Multilayered Porous Media Research Articles

Fast and Smart State Characterization of Large-Format Lithium-Ion Batteries via Phased-Array Ultrasonic Sensing Technology

Lithium-ion batteries (LIBs) are widely used in electric vehicles and energy storage systems, making accurate state transition monitoring a key research topic. This paper presents a characterization method for large-format LIBs based on phased-array ultrasonic technology (PAUT). A finite element model of a large-format aluminum shell lithium-ion battery is developed on the basis of ultrasonic wave propagation in multilayer porous media. Simulations and comparative analyses of phased array ultrasonic imaging are conducted for various operating conditions and abnormal gas generation. A 40 Ah ternary lithium battery (NCMB) is tested at a 0.5C charge-discharge rate, with the state of charge (SOC) and ultrasonic data extracted. The relationship between ultrasonic signals and phased array images is established through simulation and experimental comparisons. To estimate the SOC, a fully connected neural network (FCNN) model is designed and trained, achieving an error of less than 4%. Additionally, phased array imaging, which is conducted every 5 s during overcharging and overdischarging, reveals that gas bubbles form at 0.9 V and increase significantly at 0.2 V. This research provides a new method for battery state characterization.

Numerical calculation of groundwater geofiltration processes in multilayer porous media

In this The article presents the modeling of multilayer hydrogeological processes in porous media, the results of fundamental and applied research, numerical modeling of hydrogeological processes, computational mathematics and methods of finite-difference schemes for solving simple differential equations, the development and improvement of mathematical models, and considers computational algorithms and software tools for solving problems analysis and forecasting of processes.

Dispersion of thermoelastic guided waves in multi-layered porous media

The mechanical properties of the graphite electrode will dynamically change during the charge-discharge cycle, which will affect the propagation characteristics of guided waves in lithium-ion batteries. Meanwhile, lithium-ion batteries experience fluctuations in operating temperature during cycling, which will also influence the propagation of guided waves. This research aims to investigate the guided wave propagation problem of porous electrode material with electrolyte versus temperature. The problem is under the framework of Green-Naghdi theory and Biot theory, and a numerical approach is presented to solve the thermoelastic wave propagation characteristics in such a multi-layered porous electrode. A frequency domain simulation for a multi-layered porous anode will be established. The simulation results confirm the feasibility and accuracy of the proposed approach. The porosity of the anode material shows obvious dynamic variation during cycling, which illustrates a strong correlation with the elastic modulus of the solid skeleton. Then, the effects of porosity and temperature variations on the propagation characteristics of thermoelastic guided waves in multi-layered porous graphite electrodes will be analyzed in detail. The phase velocity of fundamental modes appears regularly shift in the low frequency range. This may provide theoretical support for the acoustic nondestructive characterization of the operating states of the lithium-ion batteries.

A Semi‐Analytical Solution for the Equivalent Permeability Coefficient of the Multilayered Porous Medium With Continuous Fracture

AbstractFractures significantly alter the permeability characteristics of the natural porous media, especially for the multilayered porous medium system. The most direct and effective approach to assess the hydraulic conductivity of a multilayered porous medium with continuous fracture is to determine its equivalent permeability coefficient (EPC). A mathematical model with second‐order accuracy is established to analysis the permeability characteristics of the multilayered porous medium incorporating a continuous fracture. The Navier‒Stokes equation is used to govern the clear fluid motion in the continuous fracture, and the seepage fluid motion in the multilayered porous matrix is governed by the Brinkman‒Darcy equation. The semi‐analytical solutions for the velocity profile and EPC of the present model are derived under the conditions of the jumping stress at the fracture‐matrix interface and the continuous velocity at the matrix(i)‐matrix(i +1) interface. The Lattice Boltzmann method, finite element method, and one domain method simulations are conducted to verify the deduced semi‐analytical solutions of the velocity profile. Furthermore, the calculated EPC of the present multilayered model is in good agreement with that of the existing classic models (i.e., one region: fracture, two regions: fracture‐matrix, three regions: fracture‐matrix1‐matrix2, and multilayered porous medium without fracture). Parameter sensitivity reveals that increasing the thickness, dip angle, and porosity of the fractured porous media increases the flow velocity, while an increase in the stress jump coefficient can result in the opposite effect. This implies that porous layers containing fracture are more susceptible to erosion, particularly under conditions of steep dip angle and strong permeability.

Optimization of diesel oxidation catalyst for enhanced emission reduction in engines

With tightening emission regulations and the advent of Zero-Carbon targets, curbing emissions from engines has become imperative. To enhance the emissions reduction of engines, a diesel oxidation catalyst (DOC) inserted within a three-layer porous media is proposed. Effects of Pd/Pt blended ratios, porous media settings, and boundary conditions on pollutant conversion are simulated and analyzed. The results indicate that increasing the Pd/Pt blended ratio and reducing the porosity favor the conversion of CO and C3H6 but hinder the generation of NO2, and there exists a balancing effect of porosity and multi-layer porous media on emission conversion. With mean porosity augment from 0.4 to 0.6, NO conversion rate is improved by 2.1 % in the DOC with incremental porous media setting at Vin = 10 m/s, Tin = 550 K, and 100 % Pt. Moreover, the differences in conversion rates are enlarged with an increased Pd catalyst content, by 3.2 %, 5.9 %, 9.6 %, and 10.6 % respectively. Besides, 50 sets of DOCs are simulated, using orthogonal experiment analysis to optimize the boundary conditions and DOC setting. The maximum conversion rate is achieved when Vin = 10 m/s, Tin = 600 K, mO2 = 0.04, and Pd/Pt catalyst blended ratio and porosity is 100%Pt+1/4 + 1/4 and 0.5 + 0.4+0.4 in porous media.

Analytical solutions for transport of organic solutes in multi-layered porous media

In this study, analytical solutions for one-dimensional transport of organic solutes in multilayered porous media are developed using the methods of matrix transfer and variable separation, where multiple factors such as advection, diffusion, mechanical dispersion, adsorption, degradation, boundary condition type and change in concentration are systematically incorporated for the first time. Compared with the existing analytical solutions solved by the techniques of integral transformation or Laplace transformation, the approaches adopted in this paper are simpler and have a quicker convergence speed. Also, the proposed analytical solutions are more practical with clear expressions and consideration of multiple factors, which can be applied to various engineering cases such as bottom liner systems at landfills, covering systems of contaminated sediments and vertical barrier systems in contaminated sites. Furthermore, the correctness of the derived analytical solutions is effectively validated by comparison with the experimental results, as well as with the existing analytical solution and a numerical method. Following this, the effects of different factors on the transport process of a single organic solute in a five-layered medium are investigated, and some novel and vital laws are obtained. Overall, this research contributes to appropriate evaluation of the transport behaviours in multilayered porous media.

Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning

Proton exchange membrane fuel cells, consuming hydrogen and oxygen to generate clean electricity and water, suffer acute liquid water challenges. Accurate liquid water modelling is inherently challenging due to the multi-phase, multi-component, reactive dynamics within multi-scale, multi-layered porous media. In addition, currently inadequate imaging and modelling capabilities are limiting simulations to small areas (<1 mm2) or simplified architectures. Herein, an advancement in water modelling is achieved using X-ray micro-computed tomography, deep learned super-resolution, multi-label segmentation, and direct multi-phase simulation. The resulting image is the most resolved domain (16 mm2 with 700 nm voxel resolution) and the largest direct multi-phase flow simulation of a fuel cell. This generalisable approach unveils multi-scale water clustering and transport mechanisms over large dry and flooded areas in the gas diffusion layer and flow fields, paving the way for next generation proton exchange membrane fuel cells with optimised structures and wettabilities.

Effects of porosity setting and multilayers of diesel particulate filter on the improvement of regeneration performance

Diesel particulate filter (DPF) is one of the most effective devices to solve automobile exhaust emission problem. A DPF model with multilayer porous media (PM) and varied porosity is proposed to improve regeneration performance and conversion rate. Effects of PM setting, inlet temperature and flow rate on pressure distribution, thermal performance and conversion rate of the DPF are investigated. The results indicate that the static pressure of DPF with multilayer PMs is increased with the improvement of temperature under the condition of porosity P = 0.4, and the static pressure of the incremental model with multilayer PMs is 22.3 Pa and 42.5 Pa lower than that of the holistic and degressive filter, respectively. The pressure distribution is more uniform and the conversion rate is higher than P = 0.5 and P = 0.6. In addition, the increase of porosity is conductive to the rapid heating and reducing the static pressure. Furthermore, the conversion rate of multilayer (P = 0.3 + 0.4+0.5) is increased by 59.24% within t = 400 s and heat transfer performance is significantly improved when the mass flow rate increases from mf = 10 g/s to mf = 30 g/s. Hence, the incremental PM setting is contribute to the achievement of high conversion rate and better thermal performance, reducing engine emissions.

A coupled BioHeat transfer model for customized whole-eye modeling in retinal laser surgery

The photothermal effects of laser on tissue are widely used in ophthalmology to treat retinal diseases. The multiscale retinal lesion from the micrometer size to the millimeter size can be thermally targeted by adjusting the pulse duration from nanoseconds to tens of seconds. A large-scale difference among target lesions has brought extra challenge for retinal laser surgery modeling. In this study, we developed a coupled whole-eye model for retinal laser surgery. In the model, the Pennes bioheat transfer equation was adapted for the whole-eye temperature modeling. Simultaneously, we treated the fundus as a multilayered porous medium made of a tissue matrix buried with highly absorbing chromophores (melanin or blood). Two-temperature equations, one for the chromophore and the other for the surrounding tissue, were developed on the basis of the local thermal nonequilibrium theory of porous media. The Pennes and two-temperature models were coupled together to calculate the thermal responses of eye during several laser retinal surgery processes with pulse duration from nanoseconds to tens of seconds. Simulation results proved that our model was capable of modeling the laser retinal surgery process at different time scales. Furthermore, the coupled model was applied in a real fundus anatomy from a patient with diabetic retinopathy to illustrate its feasibility in customized laser protocol planning.

Linear stability analysis of convection in a solid partitioned inhomogeneous multilayered porous structure

We investigate the effect of varying permeability on the onset of convection in a system of multi-layered porous medium when heated from below. Here, the interface between any two porous sublayers is a thick solid conducting plate. The porous sublayers are inhomogeneous with respect to their permeability. Results for the homogeneous case are validated against those from the literature. The solvability condition is produced for a general N– layered inhomogeneous system to study the neutral curves. Detailed results are presented for a two layered and a three layered configuration. The effect of the involved parameters such as permeability ratio, thermal conductivity ratio, and thickness ratio on the onset of convection is analyzed using linear stability analysis. The critical values of Rayleigh number and the corresponding wave number increased with the increase in the thermal conductivity of the solid partitions, irrespective of the change in the permeability of porous sublayers. Multicellular sublayer flow circulation strength is amplified by the conductivity of the solid interfaces. Higher modes are also examined for varying permeability ratio and thermal conductivity ratio. A different flow pattern is observed for mode 3 when the permeability ratio is either very much less than one or much greater than one. Onset of the convection is sensitive to the increasing number of inhomogeneous porous sublayers of the layered porous system.

Optimizing Thermo-Hydraulic Performance in Heat Exchanger with Gradient and Multi-Layered Porous Foams

In this study, the effect of gradient and multi-layered porous media is assessed for the optimized properties and arrangement in the tested novel baffle design arrangement, which results in further enhancement in its thermo-hydraulic performance. The computational study is carried out using ANSYS FLUENT; wherein the permeability and porosity for each layer is varied. It’s executed in two steps: case 1 – porous layers with variations implemented (constant, linear/stepwise, increasing/decreasing) and case 2 – porosity varied over the length. The findings show that the linear/stepwise increments in both cases give almost similar performance evaluation criteria (PEC) values. The increase in heat transfer rate and pressure drop can be compared using PEC, for better evaluation of the performance of different arrangements. With the simulation data genetic algorithm optimization model is used to find the optimal arrangement of the porous layers for both cases to maximize PEC further. The optimal arrangement for case 1 and case 2 taken individually, gives PEC of 2.425 and 2.401 respectively. And their simultaneous optimization gives highest PEC of 2.508. Additionally, to improve the heat transfer rate further, Al2O3 (5 w/v %) nanoparticles in water is tested with optimized conditions, which improves the PEC by almost double magnitude.

Applications of the Multilayer Porous Medium Modeling Approach for Noise Mitigation

Porous materials have been widely investigated as a mean for noise reduction. Numerical simulations can be used to investigate the physical mechanisms responsible for noise reduction; however, a correct modeling of the porous medium through an equivalent fluid model is essential to minimize the computational costs. This paper reports a detailed review of a few applications of the equivalent fluid model based on a three-layer approach, a method that is particularly useful to account for the variation of porous material thickness in aerospace applications. The multilayer approach has been applied in three relevant aerodynamic noise issues: leading-edge impingement noise, turbulent boundary-layer trailing-edge noise, and jet installation noise. Comparison with experiments is used to validate the simulation approach.

Transport and Lymphatic Uptake of Biotherapeutics Through Subcutaneous Injection

Drug transport and uptake in the subcutaneous tissue receives increasing attention in biomechanical and pharmaceutical researches, as subcutaneous administration becomes a common approach for the delivery of biotherapeutics, such as monoclonal antibodies. In this paper, high-fidelity numerical simulations are used to investigate the mechanisms governing drug transport and absorption in the subcutaneous tissue, which is expressed as a porous medium modeled by Darcy’s law. The effects of tissue properties (permeability and porosity), the injection flow rate, and the vascular permeability of lymphatic vessels on the lymphatic uptake are studied. Additionally, an empirical formula for the lymphatic uptake during the injection is developed based on the numerical results. The roles of lymphatic drainage, blood perfusion, osmotic pressure, and the drug binding to the cells and the extracellular matrix in the lymphatic uptake are systematically studied. Furthermore, the drug distribution and absorption in a multi-layered porous medium are investigated to illustrate the effect of heterogeneity of permeability, as the permeability varies over a wide range in different layers of the tissue (such as dermis, subcutaneous tissue, muscle). While the interstitial pressure plays an essential role in the mechanisms regulating the absorption of free monoclonal antibodies, the binding and metabolism of drug proteins also affect the drug absorption by reducing the total free monoclonal antibodies.

Recovering the aqueous concentration in a multi-layer porous media

In this paper, we consider an inverse problem for time-fractional advection-dispersion equation in a multi-layer composite medium. The main goal of our paper is to approximate the initial information, which is inaccessible for measurement, from the observation data at a certain point in second layer by constructing a regularized solution using a filter regularization method. Under appropriate regularity assumptions of the exact solution, we give convergence rate of the error between the reconstructed solution and the exact one. A numerical example is provided to illustrate the main results.

Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of n reaction–diffusion–convection equations coupled with n ordinary differential equations, which models a combustion front moving through a porous medium with n parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.

A topology optimization based design of a liquid-cooled heat sink with cylindrical pin fins having varying pitch

An improved internal structure of a liquid-cooled heat sink has been proposed numerically and experimentally. The initial motivation is based on the results of thermal and fluid-flow topology optimization, which tends to produce a porous region despite suppression through the numerical scheme. The topology optimization was conducted using a Finite-Volume (FV) based procedure with a simplified sensitivity analysis as well as the globally convergent method of moving asymptotes (GCMMA) algorithm. The Spalart-Allmaras turbulence model was modified to handle the varying solid geometry in the topology optimization. As the result of multi-objective topology optimization showed a tendency towards the porous geometry inside the heat transfer domain, new models for the internal structure were proposed: a multi-layered porous medium with metal foam and varying-pitch cylindrical pin-fin structures. An experimental rig was developed for experimental validation of the proposed idea. The results shows that the varying-pitch cylindrical pin-fin structure inside the heat sink has advantages in heat transfer, pressure drop, and the manufacturability. Details of the numerical procedure and the experimental results are summarized in both quantitative and qualitative aspects.

Generalized semi-analytical solution for coupled multispecies advection-dispersion equations in multilayer porous media

Multispecies contaminant transport in the Earth’s subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but currently limited to either one species, homogeneous media, certain reaction networks, specific boundary conditions or a combination thereof. In this paper, we develop a semi-analytical solution for the case of a heterogeneous layered medium and a general first-order reaction network. Our approach combines a transformation method to decouple the multispecies equations with a recently developed semi-analytical solution for the single-species advection-dispersion-reaction equation in layered media. The generalized solution is valid for arbitrary numbers of species and layers, general Robin-type conditions at the inlet and outlet and accommodates both distinct retardation factors across layers or distinct retardation factors across species. Four test cases are presented to demonstrate the solution approach with the reported results in agreement with previously published results and numerical results obtained via finite volume discretisation. MATLAB code implementing the generalized semi-analytical solution is made available.

Forward-Backward Alternating Parallel Shooting Method for Multi-layer Boundary Value Problems

Multi-layer boundary value problems have received a great deal of attention in the past few years. This is due to the fact that they model many engineering applications. Examples of applications include fluid flow though multi-layer porous media such as ground water and oil reservoirs. In this work, we present a new method for solving multi-layer boundary value problems. The method is based on an efficient adaption of the classical shooting method, where a boundary value problem is solved by means of solving a sequence of initial value problems. We propose, an alternating forward-backward shooting strategy that reduces computational cost. Illustration of the method is presented on application to fluid flow through multi-layer porous media. The examples presented suggested that the method is reliable and accurate.

Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally.

Thermohydraulic analysis of hybrid nanofluid in a multilayered copper foam heat sink employing local thermal non-equilibrium condition: Optimization of layers thickness

In the present study, fluid flow and heat transfer characteristics of a heat sink partially fitted with multilayered porous medium are analyzed. The multilayered copper foam contains three different layers placed at the bottom wall of the heat sink exposing to a uniform heat flux. The whole occupied volume of the porous region is 60% of the channel. The main objective of the current study is to reveal a layout for the porous medium with optimum thickness for each layer in two proposed models to maximize the heat transfer and minimize the pressure drop. In the constant particle diameter model, all three layers have an equal particle diameter of 1.5 cm with three porosities of 0.95, 0.85 and 0.75 from bottom to top. In the constant porosity model, all three layers have an equal porosity of 0.95 with three particle diameters of 0.5, 1 and 1.5 cm from bottom to top. To trade-off between the desirable (heat transfer) and undesirable (pressure drop) outcomes, the dimensionless number of performance evaluation criterion (PEC) is determined. Darcy–Brinkman–Forchheimer and local thermal non-equilibrium (LTNE) models are applied to solve the governing equations in the porous region. The CFD numerical simulations are conducted to analyze the effect of each layer thickness of the multilayered porous medium in the two proposed models on the thermohydraulic parameters such as friction coefficient, Nusselt number and PEC number. At the optimum layouts of the porous medium, water-graphene nanoplatelet/platinum hybrid nanofluid is applied to enhance the thermal performance of the heat sink. The obtained results reveal that the highest PEC number is achieved in the constant porosity model equal to 1.17 at the case in which the lower, middle and upper metal foam layer thicknesses are 0.6, 1 and 0.2 cm, respectively, resulting in 145% heat transfer enhancement. In constant particle diameter model, the highest PEC number equals to 1.26 at the case in which the lower, middle and upper metal foam layer thicknesses are 1, 0.6 and 0.2 cm, respectively, resulting in 191% heat transfer augmentation compared with the plain channel. Further increase in PEC number is observed by adding nanoparticles to the base fluid for nanofluid volume concentration of 0.1% in constant porosity and particle diameter models which are equal to 1.22 and 1.31, respectively.