Porous Media Model Research Articles

Dual scale porous medium model of lung congestion caused by tuberculosis

Dual scale porous medium model of lung congestion caused by tuberculosis

Numerical study of the particle-scale heat transfer in the HTR-PM pebble bed based on GPU-DEM

An essential aspect of the design of a pebble bed high-temperature gas-cooled reactor (HTGR) is the consideration of heat transfer. A particle-scale heat transfer model was developed based on the previous GPU-DEM numerical model. This model includes the heat conduction of the particles in contact, the radiative heat transfer among particles, and unidirectional convection heat transfer in the flow field. The comparison of the predicted results with the results of the TF-PBEC experiment demonstrates the accuracy of the conduction and radiation modules within the current model. Based on the current model and the porous media model, a numerical study of the natural convection heat transfer in the High-Temperature gas-cooled Reactor-Pebble-bed Module (HTR-PM) after reactor shutdown is performed. This paper systematically introduces the model design, pebble bed generation, flow field calculation, and heat transfer simulation. The results indicate that natural convection contributes to removing residual heat in the reactor core, and a higher pressure leads to better convection heat transfer. At extremely low Reynolds numbers (Re < 10), convection heat transfer is comparable to conduction and radiation, while for pressurized pebble beds (Re = 50–500), convection heat transfer dominates. Furthermore, the influence of different models used to calculate the Nusselt number of the results is compared and analyzed. For most cases, the differences in the temperature distribution of the pebble bed obtained from the different correlations are minor. However, the impact of porosity on the local Nusselt number cannot be ignored in the extremely low Reynolds numbers flows. Overall, the particle-scale heat transfer model can provide more effective reference information for the design and construction of an HTGR.

Numerical investigation to predict the impact of pre-heated air on the tar formation of cocoa pod husk gasification in a fixed bed downdraft gasifier

Tar production is a critical aspect of gasification thermochemistry, and it hinders the widening of biofuel utilisation in several applications. Both the gasifier configuration and the operating conditions influence the quantity of tar in PG. Since temperature plays a major role, this study examines the performance parameters of a gasifier across a spectrum of input air temperatures, from 27 to 627 °C, utilising computational fluid dynamics with species transport and porous media models. Since the deviation of numerical predictions from experimental results is within 10 %, the model's validity is confirmed. CO and H2 gas production increased from 19.23 % to 27.12 % and 9.23 %–16.2 %, respectively, over the tested air temperature range; however, the variation in methane content was not significant. Furthermore, the higher heating values of PG and cold gas efficiency were found to be 5–6.8 MJ/Nm3 and 65–69 %, respectively. The study also investigates reaction rates for gasification, combustion, and volatiles' breakdown under various operating conditions. Among the tar species studied, benzene is the most concentrated at 1.6 g/Nm3, followed by toluene at 0.9 g/Nm3, with naphthalene and phenol present in comparatively smaller amounts. Furthermore, the research indicates that an appropriate temperature of gasifying medium can control tar in PG.

Non-equilibrium overlapping grid method with two-phase porous media model for printed circuit heat exchanger based steam generator

The printed circuit heat exchanger (PCHE) is a promising alternative for the once-through steam generator (OTSG) of small modular reactors due to its compact structure and high efficiency. To study the effect of flow maldistribution on the performance of heat transfer and thermal stress, it is necessary to conduct three-dimensional full-scale simulation of two-side fluid and solid domains in the printed circuit heat exchanger based steam genarator (PCHESG). However, there is a lack of mature thermal-hydraulic models for the PCHESG. This work proposes a non-equilibrium overlapping grid method with two-phase porous media model for the PCHESG. The temperature and flow fields of the PCHESG under high-pressure conditions are evaluated. Compared to traditional methods, the new method greatly reduces the order of magnitude of the grid number from 107∼109 to 106 and the computational time from days to hours. It is found that the flow maldistribution with a threshold cold-side mass flow rate of 0.08∼0.0944 kg/s induced by the header parts of the PCHESG deteriorates the total heat transfer rate by 58.8 % and increases the spatial non-uniformity of the temperature and phase distributions. The solid domain is solved simultaneously and its temperature non-uniformity becomes significant with a threshold cold-side mass flow rate of 0.04∼0.06 kg/s. The results demonstrate that this method has great potential in achieving rapid design and optimization for the PCHESG.

Numerical study on formation characteristics of particle-crystal mixed fouling in the heat exchanger tube

A mixed fouling prediction model is developed to investigate the problem of heat exchanger fouling in cooling water systems, which considers the particle-crystal mixed fouling deposition and evolution processes. As the fouling thickness exceeds the fluid cell height, the fluid cell is converted into a porous media cell to represent the fluid flow in the fouling layer. The mixed fouling layer growth and evolution are simulated using the porous media model and a user-defined program. The fouling resistance obtained from the model agrees well with the experimental data in the literature. Additionally, the fouling thickness distribution on heat transfer surfaces is predicted. The differences between mixed fouling and single fouling are compared. Then the effect of fluid parameter variations on fouling characteristics is investigated within the heat exchange channel. The results show that fouling accumulates at the end of the pipe, exhibiting a distribution trend of being thin at the front and thick at the back. Moreover, the risk of fouling formation significantly increases with increasing inlet temperature, concentration and heat flux, while high inlet velocity leads to small fouling resistance. The asymptotic value of fouling resistance decreases by 59.1% when the inlet velocity increases from 0.25 to 0.65 m/s.

Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

The integration of a composite of porous medium with phase change material (PCM) offers significant advantages in thermal management systems, enhancing heat transfer efficiency and addressing various thermal regulation challenges. This approach utilizes the PCM's latent heat absorption and the enhanced thermal conductivity provided by the porous medium, resulting in optimized system performance. Its applicability spans across electronics cooling and building insulation systems. However, predicting the thermal behavior of this composite material is challenging, necessitating computational tools to anticipate its response under different conditions and evaluate its influence on cooling strategies. The objective of this study is to create a computational tool specifically tailored to evaluate constitutive parameters of this composite material, thereby providing a comprehensive description of its thermal behavior. To achieve this goal, the multiscale homogenization principle is employed to assess the composite's effective thermophysical material properties using the representative volume element approach. The repeating unit cell of the aluminum lattice is incorporated into the PCM to define a representative volume element. The finite element method (FEM) is utilized to solve the three-dimensional homogenization problem, yielding an orthotropic effective thermal conductivity due to the inherent symmetry of the repeating material cell. Moreover, the study leverages the apparent heat capacity method to effectively manage the phase transitions within the PCM domain, utilizing smooth and temperature-dependent functions to accurately describe the thermophysical properties of the PCM. Integrating the composite into battery pack thermal management, this study thoroughly examines thermal dynamics by comparing outcomes with and without PCM integration. The transient thermal problem is accurately tackled using the FEM, employing the evaluated effective constitutive parameters of the homogenized composite to minimize computational effort. The results indicate a notable decline in the highest temperatures of the battery pack, leading to a reduction of about 14 °C at the specific moment when the phase change material fully transitions into its liquid form. The obtained results emphasize the effectiveness and practical feasibility of the proposed thermal management strategy. The modeling approach presented provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, as the utilization of the homogenization technique notably decreases the computational time.

Brush Seal Performance with Ideal Gas Working Fluid under Static Rotor Condition

The study investigated how variations in pressure ratio affect the leakage flow of a brush seal for both contact and clearance structures, in which the clearance is measured as the distance between the bristles tip and the rotor surface. This investigation utilized the Reynolds-Averaged-Navier–Stokes (RANS) equations alongside a two-dimensional axisymmetric anisotropic porous medium model. To verify the model’s accuracy and dependability, the obtained results were compared with previous numerical results and experimental observations, showing a satisfactory level of agreement. The results indicate that the predominant pressure drop occurs downstream of the bristle pack with the clearance model exhibiting a higher leakage rate compared to the contact model. Leakage increases proportionally with the pressure ratio, while axial velocity gradually rises and radial velocity experiences a significant increase. In conclusion, the leakage in the brush seal contact structure is significantly lower than in the clearance structure, resulting in the best performance.

Long-time behaviour of a porous medium model with degenerate hysteresis.

Hysteresis in the pressure-saturation relation in unsaturated porous media, owing to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. As an extension of previous existence and uniqueness results, we prove that under physically admissible initial conditions and without mass exchange with the exterior, the unique global solution of the fluid diffusion problem exists and asymptotically converges as time tends to infinity to a possibly non-homogeneous mass distribution and an a priori unknown constant pressure.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

A true double-body method based on porous media model for simulation and froude scaling verification of an aquaculture vessel resistance

A blueprint of a novel aquaculture vessel composed of rectangular cylinders, pontoons, and nets with the capacity for self-propulsion was drawn. However, when completely different flow features are caused by non-stream shapes, resistance prediction cannot be accurately performed through conventional ship model experiments as the existing scale rules may be invalid. Besides, the existence of nets creates obstacles not only in model tests but also in numerical simulations. Therefore, resistance evaluation of the vessel with nets is very challenging. Porous media model for nets is one of feasible solutions and was validated by previously published experimental results, although a control volume was required. However, porous media model is incompatible with volume of fluid multiphase, which makes the double-body method adopted inevitably. A literally true double-body method based on porous media model was proposed. The comparison of vessels with and without a net exhibited a beneficial interaction between the net and the vessel hull, especially for nets with higher solidity. Furthermore, the Froude scaling law was adopted based on the hypothesis of Reynolds number invariance. All the full-scale resistances predicted by it in seven scale ratios demonstrated satisfactory consistency, and the relative errors grew with the increase of the scale ratios.

Enhancing Computational Efficiency in Porous Media Analysis: Integrating Machine Learning with Monte Carlo Ray Tracing

Abstract Monte Carlo ray tracing (MCRT) has been a widely implemented and reliable computational method for calculating light-matter interaction in porous media, the computational modeling of porous media and performing MCRT becomes significantly expensive when dealing with intricate structures and numerous dependent variables. Hence, Machine Learning (ML) models have been utilized to overcome computational burdens. In this study, we investigate two distinct frameworks for characterizing radiative properties in porous media for pack-free and packing-based methods. We employ two different regression tools for each case, namely Gaussian process regressions for pack-free MCRT and Convolutional Neural Network (CNN) models for pack-based MCRT to predict the radiative properties. Our study highlights the importance of selecting the appropriate regression method based on the physical model, which can lead to significant computational efficiency improvement. Our results show that both models can predict the radiative properties with high accuracy (&amp;gt;90%). Furthermore, we demonstrate that combining MCRT with ML inference not only enhances predictive accuracy but also reduces the computational cost of simulation by more than 96% using the GP model and 99% for the CNN model.

Simulation of flow and heat transfer in high‐temperature and high‐pressure reservoir based on multi‐physical field coupling model at pore scale

AbstractThe use of irregular pore‐scale models to study heavy oil reservoirs with high‐temperature, high‐pressure, and high‐stress characteristics is effective. Previous studies have typically focused on regular models and conventional environmental reservoirs, with limited exploration of irregular models and reservoirs in extreme environments. In investigating the process of water displacing heavy oil within reservoirs under high‐temperature, high‐pressure, and high‐stress conditions at the pore scale, the utilization of the four‐parameter method creates a micro‐scale irregular porous media model. The model systematically considers the variation of physical properties of rocks and heavy oil with temperature. The results indicate that an appropriate increase in water injection rate or a decrease in reservoir contact angle will increase the recovery rate, temperature, and stress of the reservoir. At a displacement time of 0.3 s, with the water injection rate increasing from 0.004 to 0.01 m ∙ s−1, the reservoir's recovery degree experiences an increase of 0.091. Simultaneously, the average temperature and average stress of the reservoir increase by 29.66 K and 1.9464 × 109 N · m−2, respectively. At a displacement time of 0.3 s and with the contact angle decreasing from 2π/3 to π/3, the reservoir's recovery degree increases by 0.44537, and the average temperature and average stress of the reservoir increase by 2.87 K and 1.86 × 108 N · m−2, respectively.

Investigation on uneven flow distribution in triply periodic minimal surface heat exchangers

The development in manufacturing engineering has made it possible to adopt the unique porous structure known as the triply periodic minimal surface to increase energy efficiency in a variety of energy-related sectors. With the unique morphological characteristics, triply periodic minimal surface exhibits remarkable mechanical strength and thermal performance, which makes it a potential candidate for compact, high-performance heat exchanger constructions. In this study, a theoretical model based on triply periodic minimal surface porous media is developed. Based on the hypothesis that the triply periodic minimal surface is isotropic and the heat transfer intensity of fluid and solid is uniform throughout the core of the heat exchanger, the simulation of the full-size heat exchanger is simplified by using a porous media model. The flow distribution characteristics of triply periodic minimal surface heat exchangers, as well as the effect mechanism of key factors, including the channel porosity, header configuration, the type of triply periodic minimal surface, the core length and Reynolds number on the flow distribution performance, are investigated. A dual-header configuration is proposed to improve the flow uniformity of triply periodic minimal surface heat exchangers. The results indicate that the flow distribution performance of triply periodic minimal surface based heat exchangers can be enhanced by the reduction of channel porosity. When the cold-side porosity is 0.7, the flow rate deviates from the mean value by 220% at its maximum for a Primitive heat exchanger. A dual-header configuration eliminates the columnar extreme high velocity space in the core and greatly reduces the “weak zone” of flow distribution, which improves the flow non-uniformity by 45–90% over the single-inlet headers. This paper provides data and theoretical support for the optimal design and practical application of the complex, high-performance triply periodic minimal surface based heat exchangers.

Research on Oil and Gas Adsorption Optimization Based on CFD Modeling and Process Simulation.

In the process of oil extraction and refining, some of the liquid light hydrocarbon components will inevitably evaporate into the atmosphere, causing serious air pollution and safety hazards. This paper is focused on oil and gas adsorption systems to comprehensively optimize key parameters by combining computational fluid dynamics (CFD) modeling with process simulation, enabling the efficient treatment of hazardous materials. First, a CFD model of the hydrocarbon adsorption process is established to the porous media model by a user-defined function (UDF). Subsequently, the mass transfer process of oil and gas in porous media is successfully simulated to obtain the gas distribution in an industrial fixed bed adsorption tower. The adsorption tank is intensified, and the gas distribution in the tank is improved by optimizing the height-to-diameter ratio of the equipment and the design of the intake distributor. Third, the cyclic two-tank adsorption model of the pressure swing adsorption (PSA) process is established for key parameters optimization. Finally, the operating parameters and conditions of the PSA process are suspected by considering five factors affecting the adsorption efficiency: adsorption time, adsorption pressure, adsorption temperature, feed flow rate, and purge ratio of the washing step.

Study on flow field of oil‐cooling permanent magnet synchronous motor with hairpin winding using porous medium model

AbstractThe oil cooling method has been widely used in the permanent magnet synchronous motor with hairpin winding. Because of the irregular shape of the hairpin end winding, there are complex oil circuits in the fluid domain, resulting in a large number of grids and a high computational cost. It is still a challenge to calculate the oil‐cooling performance of the hairpin end winding. Therefore, the porous medium model (PMM) is first proposed to replace the real hairpin end winding to analyse the oil‐cooling performance. By comparing oil volume fraction and velocity at different oil‐supplied conditions using three methods: experiments, real model (the non‐equivalent fluid domain model based on the real hairpin end winding) and PMM, the feasibility of using the PMM to calculate the oil‐cooling performance on the end winding is verified. The oil distribution of three methods is the same. The use of the PMM saves 80% of the number of grids, which improves the simulation efficiency. Relationships between the porosity, permeability and resistance coefficient and the geometry parameters of windings are determined. The results show that the flow field changes greatly with changes in porosity, permeability and resistance coefficient.

A Method to Evaluate Forchheimer Resistance Coefficients for Permeable Screens and Air Louvers Modelled as a Porous Medium

Porous medium models are commonly used in Computational Fluid Dynamics (CFD) to simulate flow through permeable screens of various types. However, the setup of these models is often limited to replicating a pressure drop in cases where fluid inflow is orthogonal to the screen. In this work, a porous medium formulation that employs a non-diagonal Forchheimer tensor is presented. This formulation is capable of reproducing both the pressure drop and flow deflection under varying inflow angles for complex screen geometries. A general method to determine the porous model coefficients valid for both diagonal and non-diagonal Forchheimer tensors is proposed. The coefficients are calculated using a nonlinear least-squares optimisation based on an analytical solution of a special case of the Navier–Stokes equations. The applicability of the proposed method is evaluated in four different scenarios supplemented by local CFD simulations of permeable screens: wire mesh, perforated screens, air louvers, and expanded mesh panels. The practical application of this method is demonstrated in the modelling of windbreaks and permeable double-skin facades, which typically employ the aforementioned types of porous screens.

Mathematical Modeling of Transient Submerged Entry Nozzle Clogging and Its Effect on Flow Field, Bubble Distribution and Interface Fluctuation in Slab Continuous Casting Mold

Submerged entry nozzle (SEN) clogging will affect the production efficiency and product quality in the continuous casting process. In this work, the transient SEN clogging model is developed by coupling the porous media model defined by the user-defined function (UDF) and the discrete phase model (DPM). The effects of the transient SEN clogging process on the flow field, the distribution of argon gas bubbles and the fluctuation of the interface between steel and slag in the concave bottom SEN in the continuous casting slab mold with a cross-section of 1500 mm × 230 mm are studied by coupling transient SEN clogging model, DPM and volume of fluid (VOF) model. The results show that the actual morphology and thicknesses of SEN clogging are in good agreement with the numerical simulation results. The measurement result of the surface velocity is consistent with the numerical simulation result. With increasing the simulation time, the degree of SEN clogging increases. The flow velocities of molten steel flowing from the outlet of the side hole increase, because the flow space is occupied with the clogging inclusions, which leads to the increased number of argon gas bubbles near the narrow wall. The steel–slag interface fluctuation near the narrow walls also increases, resulting in the increased risk of slag entrapment.

Constructing a Microdiffusion-Seepage-Stress Multifield Coupling Model for Nanopore Gas.

Existing research is difficult to fully capture the correlation between gas molecules and pore wall interactions, multiphase flow, and stress distribution in nanopores. Taking gas as an example, a microscopic model was constructed. At the same time, diffusion, seepage, and stress were considered to accurately predict and manage gas transport in nanopores. First, molecular dynamics (MD) simulation methods were adopted to simulate the motion trajectories and interactions of gas molecules in nanopores. Second, a multiscale model was established based on continuum mechanics to consider the interaction between pore walls and gas molecules, and a diffusion equation was established to describe the diffusion process of gas molecules in pores. Then, finite element analysis and porous media models were used to simulate the seepage behavior of gas in the nanopores. Finally, the stress distribution in the pores was analyzed, and the influence of the interaction between the pore wall and gas molecules on stress was considered. The multifield coupling model was experimentally evaluated from three aspects: diffusion coefficient, seepage behavior, and stress distribution. The root-mean-square error (RMSE) and mean absolute error (MAE) of the model in different testing directions were calculated using different simulation tools, such as COMSOL, ANSYS, OpenFOAM, and CFX. The mean values of RMSE and MAE were lower than 0.20 and 0.17, respectively. The constructed model can comprehensively describe gas transmission within nanopores, improving the management accuracy and efficiency.

Numerical assessment of thermomagnetic convection of ferrofluid in a porous cavity employing a local thermal nonequilibrium model

Utilizing a two-temperature model, this study investigates the thermomagnetic convection of a ferrofluid within a porous cavity. The cavity is heated from the bottom and cooled from the sides to establish thermo-gravitational convection, whereas the thermomagnetic convection is induced by permanent magnets. The equations that govern flow and heat transfer are discretized using the finite volume method and the SIMPLE algorithm. The first part of the study evaluates the impact of the permanent magnet’s position on the flow pattern and ferrofluid and solid temperature fields. The results showed that positioning the magnet at the bottom of the cavity enhances heat transfer rate. The second part investigates the impact of the distance between two magnets at different magnetic, Rayleigh, and Darcy numbers, as well as the conduction ratio. The numerical findings exhibit that the heat transfer rate attains a peak at a certain distance between the magnets, depending on the Rayleigh number. With increasing Rayleigh number and conduction ratio, or decreasing Darcy number, the role of the magnetic field in improving heat transfer becomes less important. It is observed that thermomagnetic convection is replaced by thermo-gravitational one at high conduction ratios. The study emphasizes the need to use a local thermal non-equilibrium model in porous media with high magnetic and Darcy numbers, as well as large conduction ratios, to accurately capture the heat transfer phenomenon. It is observed that by placing two magnets at an appropriate distance, the heat transfer rate could be augmented by more than 136 %.

Hydrodynamic interactions between the cylinder and nets of a typical offshore aquaculture structure in steady current: Numerical investigation and coupling mechanism

The expansion of aquaculture fish farms into deep sea has become a trend today. Several new types of offshore fish farming structures have been designed and tested in real sea, a typical of which is the semi-submersible structure. To ensure structural safety in harsh sea environment, detailed investigations on the hydrodynamic characteristics of offshore aquaculture structures are necessary and meaningful. The study focuses on the basic components of a semi-submersible net cage, namely the combined cylinder-net structure, and conducts CFD-based numerical research on its hydrodynamic coupling characteristics under uniform flow. The net structure is numerically simulated based on the porous media model. The drag and lift force and corresponding flow field of only the cylinder, only the nets, and the combined cylinder-net structure are measured under different inflow angles and solidity ratios of nets. The results indicate that the presence of the cylinder increases the drag of nets, and its impact on lift force of nets is closely related to the inflow angle. On the other hand, the presence of the net structure also amplifies the resistance of the cylinder. Meanwhile, the disturbance law of the flow field caused by the cylinder and the net structure is analyzed. By combining numerical and existing experimental results, the hydrodynamic coupling mechanism between the cylinder and the net structure is preliminarily revealed. This study indicates that when conducting hydrodynamic analysis of offshore structures such as the new semi-submersible net cage, the hydrodynamic interaction between the columns and the net structure should be considered.

A simplified numerical method based on anisotropic porous media model for the precooler of the hypersonic precooled engine

The precooler is a key component of hypersonic precooled engine, and its actual structural have a high anisotropy in the axial, circumferential, and radial direction. Considering the non-uniform flow inside the precooler is crucial to study the flow and heat transfer characteristics of the precooler. The previous simplified method for the precooler has not fully considered the flow non-uniformity of the axial, radial and circumferential direction. In this paper, a simplified numerical method based on anisotropic porous media model for the precooler was proposed. The unique aspect of this method is the integration of anisotropic surface porosity of porous media model with the zero-dimensional heat transfer model. In addition, the influence of key structural parameters on the flow and heat transfer characteristics of precooler was studied. It is found that as the tube transverse pitch increases from 2 to 3.5, the total flow rate increases by 11%, and the heat exchange rate decreases by 25%. As the number of tube rows increases from 7 to 13, the heat exchange rate increases by 22%, but the total pressure loss coefficient increases from 0.046 to 0.082. In addition, the decrease of inner diameter of the precooler improves the heat exchange rate, but reduces the flow capacity of the precooler. These results indicate that the simplified numerical method is capable of simulating the behavior of precooler and provides some guidance on the design of precooler.