Porous Media Model Research Articles

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.

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.

Modeling of adsorption-controlled binary gas transport in ultratight porous media

Organic-rich ultratight porous media such as shales have complicated pore types and sizes, dictating their unique fluid transport and storage mechanisms. This paper introduces a diffusion-based binary gas (CH4 and CO2) transport model in such porous media, incorporating key transport and storage mechanisms. Binary gas mixture within the pore volume is divided into two domains: the free-phase and the sorbed-phase, both of which contribute to gas mass transport. Thermodynamic properties of the free phase are determined using the Peng-Robinson equation of state, while a modified extended Langmuir isotherm describes the sorbed phase. The bulk diffusion, Knudsen diffusion, and viscous diffusion are reconciled to describe binary gas transport in the free phase, while the surface diffusion is considered in the sorbed phase. The mass flux is finally related to the effective diffusion coefficient and the free-phase concentration gradient through coupling all transport mechanisms via the equivalent resister network model. The governing equations are solved numerically using a finite difference approach to simulate co-diffusion and counter-diffusion of a binary gas mixture in two nanoporous media, shale and coal.The results reveal that surface diffusion is more pronounced in coal than in shale due to coal's higher adsorption capacity. In co-diffusion cases, both free-phase and sorbed-phase concentrations decrease over time. However, the decline of sorbed-phase concentrations is slower than that of the free-phase. Moreover, CO2 tends to remain adsorbed within the coal matrix due to its stronger adsorption affinity, unlike CH4, which is more likely to flow out. In counter-diffusion cases, injected CO2 first accumulates near the fracture region and then diffuses further into the matrix. Despite shale's pore volume being twice that of coal, similar amounts of CO2 are injected, which can be attributed to coal's higher CO2 adsorption capacity.

On the influence of matrix flow in the hydraulic permeability of rough-walled fractures

Fractured porous media models may account for the influence of matrix flow in fracture permeability estimates through the slip boundary condition effect, i.e. permeable walls allow fluid to flow along them without viscous resistance. However, matrix flow may also create fluid pathways that unlock further fracture flow capacity, thus increasing its overall apparent permeability. We investigate this effect through numerical experiments by simulating fluid flow in a single fracture-matrix system with varying matrix permeability and calculating the apparent fracture permeability. We observe a consistent increase in fracture permeability with matrix permeability, which is yet underestimated by analytical models that factor in slip boundary conditions. Our study highlights the critical role of the surrounding porous matrix in accurately determining fracture permeability to prevent underestimations of the flow capacity of fractured porous media.

COMPARATIVE STUDY USING CFD OF COUNTER-CURRENT AND CO-CURRENT HYDROTREATING REACTORS USING JATROPHA CURCAS L VEGETABLE OIL

In this work, mathematical modeling and CFD simulation of two countercurrent and cocurrent hydrotreatment reactors were carried out, validating the results with a drained bed reactor (TBR), a commercial CoMo/γ-Al2O3 catalyst was used, the material the raw material was Jatropha Curcas L vegetable oil. The operating conditions were temperature 380 ° C, pressure 8 MPag. The kinetic model that was used considered 13 reactions that involve processes of decarboxylation, decarbonization, hydrodeoxygenation and hydrocracking reactions for triolein and tristearin triglycerides. The CFD simulation was carried out in Fluent 18.2 in a transient state and in 3D, considering the standard κ - ε turbulence models, Eulerian multiphase model and porous medium model, it was shown that the countercurrent reactor has less pressure drop than the countercurrent, the conversion the countercurrent reactor has a greater conversion of reactants of 99%, the generation of products from the countercurrent reactor has higher concentrations than the cocurrent reactor, this is because it has more contact areas between phases in the reactor.

Modeling CSF circulation and the glymphatic system during infusion using subject specific intracranial pressures and brain geometries

BackgroundInfusion testing is an established method for assessing CSF resistance in patients with idiopathic normal pressure hydrocephalus (iNPH). To what extent the increased resistance is related to the glymphatic system is an open question. Here we introduce a computational model that includes the glymphatic system and enables us to determine the importance of (1) brain geometry, (2) intracranial pressure, and (3) physiological parameters on the outcome of and response to an infusion test.MethodsWe implemented a seven-compartment multiple network porous medium model with subject specific geometries from MR images using the finite element library FEniCS. The model consists of the arterial, capillary and venous blood vessels, their corresponding perivascular spaces, and the extracellular space (ECS). Both subject specific brain geometries and subject specific infusion tests were used in the modeling of both healthy adults and iNPH patients. Furthermore, we performed a systematic study of the effect of variations in model parameters.ResultsBoth the iNPH group and the control group reached a similar steady state solution when subject specific geometries under identical boundary conditions was used in simulation. The difference in terms of average fluid pressure and velocity between the iNPH and control groups, was found to be less than 6% during all stages of infusion in all compartments. With subject specific boundary conditions, the largest computed difference was a 75% greater fluid speed in the arterial perivascular space (PVS) in the iNPH group compared to the control group. Changes to material parameters changed fluid speeds by several orders of magnitude in some scenarios. A considerable amount of the CSF pass through the glymphatic pathway in our models during infusion, i.e., 28% and 38% in the healthy and iNPH patients, respectively.ConclusionsUsing computational models, we have found the relative importance of subject specific geometries to be less important than individual differences in resistance as measured with infusion tests and model parameters such as permeability, in determining the computed pressure and flow during infusion. Model parameters are uncertain, but certain variations have large impact on the simulation results. The computations resulted in a considerable amount of the infused volume passing through the brain either through the perivascular spaces or the extracellular space.

Analysis and structure optimization of the flow and temperature fields of the large-scale hot air drying room

Large-scale hot air drying rooms play a crucial role as efficient drying equipment across various industries. The uniform distribution of hot air is a crucial factor influencing the drying quality of large-scale hot air drying rooms. This study focuses on camellia seeds as the drying subject. Building on a porous media model and the drying kinetics of camellia seeds, a CFD model of the drying room was established. Three-dimensional simulations of the internal flow and temperature fields were performed using CFD software, and the simulated results aligned well with experimental data. To improve the uniformity, this study introduced an optimized design featuring a combination of a Type E3 air guide hood with five guiding plates and a fan, selected based on optimized angles (θ1 = 5°, θ2 = 10°). Under the condition of improving the structure without introducing a new heat source, the optimization ensured a significant improvement in flow field uniformity while making the temperature field closer to the desired ideal temperature. This offers a reference for the design and research of hot air drying equipment and hot air drying rooms.

Application of Deep Neural Network Technology for Multi‐scale CFD Modeling in Porous Media

Application of Deep Neural Network Technology for Multi‐scale CFD Modeling in Porous Media

Wave propagation through a dense cluster of cylinders: a radiative transfer model

Clusters of cylinders are a useful way to model the wave propagation through several natural and complex media: crowds of people, forests, arrays of scatterers, or various materials. Depending on the absorption properties of the cylinders, as well as their size- and distance-to-wavelength ratio, different physical mechanisms are at play: scattering, viscous and thermal dissipation, absorption within the material of the cylinders themselves. We consider the low frequency case when the wavelength is larger than both the cylinder diameter and spacing. Most multiple scattering theories require larger than wavelength spacing and are not applicable in the case of dense clusters and at low frequencies. As a first approximation, a porous medium model is used to calculate the speed of sound in the cluster. However, this approach does not readily give access to the coherency of the signal. Recently, a radiative transfer approach was used to model forest acoustics to examine the transformation of the coherent sound field into an incoherent sound field. We use this approach to examine the coherent to incoherent field transition depending on the wavelength to diameter and spacing.

Numerical investigation on the core thermal hydraulic behavior of pool-type sodium-cooled fast reactor (SFR)

A thorough understanding of the reactor core thermal hydraulic behavior is essential for the design and safety analysis of Sodium-cooled Fast Reactors (SFR). Due to the application of hexagonal subassembly, the core thermal hydraulic behavior is significantly affected by the flow field within the subassemblies, the inter-wrapper region and the hot pool. Analysis of the core thermal hydraulic behavior requires a model coupling the three regions mentioned above, which has been identified as one of the thermal hydraulic challenges in SFR. In the present study, a 3D model that covers the three regions was developed for the core of the China Experimental Fast Reactor (CEFR) with the Computational Fluid Dynamic (CFD) code, Fluent. The inter-wrapper region and the hot pool were modeled in detail, while the subassemblies were modeled with a special porous medium model. The core thermal hydraulics behavior under steady state was studied, more specifically, information for the flow field distribution at the core outlet, the inter-wrapper flow and the duct wall temperature distribution was obtained. Under steady state, liquid sodium in the inter-wrapper region is supplied by the inner region of the hot pool. And it enters the inter-wrapper region from the core outer region and returns back to the hot pool inner region from the core central region. The inter-wrapper flow is cooled by non-fuel subassemblies and heated up by fuel subassemblies. For non-fuel subassembly, the ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies could reaches 96%; for fuel subassemblies, the maximum ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies is 2.45%. Significant temperature gradients have been observed on the duct wall, with maximum values of 156.69 K/m in the vertical direction and 2,196.00 K/m in the circumferential direction. The largest temperature gradient appears on the duct of subassemblies adjacent to the transition region of fuel subassemblies and non-fuel subassemblies.

Stabilized equal lower-order finite element methods for simulating Brinkman equations in porous media

This paper demonstrates the mixed formulation of the Brinkman problem using linear equal-order finite element methods in porous media modelling. We introduce Galerkin least-squares (GLS) and least-squares (LS) finite element methods to address the incompatibility of finite element spaces, treating velocity, pressure, and vorticity as independent variables. Theoretical analysis examines coercivity and continuity, providing error estimates. Demonstrating resilience in theoretical findings, these methods achieve optimal convergence rates in the L 2 norm by incorporating stabilization terms with low-order basis functions. Numerical experiments validate theoretical predictions, showing the effectiveness of the GLS method and addressing finite element space incompatibility. Additionally, the GLS method exhibits promising capabilities in handling the Brinkman equation at low permeability compared to the LS method. The study reveals an increase in the average pressure difference in the Brinkman problem compared to the Stokes equations as the inlet velocity rises, providing insights into the behaviour of Brinkman equations.

Adaptability analysis of flow and heat transfer multi-scale numerical method for printed circuit heat exchanger

The printed circuit heat exchanger (PCHE) is a high-efficiency and compact mini-channel heat exchanger. Due to the large number of fine channels, it is difficult to conduct the flow and heat transfer numerical simulation of the entire heat exchanger based on the actual channels, which requires a lot of computational resource and time. In this paper, a simplified multi-scale numerical method with a non-equilibrium porous media model (NOPM) is proposed to study the flow and heat transfer performance of PCHE at high temperature and pressure. The pressure field, velocity field and temperature field of NOPM and actual multi-channel model (MC) under different working conditions are compared to study the adaptability of NOPM for the PCHE. The results indicate that the NOPM can accurately predict the flow and heat transfer performance under PCHE configurations with a large number of channels. However, as the channel number decreases, the relative errors in the temperature and pressure prediction significantly increase due to the increased flow maldistribution. Similarly, the NOPM can well predict the overall temperature distribution of the PCHE solid when the channel number is numerous. This work could support accurate thermal design, and provide accurate temperature field for the thermal stress analysis of PCHE.

Internal flow analysis and design optimization of a membrane oxygenator

Abstract The membrane oxygenator is an essential component in the Extracorporeal Membrane Oxygenation (ECMO) system to offer temporary support to the respiratory system. This study aims to optimize the hemodynamic performance and reduce the thrombosis risk of a membrane oxygenator prototype using computational fluid dynamics. Numerical simulations of steady laminar flow in a full-scale oxygenator prototype (model 1) and two optimized structure Models 2 and 3 at flow rates of 5∼7L/min are carried out using the porous media model. Flow-field-based hydraulic performance indicators and the thrombus risk indicator of the three models are compared extensively. Detailed internal flow analysis revealed that adverse flow states such as insufficient flow circulation in the inlet shunt cone zone, large flow separations at the top corners of heat exchangers, and intensive flow impingement at the exit elbow tube are notably improved in the optimized model 2 and 3. The improvement is more significant at high flow rates. Performance parameters quantitatively validate the effect of optimized configurations. Specifically, at a flow rate of 7L/min, the flow uniformity indexes for the original model at the shunt cone exit increase from 0.884 to 0.923 and 0.890 in the two modified models. The total pressure loss is reduced by over 14%, and maximum wall shear stress is notably reduced from 241.46Pa to 135.9Pa. Additionally, the optimized models exhibited lower thrombus risk. The optimized designs emphasize the importance of smooth transitions between cross-sections and minimizing abrupt changes in flow direction. The employment of flow-field-based parameters allows for the establishment of the relationship between geometric and performance parameters to guide effective design optimization and ensure the safe clinical operation of oxygenator prototypes.

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.

Heat transfer enhancement in pressurized solar cavity receivers with densely packed metallic wire mesh

Pressurized solar receivers are promising candidates as heat sources for integration with high-efficiency closed-loop air and supercritical carbon-dioxide based Brayton cycles. This paper focuses on the heat transfer enhancement of such a solar receiver using inline stacked wire mesh fibers in the heat transfer fluid flow path. The study involves modelling, characterization, and performance evaluation of a cavity-receiver with densely packed wire meshes. A new experimentally validated hybrid numerical approach is presented for modelling the inline stacked wire mesh layers. Initially, a direct numerical simulation at the pore scale on a representative elementary volume (REV) of the wire mesh geometry is performed for determining the hydrodynamic and thermal characteristics of the medium. Subsequently, these hydrodynamic and thermal properties are used to define a volume-averaged macroscopic porous medium. Experiments are performed using a rectangular channel stacked with stainless steel wire meshes, heated using a plate heater, and pressurized air supplied using a reciprocating compressor. Both numerical and experimental studies are performed for a Reynolds number range of 28 to 213 resulting in a Nusselt number range of 7.2 to 213. The porous medium model predictions for pressure gradient are within 17 %, while predictions for outlet air temperature are within 5 % of the experimentally obtained values. The study predicts a maximum heat transfer enhancement of five times in a channel stacked with wire meshes compared to the case of a clear channel, but incurring a peak pressure drop of only about 1.1 kPa.

Prediction of Leakage Flow Rate and Blow-Down in Brush Seals via 2D CFD Simulation with Porosity Correction

Brush seals are extensively used in rotating equipment, such as gas turbines and compressors, providing effective sealing while accommodating radial, axial, and angular movements between components. In this study, the performance of brush seals with and without clearances was predicted through axisymmetric 2D computational fluid dynamic (CFD) simulations using a porous media model. Because the accurate modeling of a brush seal requires the appropriate porosity to be determined and the flow resistance to be calculated, a porosity correction was performed based on the brush seal’s geometry and pressure ratio. The corrected porosity was then used to calculate the flow resistance and the leakage flow rate was predicted. Based on the results, the corrected porosity significantly improved the accuracy of the previously unreliable leakage flow rate predictions, regardless of the presence of clearances. For cases with a clearance, the blow-down effect was determined through CFD simulations for the given geometry and was compared with experimental data. The leakage flow rate predictions were highly accurate, with a relative error of less than 5% across a pressure ratio range of 1.5–4.

Drying model and drying characteristic analysis of multiphase porous medium for flake materials

The main purpose of this paper is to optimize the drying process and gain a fundamental understanding of the movement of different phases during the drying process of cigarette flakes. Therefore, the drying model of a multiphase porous medium for cigarette flakes has been established in this paper. Binary diffusion of water vapor and gas pressure transport, as well as capillary diffusion of liquid water and gas pressure transport, are considered in this model. The non-equilibrium equations are used to calculate the evaporation rate, and the fluxes of water vapor and liquid water are also obtained. The results indicated that the stochastic stacking model is suitable for studying cigarette flake drying. Because water evaporation absorbs more heat than hot air, the temperature of the cigarette flakes decreases during the drying process. The water activity, vapor density, and vapor mole fraction of the medium layer of cigarette flakes were significantly higher than those of the upper and lower layers. The highest water vapor and liquid water fluxes occur in the medium of the drying process. Additionally, it was observed that the saturated vapor pressure was higher than the equilibrium vapor pressure and steam pressure, non-equilibrium evaporation occurs in the medium of drying. The correlation between the evaporation rate and the drying temperature and humidity of the cigarette flakes was found to be positive.

Two-Phase Incompressible Flow with Dynamic Capillary Pressure in a Heterogeneous Porous Media

We prove the existence of weak solutions of a two-incompressible immiscible wetting and non-wetting fluids phase flow model in porous media with dynamic capillary pressure. This model is a coupled system which includes a nonlinear parabolic saturation equation and an elliptic pressure–velocity equation. In the regularized case, the existence and uniqueness of the weak solution are obtained. We let the regularization parameter be η→0 to prove the existence of weak solutions.

Investigation of smoothed particle hydrodynamics (SPH) method for modeling of two-phase flow through porous medium: application for drainage and imbibition processes

The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.