species dissolved in water) and non-linear algebraic equations (to obtain the concentration of all the chemical species involved), which in this study has been performed via the Finite Element software Comsol Multiphysics ®, according to the approach presented in [8].
 The numerical model has been validated according to the numerical benchmark proposed in [5], developed to reproduce a geo-chemical scenario where mineral dissolution causes permanent alterations in the transport properties of a porous medium. In partic-ular, the benchmark reproduces a flow-through columns experiment, with the porosity and permeability of a calcite-rich interlayer changing under sulfuric acid attack. Figure 1 shows a comparison between the predictions of the current model and the model proposed in [5] in terms of the spatial evolution of porosity, permeability and dissolved calcite, after 400 hours since the injection of sulfuric acid. The model is able to reproduce that, as the acidic front proceeds into the sample from left to right, calcite is progressively dissolved causing porosity changes and the consequent permeability increase. The agreement between the two models is satisfactory, despite some slight differences that may be attributed to the different numerical mesh and the different numerical solver scheme.

Multi-scale simulation of the effect of microbial growth on the permeability of porous media

In this study, a novel algorithm coupling the flow at the pore and representative elementary volume (REV) scales was developed to analyze the effect of microbial growth at the pore scale on the permeability decay of porous media at the REV scale. This provides a new method for investigating microbial clogging in porous media. At the pore scale, an immersed boundary-lattice Boltzmann model was used to simulate the flow field and solute transportation in porous media, and the cellular automata (CA) model was employed to investigate microbial growth. According to Ergun's empirical relationship, the equivalent porosity change at the pore scale caused by microbial growth was calculated and used in a generalised seepage model describing the fluid flow in the porous medium at the REV scale. First, the microbial growth experiments were conducted to validate the coupling algorithm. Second, the spatial and temporal characteristics of microbial growth at the pore scale were analyzed. Third, we investigated the effects of nutrient inlet concentrations and pH on microbial growth at the pore scale and the macroscopic permeability properties of porous media. The main results are as follows. (1) Microbial growth changes the local porosity and dominant flow path. Spatial non-uniformity in microbial growth depends on the availability of nutrients in the dominant flow path. (2) The discrepancy in microbial growth under different nutrient inlet concentrations was gradually amplified from the pore scale to the REV scale. (3) The microbial clogging period was the shortest at a pH of 6.7. When the pH was >6.7, the microbial clogging period slightly increased at a rate of 6.1 h/pH. When the pH was <6.7, the microbial clogging period increased significantly with decreasing pH at a rate of 20.0 h/pH. (4) A linear relationship was observed between the microbial clogging periods at the REV and pore scales, which enriches the theory about microbial clogging in porous medium.

A surrogate-assisted uncertainty-aware Bayesian validation framework and its application to coupling free flow and porous-medium flow

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid–porous interface. These models include a porous-medium model using Darcy’s law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems’ behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model’s predictive capabilities, and make a probabilistic model comparison.

Smoothed Particle Hydrodynamics Simulations of Porous Medium Flow Using Ergun’s Fixed-Bed Equation

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity (ϕ=0.44 and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array.

A Geometry-Dependent Void Closure Model Considering Void Deformation and Orientation Changes during Hot Metal Formation

In this paper, a void closure model applicable to the general hot forming process has been proposed. Through the representative volume element (RVE) method, the influences of void shape, orientation, and stress state on void closure tendency were analysed. The void closure model was established so that it could consider these cross effects. The model calculates the changing void radius and orientation during deformation by considering the rate of change of the parameters affecting void deformation with respect to the effective strain. The model predicted the void closure tendency well on the RVE scale and predicted the void closure adequately in a multi-stage process with random voids. The results were compared with the stress-triaxiality-based (STB) model, which showed that the void closure model proposed in this study is applicable in general situations. A cogging process was analysed, and the degree of void closure at the end of each pass was compared with the calculated results of the void closure model. For the experimental verification of the proposed model, spherical and ellipsoid voids were placed in a rectangular specimen, and the radii of the voids after compression were measured. The measurement results were compared with the calculation results of the proposed model.

Using entropy generation as evaluating indicator of charging completion in a latent thermal energy storage system

To further promote the melting rate of latent thermal storage (LTES) system, the gradient porosity has been proved to be a feasible method. Entropy, as a long developed characteristic parameter to evaluate the irreversibility of a system, can be a good measurement to estimate the completion of charge process of latent thermal energy storage system. In this paper, a representative elementary volume-scale (REV-scale) solid-liquid phase change lattice Boltzmann model is established to study the melting of PCM in a gradient porosity enhanced LTES unit. The entropy generation is realized and verified, and applied in LTES unit analysis. The result shows that, a bigger porosity gap of 0.82–0.98 and more addition of porous matrix below the system can better promote the melting and entropy generation. The stepped and linear porosity distribution reduce the melting time by 17.4% and 13.3% respectively. By researching the entropy generation, it is found that, the friction-caused entropy dominates the entropy generation during charge process. By studying the melting in different Rayleigh number, it is found that, the gradient porosity can only accelerate the melting in high natural convection conditions of approximately Ra > 2 × 106.

Modeling Biomass Particle Evolution at Pyrolysis Conditions Considering Shrinkage and Chemical Kinetics with Conjugate Heat Transfer

Biomass pyrolysis is an attractive method to produce renewable biofuel in a short time scale. This paper discusses a computational study considering particle shrinkage and reaction kinetics to characterize biomass particle evolution under pyrolysis conditions. A representative elementary volume (REV) scale simulation was conducted in three dimensions to resolve the gas and solid domains. The interface was modeled using the conjugated heat transfer (CHT) and the adapted partially saturated method (PSM) in the lattice Boltzmann (LB) framework. A sufficient gas thickness was considered to simulate the interface physics, such as the thermal boundary layer and product gas outflux. The current simulation was validated using three different experiments. The particle conversion time, temperature, and shrinkage were well predicted. A parametric study investigated the effect of different modeling approaches and operating conditions. Results show that the internal heat transfer is affected by the particle size, inlet gas velocity, reactor temperature, and geometry. The Fourier number decreases to a nearly constant value as the particle size increases. The Péclet number increases linearly with the reactor temperature. Sub-particle scale simulation results reveal that the CHT model and permeability need to be considered when simulating gaseous product efflux out of the biomass particle. Three regimes are identified based on the particle permeability: diffusion-limited, mixed, and advection-limited. The gaseous product efflux delays the overall conversion in the mixed regime. A modified heat transfer coefficient is formulated based on the current numerical study.

Impacts of liquid phase distribution on the effective thermal conductivity of closed-cell thermal insulation

This paper proposes a multiscale effective thermal conductivity model combined with liquid phase distribution to explore in detail the influence of the internal structure of closed-cell thermal insulation on the thermal behavior in the presence of moisture. By simulating the liquid phase distribution in the cracks between the insulation cell skeleton and combining it with the representative elementary volume (REV) scale and macroscopic scale thermal conductivity models, the correlations between the structural parameters, saturation, and effective thermal conductivity of phenolic thermal insulation are analyzed. A critical saturation point is proposed for the first time, and the related impact factors are discussed. For the heat and moisture transfer in porous media, the larger the critical saturation, the better the insulation performance. Based on the newly developed improved effective thermal conductivity model, nine groups of phenolic samples with different structural parameters were investigated to compare the impact of porosity, closed-open pore volume ratio, relative deviation ratio, contact angle, and closed-pore diameter on the effective thermal conductivity. Simulation results indicate that the influence of the liquid phase distribution is mainly reflected at low saturation at the REV scale; at the macroscale, the influence of the liquid phase distribution is significantly reduced.

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.

GPU-optimized LBM-MRT simulation of free convection and entropy generation of non-Newtonian power-law nanofluids in a porous enclosure at REV scale

The present research investigates the heat transfer and entropy generation of a non-Newtonian power-law Cu-water nanofluid in a square porous enclosure at a representative elementary volume (REV) scale using the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). The Graphics Processing Unit (GPU) accelerated the computations involved. The Brinkman-Forchheimer-extended Darcy model and the shear rate dependent power-law viscosity model were taken into account to characterise the non-Newtonian fluid flow in porous medium. Three types of model validations have been conducted, followed by the mandatory grid independence test, to demonstrate the precision and accuracy of the computational code. The numerical results were obtained by varying five key parameters namely, Darcy number (Da = 10−3, 10−2, 10−1); power-law index (n = 0.6–1.0); Rayleigh number (Ra = 104, 105, 106); porosity parameter (ϵ = 0.6); volume fraction of nanoparticles (ϕ = 0.0–0.05), and the Darcy Rayleigh number (Ram = 100, 1000). The numerically simulated outcomes were presented in terms of streamlines, isotherms, velocity, and temperature profiles as well as the Nusselt (Nu) numbers. Furthermore, a correlation among the parameters to determine the average Nu was developed using the Levenberg-Marquardt (LM) algorithm. The mathematical correlation was also subject to validations, and, in general, good correlation coefficients were obtained.

Topology optimisation of architected cellular materials from additive manufacturing: Analysis, design, and experiments

This work deals with an experimental/numerical validation of the optimised topologies found through a special density-based topology optimisation (TO) method wherein the topological descriptor, i.e., the pseudo-density field, is represented through a non-uniform rational basis spline (NURBS) hyper-surface. The framework is that of multi-scale TO methods to design architected cellular materials (ACMs). Specifically, in the most general case, the topological variables are defined at the scale of the representative volume element (RVE) of the ACM and at the macroscopic scale of the structure. The transition among scales is performed via a numerical homogenisation scheme based on the strain energy of elements. The proposed formulation exploits the properties of NURBS entities to determine the relationships occurring among the topological variables defined at different scales to correctly state the optimisation problem and to satisfy the hypotheses at the basis of the homogenisation method. Three design cases are considered: in the first one, TO is performed only at the macroscopic scale; in the second one, TO is performed only at the RVE scale; in the last one, TO is performed simultaneously at both scales. Multiple design requirements related to lightness, scale separation condition (to ensure the validity of the results of the homogenisation method) and minimum printable size are included in the problem formulation. Particularly, the last two requirements are implicitly satisfied by controlling the integer parameters of the NURBS entity (describing the pseudo-density field at each scale) without introducing explicit optimisation constraints. The multi-scale TO strategy is applied to a structure made of ACM subject to three-point bending test-like boundary conditions: for each design case, the optimised topology is manufactured through stereo-lithography and a comparison between experimental and numerical results (obtained through non-linear analysis conducted a posteriori on the optimised topology) is performed to assess the effectiveness of the approach.

Trans-level multi-scale simulation of porous catalytic systems: Bridging reaction kinetics and reactor performance

Multi-scale porous structures inside and/or between the catalyst pellets or particles are found in many chemical processes, where strong coupling of reaction and transport results in complex apparent reaction kinetics influential to the reactor performance. Traditional continuum-based porous media models and simulation methods can hardly describe such structures and their scale effects faithfully. A trans-level multi-scale discrete computational framework is hence proposed to address this complexity and implemented for an olefin catalytic cracking (OCC) process. The apparent reaction kinetics at the REV (representative elementary volume) scale is obtained by hard-sphere pseudo-particle modeling (HS-PPM), and coupled with computational fluid dynamics / discrete element method (CFD-DEM) for the reactor-level hydrodynamics via a one-dimensional (1D) finite difference scheme for particle-level diffusion. The mesoscales of the REVs and the flow networks between the particles are thus covered by the framework, which are previously described by simple average quantities in the continuum methods. The reactant conversion rate and target product selectivity obtained agree well with experimental results, while a continuum approach may give significantly different and unreasonable results. The multi-scale method is, therefore, demonstrated to be necessary and effective for bridging the intrinsic reaction kinetics with the performance of porous catalytic reactors.

Identification of RVE length scale in fiber composites via combined optical and SEM digital image correlation

The representative volume element (RVE) in fiber composites refers to the smallest volume of material that contains all constituents of the composite, i.e., fiber and matrix, and is a domain in which the homogenization of microscale response will lead to the macroscale behavior. Therefore, the RVE size in fiber composites is the length scale at which micro to macroscale transition occurs. In this work, a multiscale experimental approach is developed to experimentally characterize the length scale of RVE in a carbon fiber composite with a random fiber distribution. The approach is based on combining optical and scanning electron microscope (SEM) digital image correlation (DIC) measurements. A statistical procedure based on spatial averaging of local strain data is applied to the strain fields obtained from optical and SEM DIC measurements. The convergence between local strains averaged over a carefully selected domain and global strains is used as the criterion for identifying the RVE size in the examined composite. The RVE sizes determined using this approach are stress dependent and increase with the evolution of internal damage in the composite.

A solid–liquid model based on lattice Boltzmann method for phase change material melting with porous media in cylindrical heat exchangers

Phase change materials (PCMs) are widely used in thermal energy storage systems as they can absorb and release a large amount of heat during the phase change process. The numerical study of PCM heat exchangers is an efficient method to analyze PCM behaviors. In this paper, a solid–liquid phase change model is developed based on the lattice Boltzmann method (LBM) to simulate transient phase change in the porous media. This model combines the axisymmetric porous LBM with an enthalpy-updating scheme, which enables it to simulate the axisymmetric porous PCM phase change efficiently. The enthalpy-based LBM at the scale of representative elementary volume is adopted for the modeling of the PCM phase change and the porous media. Moreover, double distribution functions coupled with a multi-relaxation-time scheme are utilized in LBM for the simulation of the fluid flow and temperature field. This improved model is validated using experimental results for a copper-foam enhanced PCM heat exchanger. Validation results indicate that the new model can successfully simulate the temperature glide of the PCM and the effect of natural convection on the PCM temperature field with an error of 10%. A parametric study is then conducted to evaluate the effect of natural convection on PCM melting and results indicate that the average acceleration of PCM melting due to the natural convection can be up to 10%. Based on the validation and parametric study, the new model can predict the performance of the cylindrical PCM heat exchanger. The new model is expected to be applied in a wider field of PCM phase change, which can benefit the design and improvement of PCM heat exchangers in thermal energy storage systems.