Transport in Porous Media最新文献

This study aims to investigate forced convection and heat transfer in a two-dimensional channel featuring a backward-facing step, a stationary adiabatic porous cylinder, and a deformable upper wall. The research addresses the complex coupling of fluid–structure interaction and porous media effects, a novel configuration not extensively explored in the existing literature. A numerical approach based on the finite element method within an arbitrary Lagrangian–Eulerian (ALE) framework is employed to simulate laminar flow and heat transfer over ranges of Reynolds (10 ≤ Re ≤ 200), Darcy (10⁻⁶ ≤ Da ≤ 10⁻¹), and Cauchy (10⁻⁷ ≤ Ca ≤ 10⁻⁴) numbers. The results, illustrated through isotherms, streamline patterns, and both local and average Nusselt number distributions, demonstrate that increasing the Reynolds number significantly enhances convective heat transfer. A decrease in the cylinder’s porosity strengthens vortex formation and thermal gradients, leading to a 36.4% increase in the average Nusselt number. Moreover, greater wall elasticity yields a modest 2.3% improvement in heat transfer. Regarding fluid–structure interaction, the maximum deformation of the upper elastic wall increases markedly with the Cauchy number, decreases by approximately 52.6% as the Reynolds number increases from 10 to 200, and reaches a peak at an intermediate Darcy number (Da = 10⁻³), highlighting the coupled influence of flow inertia and porous permeability. These findings provide quantitative insights into the interplay between structural deformation and porous media, contributing to the optimization of thermal management strategies in deformable thermo-fluidic systems.

Flow through the configuration of a three-layer channel containing a transition porous layer of variable permeability is revisited in this work to illustrate how Brinkman’s equation, which governs the flow in the transition layer, is reduced to the classic inhomogeneous differential equations of Airy and Weber, with constant forcing terms. Solutions to the homogeneous parts of these equations are given in terms of Airy’s and Weber’s special functions. Particular solutions to the resulting inhomogeneous equations give rise to three Nield-Kuznetsov functions of the first kind, which are analyzed in this work and extended to obtain general solutions to equations with variable forcing terms whose general solutions are expressed in terms of three Nield-Kuznetsov functions of the second kind. Methods of evaluation of all resulting special functions are presented.

Current underground nuclear explosion (UNE) detection strategies rely heavily on atmospheric noble gas sampling of radioxenon. However, discriminating nuclear weapons testing programs from civilian sources is difficult due to highly variable atmospheric radioxenon backgrounds and processes affecting subsurface transport of parent radionuclides. We aim to study the transport of gases produced by subsurface explosions as novel stable signatures for underground nuclear explosion (UNE) monitoring. These gases may be produced in large quantities with distinct molecular ratios, which will be impacted by subsurface transport processes. To demonstrate how ratios of gases produced by explosions can change during transport in geomaterials, we conducted laboratory benchtop experiments on the transport of carbon dioxide (CO₂) and hydrogen (H₂) gases through variably saturated zeolitic tuff, which is abundant at the historic US testing site. We observed that zeolitic tuff sorbs substantial quantities of CO₂ while allowing H₂ to transport more freely, leading to changes in the molecular ratios of the two gases along the transport pathway. Gas uptake in the dry zeolitic tuff core was 72.3% for CO₂, compared with 53.4% for xenon and 7.6% for H₂. The presence of 20% water saturation disrupted the CO₂ sorption process, though to a lesser extent than observed for noble gases, with a 36.7% drop in xenon sorption compared with a 21.9% drop for CO₂. These results represent the first observations of zeolite sorption altering explosive gas ratios during transport through geomedia relevant to nuclear proliferation monitoring.

Convolution neural networks (CNNs) are well-suited to model the nonlinear relationship between the microscale geometry of porous media and the corresponding flow distribution, thereby accurately and efficiently coupling the flow behavior at the micro- and macroscale levels. In this paper, we have identified the challenges involved in implementing CNNs for macroscale model closure in the turbulent flow regime, particularly in the prediction of the drag force components arising from the microscale level. We report that significant error is incurred in the crucial data preparation step when the Reynolds averaged pressure and velocity distributions are interpolated from unstructured stretched grids used for large eddy simulation (LES) to the structured uniform grids used by the CNN model. We show that the range of the microscale velocity values is 10 times larger than the range of the pressure values. This invalidates the use of the mean squared error loss function to train the CNN model for multivariate prediction. We have developed a CNN model framework that addresses these challenges by proposing a conservative interpolation method and a normalized mean squared error loss function. We simulated a model dataset to train the CNN for turbulent flow prediction in periodic porous media composed of cylindrical solid obstacles with square cross-section by varying the porosity in the range 0.3 to 0.88. We demonstrate that the resulting CNN model predicts the pressure and viscous drag forces with less than 10% mean absolute error when compared to LES while offering a speedup of O(10⁶).

To characterize turbulence over porous media with porosities (varphi <0.5), three types of packed-beds were manufactured: cubically packed spheres (case S), randomly packed rice-grain-shaped pellets (case E), and crushed stones (case C), with measured porosities of (varphi =0.45), 0.37, and 0.30, respectively. After measuring their permeabilities, particle image velocimetry (PIV) measurements were conducted for flows under conditions characterized by the permeability Reynolds number ((Re_K)) ranging from 2.1 to 18.3. The results were then compared with previous data on turbulent flows over foamed ceramics with a porosity of (varphi simeq 0.8), reported by Suga et al. (Int J Heat Fluid Flow 31(6), 974–984, 2010). The measured turbulence characteristics were analyzed to examine their correlation with (Re_K) and to evaluate the applicability of a unified scaling approach across a wide range of porous beds. The findings suggest that while some distribution profiles generally follow (Re_K), this parameter alone is insufficient as a universal scaling factor for turbulence over packed-beds, as the roughness scale also exhibits significant dependence on surface shape rather than the porosity.

A bounded porous domain saturated with a Newtonian fluid and subjected to time-dependent temperature variation has various practical applications, such as in solar energy storage, nuclear reactors, food processing industry, and agricultural science. In the current work, we study Darcy–Bénard convection in a horizontal fluid-saturated porous layer that is heated from below and confined in all directions. We look into an intricate form of the modulated Darcy–Bénard problem, where the temperatures at the bottom and top boundaries undergo sinusoidal temporal modulation about their mean values. We perform linear stability analysis to understand the onset of convection using a two-phase heat model based on the assumption that the solid and fluid phases of the system are not in local thermal equilibrium. The time-periodic eigenvalue problem obtained here is solved using the Floquet theory to find the onset threshold value of critical Rayleigh number. Our results suggest that the convection through subharmonic modes is preferable for either small ((text {H} < 4.3)) or large (H (> 175)) interphase heat transfer coefficient, while for the moderate values of H, convection takes place through harmonic mode only. In the paper, we discuss the results in detail and present a comparison with those from previous studies.

Mathematical modelling of coupled flow systems containing a free-flow region in contact with a porous medium is challenging, especially for arbitrary flow directions to the fluid–porous interface. Transport processes in the free flow and porous medium are typically described by distinct equations: the Stokes equations and Darcy’s law, respectively, with an appropriate set of coupling conditions at the common interface. Classical interface conditions based on the Beavers–Joseph condition are not accurate for general flows. Several generalisations are recently developed for arbitrary flows at the interface; some of them are however only theoretically formulated and still need to be validated. In this manuscript, we propose an alternative to couple free flow and porous-medium flow, namely the hybrid-dimensional Stokes–Brinkman–Darcy model. Such formulation incorporates the averaged Brinkman equations within a complex interface between the free-flow and porous-medium regions. The complex interface acts as a buffer zone facilitating storage and transport of mass and momentum and the model is applicable for arbitrary flow directions. We validate the proposed hybrid-dimensional model against the pore-scale resolved model in multiple examples and compare numerical simulation results also with the classical and generalised coupling conditions from the literature. The proposed hybrid-dimensional model demonstrates its applicability to describe arbitrary coupled flows and shows its advantages in comparison to other generalised coupling conditions.

Thermal properties play a critical role in environments and processes involving heat exchange and transfer. Heat transport in porous media has been a subject of extensive study due to its significant impact on applications ranging from in situ hydrocarbon production to geothermal energy projects. Micro-CT imaging has become a powerful tool for characterizing porous media, with its use increasingly expanding in recent years, driven by progress in computational techniques. Homogenization approaches provide a powerful means to analyze transport phenomena in Micro-CT images, offering reliable accuracy while reducing computational errors. In this study, the application of the hierarchical homogenization (HH) technique for thermal conductivity was explored. Various sources of error, including the choice of homogenization scale and numerical conditions such as padding thickness, were systematically investigated and compared to validation dataset acquired by Micro-CT data and high-fidelity direct numerical simulations. The results indicated less than 5% error in the first-order single-stage HH approach for all studied material schemas. Hyperbolic trend of the error was observed with the order of homogenization. Subsequently, telescopic hierarchical homogenization (THH) was found effective as a new approach for more complex systems with a negligible (less than 1.5%) error compared to single-stage HH. Furthermore, the HH error was investigated for a set of 19 synthetic and real samples to assess the effect of porosity and porosity variation in subsamples on the final error values, and a mathematical model was obtained for each of the material schemas. Results showed that in the similar porosity cases, sample with the higher dispersion of porosity will result in more error of thermal conductivity through HH procedure.

Applications of porous media are increasing in various scientific disciplines, such as energy storage or conversion systems and giant capacitors. It has been recognized that the transport and reaction processes occurring within pores significantly influence the performance of porous media, while transport phenomena at the pore scale are not well-characterized. The experimental effective diffusion coefficient of naphthalene-nitrogen was studied using a regression method based on a radial dimension transient model of diffusion in the porous medium. The weight of samples containing naphthalene was continuously recorded by a digital precision balance. This study was performed at three different temperatures: 303.15 K (30 °C), 323.15 K (50 °C), and 343.15 K (70 °C) at atmospheric pressure, with porous metal matrices of 90% porosity containing different amounts of naphthalene in a laminar nitrogen stream. The fitting of the diffusion equation in spherical coordinates and the weight changes provided the mass transfer coefficients; as a result, a power correlation to estimate the effective diffusion coefficient was obtained.

Evaporation from a porous medium partially saturated with saline water, causes the salinity (salt concentration) to increase near the top of the porous medium as water leaves while salt stays behind. As the density of the water increases with increased salt concentration, the evaporation leads to a gravitational unstable setting, where density instabilities can form. Whether density instabilities form, depends on a large range of parameters like the evaporation rate and intrinsic permeability of the porous medium, but also on the water saturation. As water saturation decreases, the storage, convection and diffusion of salt also decrease, which all influence the onset of instabilities. By performing a linear stability analysis on the governing equations, we give criteria for onset of instabilities, with a particular focus on impact of saturation. While decreased storage and diffusion make onset of instabilities more unstable, decreased convection has a stabilizing effect on the onset of instabilities. We find that their combined influence is that lower saturation overall gives earlier onset times. Numerical simulations give information about the further development of these instabilities. With this knowledge we can predict whether and when density instabilities occur, and how they will influence the further development of salt concentration in the porous medium.