Porous Media Model Research Articles

Permeability Model for Fractal Porous Media with Rough Capillary Walls

The pore space of a porous medium is typically considered to consist of a collection of curved capillaries with rough walls. A model describing roughness is established by applying fractal theory. As a result, a modified permeability model is derived theoretically, which is closely related to roughness. To validate this model, a new form of Kozeny–Carman (KC) equation is also developed for estimating permeability on a set of benchmark rock samples, and a good agreement was achieved in terms of small relative error between measured and predicted permeabilities. Therefore, we can conclude that pore roughness should not be ignored in predicting permeability. Although the improved KC equation can predict permeability effectively too, it is not practical as the KC constant is difficult to determine.

Porous media model with multiphase transport and solid mechanics bidirectional coupling for SiO2 soot preform sintering process

SiO2 soot preform sintering is a critical step in the indirect chemical vapor deposition (CVD) method for synthesizing high-quality silica glass, which involves hydroxyl (OH) decomposition, heat and mass transfer, as well as densification. These phenomena are not fully coupled in the traditional models, which leads to inaccurate numerical predictions. To address this, a porous media model with multiphase transport and solid mechanics bidirectional coupling (MTM) is proposed for the soot preform sintering process in this paper. The model is validated by experimental results. Using this model, the densification behavior of soot preform during sintering process is predicted, and the effects of densification on heat and mass transfer are thoroughly examined. The OH decomposition rate and gas phase transport are intensified in the later sintering stage when densification occurs significantly. Consequently, the OH is concentrated, presenting a ringed-shape distribution. The temperature distribution is also affected, which transforms from a layered shape to a ringed shape, with the maximum temperature decreasing by approximately 20 °C. Furthermore, the effects of the temperature rise curve are explored. It is found that a higher preheating temperature and a longer holding time are preferable for the synthesis of high-quality silica glass.

EFFECT OF SUSPENDED PARTICLES ON THE STABILITY ANALYSIS OF CASSON NANOFLUID IN A DARCY-BRINKMAN POROUS MEDIUM

This article presents graphical and numerical examination of the initiation of thermal convection in porous media, with a specific focus on Casson nanofluids containing suspended particles. The study employs the Darcy-Brinkman model to characterize fluid behavior within porous media, considering the influence of suspended particles. This whole investigation is carried out by the employment of normal mode analysis and the Galerkin first approximation approach, which led to the derivation of expressions for the Rayleigh-Darcy number under stationary convection across different boundary conditions: free-free, rigid-rigid, and rigid-free configurations. We have analyzed the interaction between Casson nanofluids (non-Newtonian fluids), the Darcy-Brinkman porous media model, and the influence of suspended particles on thermal convection. The study explores the effects of various parameters, such as the Casson parameter, suspended particles parameter, Brinkman-Darcy number, porous media porosity, nanoparticle Rayleigh number, Lewis number, and modified diffusivity ratio on stationary convection, which are presented numerically and graphically under all boundary conditions. Most importantly in this investigation we find that under realistic rigid-rigid boundary conditions, the system displays greater stability compared to other boundary conditions (i.e., free-free and rigid-free).

Effects of Congestion in Human Lung Investigated Using Dual-Scale Porous Medium Models.

Chronic obstructive pulmonary disease (COPD) is a primary chronic respiratory disease associated with pulmonary congestion that restricts airflow and thereby affects the exchange of gases between the alveoli and the blood capillaries in the lungs. Dual scale-global and local-porous medium models have been developed and reported in this work, to study the effects of air-side congestion on the blood-oxygen content in the alveolar region of the human lung. The human lung is model as a global, equivalent, heterogeneous porous medium comprising three zones with distinct permeabilities related to their progressively complex branching structure. Airflow for each breathing cycle is determined by solving mass and momentum transfer equations across the three porous medium zones. The congestion is introduced by appropriate modification of the porous medium properties of the zones considered. The congestion-affected air velocity reaching Zone 3 is given as input to a separate "local model" employed at several locations of the alveoli of Zone 3. The local model determines the oxygen content in the blood flow in the capillaries of the alveoli by solving suitable mass, momentum and species transport equations. The transient simulation results performed for a long duration of multiple breathing cycles, demonstrate that a normal, healthy human lung is functional for up to 40% volume congestion or when 50% of the lung is congested to about 23.5%. Increasing congestion beyond this value, quickly-within a few hours-depletes the oxygen exchange in the blood flow of the alveolar region (of Zone 3), leading to hypoxemia. The effects of congestion progression on oxygen exchange dynamics determined through the dual-scale porous medium modelling approach provide researchers and medical professionals with in silico predictive estimates to generate treatment strategies for chronic respiratory diseases.

Homogenization of the Stokes-type model in porous media with slip boundary conditions

Homogenization of the Stokes-type model in porous media with slip boundary conditions

Development of heat exchanger modelling capability for a finite volume aeroelasticity solver

Abstract Heat exchangers are frequently used in aero engines and are known to significantly affect the surrounding steady and unsteady flow. In certain applications, they may thereby also influence the aeroelastic stability of upstream or downstream components but there is limited research on this in the public domain. This paper aims to demonstrate the influence of heat exchangers on unsteady flows relevant to aeroelastic problems. This is achieved by developing heat exchanger modelling capability for an in-house finite volume aeroelasticity solver, for which heat exchanger is represented as a porous medium, as this is the established approach in existing aerodynamic studies using commercial CFD software. The governing equations for a Darcy-Forchheimer porous media model suitable for unsteady and compressible flows are presented, which are derived by the application of volume averaging theory to the Navier-Stokes equations. The implementation of this model within the time integration method used for the solver is then described and verified by comparison of results for steady flows against an established commercial CFD solver, where close agreement between both in-house and commercial solvers has been observed. Lastly a preliminary demonstration of the capability to model unsteady heat exchanger flows is presented by application to an aeroacoustic problem, where the interaction of the pressure waves and the heat exchanger is investigated.

Applying Numerical Simulation to Model Varying Process and Cell Parameters during the Electrolyte Filling Process of Lithium‐Ion Batteries

The electrolyte filling process is considered one of the bottlenecks of lithium‐ion battery production due mainly to the long electrolyte wetting times. Additionally, the required experimental process design is time and material‐intensive, increasing the development costs of new materials or cell designs. A model of the filling process would allow for more efficient cell production, but until now, the published models have mainly been focused on individual components on a pore scale. Within the scope of this work, the model setup for a holistic examination of the electrolyte filling process is shown, allowing the study of the electrolyte wetting on a cell scale. The characteristic values of a porous medium, such as the permeability, are calculated with a microsimulation of an anode and a cathode pore structure. These values are then transferred to the ANSYS porous media model, and cell scale simulations are performed. Two cell formats and variations in the evacuation pressure and electrolyte temperature are simulated and compared to experimental wetting data. The results show that the simulation successfully models the wetting behavior for the investigated cell formats and cell assembly types, validating the model with experimental data both qualitatively and quantitatively.

Hydrodynamic Analysis of Flow Stabilization Process in a Miniature Circulating Water Channel Equipped with Combined Porous Plate Structures

As a foundational platform for fluid dynamics research on underwater devices, the quality of stable and uniform incoming flow in a circulating water channel (CWC) is essential. Due to the inherent structural characteristics of porous media, their application has become widespread in offshore and marine engineering. This study presents the design of a miniature circulating water channel, alongside the development of a computational fluid dynamics (CFD) numerical model to simulate the interaction between porous media and incoming flow. By analyzing the pressure loss of fluid within the porous plates and incorporating it as a source term in the momentum equation, heavy computational costs associated with fine mesh requirements in micro porous models were avoided. Simulations were conducted to investigate the effects of combined porous plates on the flow field, and the porous media model was validated by comparisons with experimental data. The distribution of the flow field within the channel was analyzed to define the test section, which was conducive to further structural optimization. The results indicated that the combined porous plates stabilized the flow field of the CWC, and, following structural optimization, the occurrence of backflow was reduced, thereby expanding the effective test section range.

Effect of pore plugging on transpiration cooling performance implemented with perforated flat plates

Transpiration cooling is expected to be one of the most effective cooling technologies for gas turbine blades. However, dust deposition can easily lead to pore plugging, which limits its practical application in engineering. The plugging of pores in conventional porous media models is difficult to predict, so it is essential to construct computational models with finely controllable porous structures. In this study, a transpiration cooling configuration with straight holes perforated with a diameter of 0.5 mm was adopted. The effects of plugging ratio and region on flow and heat transfer under different coolant injection ratios and pump power conditions were investigated by numerical simulation. The results showed that at constant mass flow rate, the overall cooling performance increased as the plugging ratio increased at low injection ratios. At high injection ratios, the opposite was true. With a certain pump power, as the plugging rate increased, the flow loss coefficient rose, leading to a decrease in cooling efficiency. Transpiration cooling efficiency was also highly sensitive to the distribution of plugged holes at the same plugging ratio. When the coolant flow was sufficient, the farther the plugged area was from the leading edge, the smaller the reduction in cooling efficiency.

A heat pipe calculation method based on the two-phase mixture model of porous medium

This paper proposes a new method for calculating heat pipes, in which the porous wick inside the heat pipe is described by the two-phase mixture model (TPMM) of porous medium based on the modified temperature model that adopts the local thermal equilibrium assumption. The capillary pressure inside the wick is characterized by the Leverett capillary pressure model. This model can calculate the two-phase flow within the heat pipe wick at the macroscopic scale level and achieves a full-field coupled solution for the wick-vapor-wall flow and heat transfer process by a specific coupling method. Finally, the paper conducts a coupled heat transfer calculation for a heat pipe using potassium as the working fluid, verifies the correctness of the model and solution method by comparing it with the experimental results, and studies the flow and phase transition patterns of the heat pipe under multiple heating and different overload conditions. Compared with the traditional single-phase porous medium model of heat pipes, the new model can consider phase transition within the porous wick. While compared with pore-scale methods, the macroscopic research scale of the new model can reduce the computational resources required.

(Digital Presentation) The Influence of Pore Geometry on Water Transport in the Gas Diffusion Layer of PEM Fuel Cells

The water transport behavior in the Gas Diffusion Layer (GDL) depends on the pore characteristics, which include the pore size distribution, the wetting properties of the fibers, and the shape of the pore. In this study we investigate the impact of pore geometry on the breakthrough pressure of the GDL. The study shows the importance of the inclusion of different types of pore shapes in the analysis of the water transport behavior. The water invasion process through a pore inlet is simulated using a surface energy minimization model. In a GDL coated with a non-wetting coating such as PTFE, water makes contact with non-wetting fibers and with defects which pin the gas-liquid interface. The mixed-non-wetting (MNW) pore inlet is defined by fiber segments of varied wetting properties, in order to capture the water percolation process in the presence of coating defects. The shape of the pore is quantified according to its aspect ratio (AR). The high aspect ratio pores present the characteristics of micro-cracks. High to moderate aspect ratio pores up to a value of one, corresponding to the unskewed pore, are considered. For wetting pores with AR close to one, the changes in breakthrough pressure are minimal. The breakthrough pressure changes significantly in the case of mixed-non-wetting pores. MNW pores with few coating defects are further investigated by varying the AR and determining the corresponding Laplace pressure for each case. The breakthrough pressure and the droplet volume at breakthrough have direct implication on water management, through their influence on liquid finger formation. The changes in breakthrough pressure with the aspect ratio point to the necessity to include the pore shape distribution in porous media models, to accurately predict the water transport behavior in the GDL.

Leak-Rate Through Carbon Brush Seals: Experimental Tests Versus Predictions From a Porous Medium Approach

Abstract This study presents a detailed comparative analysis between experimental leakage flow rates and numerical predictions for carbon brush seals with long bristles, utilizing a porous medium model approach. A series of tests were carried out on a static rig (without rotor rotation). The experimental setup allows tests under various interference conditions, revealing significant insights into the flow behavior through the brush seal. A numerical model based on the Darcy–Forchheimer equation is developed to interpret the complex flow dynamics within the brush seal, accounting for viscous, compressible, and inertial effects. The study evaluates the impact of brush deformation and porosity on flow resistance, leveraging experimental data to refine the numerical model parameters. This investigation not only deepens the understanding of brush seal flow physics but also improves the predictive accuracy of the numerical model in simulating operational conditions.

Numerical study on wave propagating characteristics through an offshore pile-net enclosure structure

Large-scale pile-net enclosures are increasingly utilized in marine engineering. However, simulating their interactions with waves remains a significant challenge. This study presents a numerical model that coupled porous media model and direct-forcing immersed boundary method to simulate the interaction between the pile-net enclosure structure and waves. The damping effect of the netting was simulated by porous media, while the pile was simulated using the direct-forcing immersed boundary method. The numerical model was verified based on experimental results obtained from corresponding physical model tests. Using the proposed numerical approach, this paper investigates the effects of wave period, net solidity, spacings of piles and wave incident angles on the hydrodynamic of the pile-net enclosure structure, including wave field and pile group coefficients. The results show that the pile-net enclosure structure demonstrates a damping effect on wave propagation, particularly for high-frequency waves. An increase in net solidity significantly impacts the wave forces on downstream piles. Additionally, the angle of incidence of the wave affects the orientation of the reflected wave crest line. When the piles are symmetrically positioned in pairs along the wave propagation direction, the wave height inside the structure decreases.

3D thermodynamics and parameters analysis of the external combustion hot blast stove

The external combustion hot blast stove is widely used in the steelmaking industry due to the advantage of providing a large amount of high-temperature and stable hot blast for blast furnaces. To research the thermal efficiency and stability of external combustion hot blast stoves, the non-equilibrium porous medium model coupled with transient thermal analysis is used to discuss the characteristics of two types of external combustion hot blast stoves during the cyclic operation process. In this paper, a comparison of the numerical data and in situ data during one cycle to ensure the accuracy of the calculation, which of the results showed that the temperature maximum relative error value is within 3%. The numerical results displayed that the velocity and temperature distribution of fluid are mainly affected by pressure, flow rate, cycle time, and geometric structure, where the hot blast temperature is affected by the cycle time but the distribution of velocity and relative pressure are affected by the height of hot blast branch. It can be concluded that the flow field and the structure of type A hot blast stove are more stable than that of type B by comparing the results of two types of hot blast stoves.

Analysis of the Vertical Dynamic Response of SDCM Piles in Coastal Areas

The stiffened deep cement mixing (SDCM) pile, as a new type of rigid–flexible composite pile, significantly enhances the vertical bearing capacity of traditional precast piles, thus holding broad application prospects in the substructure construction of nearshore bridges and marine energy structures. This paper investigates the vertical dynamic response of SDCM piles through theoretical derivation and parameter analysis. Firstly, based on elastic dynamics theory and the three-phase porous media model, vertical vibration control equations for both SDCM piles and fractional-order viscoelastic unsaturated soils are established. Secondly, theoretical derivations yield exact analytical solutions for the surrounding dynamic impedance, top dynamic stiffness, and dynamic damping of the SDCM pile. Finally, through numerical examples and parameter studies, the impact mechanisms of physical parameters in the SDCM pile–unsaturated soil dynamic coupling system on the top dynamic stiffness and dynamic damping of the SDCM pile are analyzed. The research results presented in this paper indicate that reducing the radius of the rigid core pile while increasing the thickness of the exterior pile has a positive effect on enhancing its vibration resistance. Additionally, increasing the length of SDCM piles contributes to improved vibration performance. However, an increase in the elastic modulus of the cement–soil exterior pile is detrimental to the vibration resistance of the rigid composite pile. On the other hand, an increase in the elastic modulus of the concrete core pile only enhances its ability to resist vibration under low-frequency load excitation. Furthermore, enlarging the soil saturation, decreasing the intrinsic permeability, and enlarging the soil relaxation shear modulus have a significant positive impact on improving the vibration resistance of SDCM piles. In contrast, changes in porosity have a negligible effect on the ability to resist vertical vibrations of SDCM piles.

Microvoiding and constitutive damage modeling with artificial neural networks

Continuum models of porous media have revolutionized computational fracture mechanics for traditional ductile materials, but the inherent assumptions have limited generalizability to other target materials or loading conditions. Here, we adopt a series of artificial neural networks (ANNs) to predict both the microscopic voiding characteristics (void shape, porosity) and macroscopic stress–strain constitutive response of porous elasto-plastic materials under various deformation states. We train the ANNs on a dataset generated from finite element models of 3D representative volume elements (RVEs), each containing a discrete spherical void, subjected to combinations of loading states. Results show that the data-driven model is capable of interpolative predictions as well as some levels of extrapolative predictions across a wide range of initial porosities (0–20%) and loading states outside of the training dataset, even at high deformation strains which induce extensive material softening and void growth. Through transfer learning, we further demonstrate that the ANNs, originally trained on a specific porous material dataset, can be readily adapted to other porous materials with substantially different properties through a significantly reduced training dataset. We discuss the implications of this machine learning approach vis-à-vis the extensively-developed Gurson model for porous material damage and failure predictions.

Pressure Drop in a Metal Foam Centrifugal Breather: A Simulation Approach

One of the main issues faced in the operation of a metal foam centrifugal breather is the high pressure drop. This study investigates the pressure drop of a metal foam centrifugal breather. The numerical simulation research method is adopted. The DPM model is used to calculate the two-phase flow field of the metal foam breather, and the porous medium model is used to replace the metal foam at the breather. The resistance caused by the metal foam is replaced by a distributed resistance added to the fluid. The effects of flow rate, rotational speed, porosity, PPI (pores per inch), and temperature on the pressure drop of the breather are analyzed. The results indicate that rotational speed, flow rate, porosity, and PPI significantly influence the resistance of the metal foam centrifugal breather. The resistance of the breather is directly proportional to the rotational speed, flow rate, temperature, and metal foam pore density, and inversely proportional to the porosity. Temperature has a minor impact on the resistance of the metal foam centrifugal breather. Therefore, the metal foam centrifugal breather is more suitable for low-speed operating conditions.

Characteristics and optimization strategy of microwave thermal regeneration of spent activated carbon based on a multi-physical field model

Microwave thermal regeneration is an efficient and low-consumption way to recycle spent activated carbon. However, traditional experimental approaches are difficult to analyze the electromagnetic field distribution in the microwave cavity, heat and mass transfer process of adsorbates, and optimization of the microwave reactor. Therefore, in this work, a multi-phase porous media model coupled with electromagnetism, heat and mass transfer is established to study the characteristics of microwave thermal regeneration procedure and to propose an optimization strategy for the microwave reactor. The results showed that the absorption of microwave by the sample can be strengthened by adjusting the width to height ratio of the waveguide. The optimal waveguide size (width:length = 80 mm:10 mm) increased the microwave utilization efficiency from 65.4 % to 98.5 %. In addition, the combination of rotary and intermittent microwave heating significantly optimized the temperature uniformity in both lateral and vertical directions and reduced the microwave heating time. The combined microwave heating time was reduced from the initial 136 s to 80 s, saving 41 % of energy consumption. The temperature difference of the sample was also reduced from the initial 536 K to 191 K, and the covariance COVT decreased from 0.52 to 0.24. The results provide a valuable technical guideline for the optimization of the microwave reactor in order to improve the regeneration efficiency and the quality of the regenerated carbon.

Three-dimensional CFD modeling for hollow fiber gas separation membrane modules based on a dual porous media model

Mathematical modeling is crucial to optimizing the design of the hollow fiber membrane (HFM) module. A Computational Fluid Dynamics (CFD) model enables efficient three-dimensional (3D) simulations of HFM modules, which integrates a dual porous media approach, significantly reducing computational costs. Validation against alternative simulations and experimental data confirms its prediction capability (<7% deviation). Comparative analyses demonstrate the superior reliability of the 3D approach over one-dimensional simulations. Detailed velocity, pressure, and concentration profiles for the shell and tube sides reveal optimization opportunities such as dead zones within the module. Aerometric studies show significant pressure drops (>30%) for smaller fiber diameters (<100μm) on the permeate side. The model's adaptability suggests broader applications in membrane gas separation processes with modifications. This research highlights the efficacy of CFD modeling in enhancing the design and optimization of HFM modules, highlighting the cost savings of the dual porous media approximation.

Dot-array porous medium model for windscreen and its simulation accuracy analysis

Porous medium models have long been prevalent numerical computation tools. Although they exhibit swift computational speed, their accuracy in simulating windscreen perforation structures is challenged. This paper introduces the innovative dot-array porous medium (DAPM) model, which accurately portrays the perforation structure and material characteristics of a windscreen by establishing virtual holes on the porous medium. Not only does it simplify modeling by eliminating complex perforation processes, but it also adeptly simulates the flow behavior of the windscreen. The comprehensive comparison between the DAPM model and the physical mesh model, traditional porous medium model, as well as wind tunnel test results, demonstrates that the DAPM model not only possesses rapid computational speed but also delivers outstanding precision in results. In terms of velocity distribution, vortex distribution, and flow intensity in the flow field, the model indicates a high level of accuracy, clearly exceeding that of the porous medium model. Moreover, the DAPM model showcases high versatility and adjustability in practical applications. By adjusting dimension parameters, it demonstrates the capability to precisely simulate any windscreen with holes arranged in a matrix pattern. This research provides an efficient and reliable tool for the numerical simulation of windscreens, with broad application prospects.