Search Results (246)

This paper presents a finite element implementation of a fractional rheological consolidation model in ABQUS, in which the fractional Merchant model governs the mechanical behavior of the soil skeleton, and the water flow is controlled by the fractional Darcy’s law. The implementation generally involves two main parts: subroutine-based fractional constitutive models’ development and their coupling. Considering the formal similarity between the energy equation and the mass equation, the fractional Darcy’s law was implemented using the UMATHT subroutine. The fractional Merchant model was then realized through the UMAT subroutine. Both subroutines were individually verified and then successfully coupled. The coupling was achieved by modifying the stress update scheme based on Biot’s poroelastic theory and the effective stress principle in UMAT, enabling a finite element analysis of the fractional consolidation model. Finally, the model was applied to simulate the consolidation behavior of a multi-layered foundation. The proposed approach may serve as a reference for the finite element implementation of consolidation models incorporating a fractional seepage model in ABAQUS. Full article

Fish protection and guidance are critical factors in the design and operation of water intakes at hydropower plants. In this study, the hydraulic performance of the angled Oppermann fine screen has been investigated in a hybrid model with and without a guidance wall. The experiments were conducted under two different angles of 30° and 45°, and a bar spacing of 10 mm at a large-scale flume with a width of 2 m. Just up- and downstream of the screen, three-dimensional velocities were measured with Acoustic Doppler Velocimetry (ADV). In the computational fluid dynamics (CFD) model, the Large Eddy Simulation (LES) coupled with the Darcy–Forchheimer law, in which screens were modeled as homogeneous porous media, was employed. The experimental results revealed that velocities less than 0.5 m/s just upstream of the Oppermann fine screen and tangential velocity gradients over the entire cross-section of the screen were found to be 0.04–0.338 m/s/m and 0.04–0.856 m/s/m for α = 30° and α = 45°, respectively, creating favorable hydraulic conditions for effective downstream fish guidance. The CFD model was validated against the experimental data within an acceptable error range, both for the velocity and the turbulent kinetic energy. Numerical simulations showed that implementing a curved guidance wall creates a symmetrical and homogeneous downstream flow field without the formation of recirculation zones behind the angled screen. Full article

The placement of hydraulic elements in existing pool-type fishways to make them more suitable for Cyprinid fish is an issue of increasing interest in fishway research. Hydrodynamic characteristics and fish behavior at the representative pool of the fishway with bottom orifices and notches were assessed at the Dagdelen hydropower plant in the Ceyhan River Basin, Türkiye. Three-dimensional velocity measurements were taken in the pool of the fishway using an Acoustic Doppler velocimeter. The measurements were taken with and without a brush block at two different vertical distances from the bottom, which were below and above the level of bristles tips. A computational fluid dynamics (CFD) analysis was conducted for the studied fishway. The numerical model utilized Large Eddy Simulation (LES) combined with the Darcy–Forchheimer law, wherein brush blocks were represented as homogenous porous media. Our results revealed that the relative submergence of bristles in the brush block plays a very important role in velocity and Reynolds shear stress (RSS) distributions. After the placement of the submerged brush block, flow velocity and the lateral RSS component were reduced, and a resting area was created behind the brush block below the bristles’ tips. Fish movements in the pool were recorded by underwater cameras under real-time operation conditions. The heatmap analysis, which is a 2-dimensional fish spatial presence visualization technique for a specific time period, showed that Capoeta damascina avoided the areas with high turbulent fluctuations during the tests, and 61.5% of the fish presence intensity was found to be in the low Reynolds shear regions in the pool. This provides a clear case for the real-world ecological benefits of retrofitting existing pool-weir fishways with such flexible hydraulic elements. Full article

Thermal wick-debinding, commonly used in low-pressure injection molding, remains challenging due to complex interactions between binder transport, capillary forces, and thermal effects. This study presents a numerical simulation of binder removal kinetics by coupling Darcy’s law with the Phase Transport in Porous Media interface in COMSOL Multiphysics. The model was validated and subsequently used to study the influence of key debinding parameters. Contrary to the Level Set method, which predicts isolated binder clusters, the Multiphase Flow in Porous Media method proposed in this work more accurately reflects the physical behavior of the process, capturing a continuous binder extraction throughout the green part and a uniform binder distribution within the wicking medium. The model successfully predicted the experimentally observed decrease in binder saturation with increasing debinding temperature or time, with deviation limited 3–10 vol. % (attributed to a mandatory brushing operation, which may underestimate the residual binder mass). The model was then used to optimize the debinding process: for a temperature of 100 °C and an inter-part gap distance of 5 mm, the debinding time was minimized to 7 h. These findings highlight the model’s practical utility for process design, offering a valuable tool for determining optimal debinding parameters and improving productivity. Full article

This paper explores the complex dynamics of mixed convective flow in a Casson fluid saturated in a non-Darcy porous medium, focusing on the influence of gyrotactic microorganisms, internal heat generation, and multiple convective mechanisms. Casson fluids, known for their non-Newtonian behavior, are relevant in various industrial and biological contexts where traditional fluid models are insufficient. This study addresses the limitations of the standard Darcy’s law by examining non-Darcy flow, which accounts for nonlinear inertial effects in porous media. The governing equations, derived from conservation laws, are transformed into a system of no linear ordinary differential equations (ODEs) using similarity transformations. These ODEs are solved numerically using a finite differencing method that incorporates central differencing, tridiagonal matrix manipulation, and iterative procedures to ensure accuracy across various convective regimes. The reliability of this method is confirmed through validation with the MATLAB (R2024b) bvp4c scheme. The investigation analyzes the impact of key parameters (such as the Casson fluid parameter, Darcy number, Biot numbers, and heat generation) on velocity, temperature, and microorganism concentration profiles. This study reveals that the Casson fluid parameter significantly improves the velocity, concentration, and motile microorganism profiles while decreasing the temperature profile. Additionally, the Biot number is shown to considerably increase the concentration and dispersion of motile microorganisms, as well as the heat transfer rate. The findings provide valuable insights into non-Newtonian fluid behavior in porous environments, with applications in bioengineering, environmental remediation, and energy systems, such as bioreactor design and geothermal energy extraction. Full article

Porous media have great application prospects, such as transpiration cooling for the aerospace industry. The main challenge for the prediction of gas permeability includes the geometrical complexity and high Knudsen number of gas flow at the nano-scale to micro-scale, leading to failure of the conventional Darcy’s law. To address these issues, the Quartet Structure Generation Set (QSGS) method is improved to construct anisotropic and heterogeneous three-dimensional porous media, and the lattice Boltzmann method (LBM) with the multiple relaxation time (MRT) collision operator is adopted. Using MRT-LBM, the pressure boundary conditions at the inlet and outlet are firstly dealt with using the moment-based boundary conditions, demonstrating good agreement with the analytical solutions in two benchmark tests of three-dimensional Poiseuille flow and flow through a body-centered cubic array of spheres. Combined with the Bosanquet-type effective viscosity model and Maxwellian diffuse reflection boundary condition, the gas flow at high Knudsen (Kn) numbers in three-dimensional porous media is simulated to study the relationship between pore-scale anisotropy, heterogeneity and Kn, and permeability and micro-scale slip effects in porous media. The slip factor is positively correlated with the anisotropic factor, which means that the high Kn effect is stronger in anisotropic structures. There is no obvious correlation between the slip factor and heterogeneity factor. Full article

Nitric oxide (NO) is a well-known member of the reactive oxygen species (ROS) family. The extent of its concentration influences whether it produces beneficial physiological effects or harmful toxic reactions. In a blood system, NO is generally produced by nitric oxide synthase (NOS) in the endothelium. Then, it diffuses into the smooth muscle wall causing a vasodilatation, and it can also be diluted in a lumen blood stream. In the present study, we analyzed a convectional reaction–diffusion of NO in a 3D digital phantom of a short segment of small arteries. NO concentrations were analyzed by applying numerical solutions to the boundary problems, which included the Navier–Stokes equation, Darcy’s law, varying consumption of NO, and the dependence of NOS activity on shear stress. All the boundary problems were evaluated using COMSOL Multiphysics software ver. 5.5. The role of two diffusive barriers surrounding the endothelium producing NO was theoretically proven. When the eNOS rate remains unchanged, an increase in the fenestration of the internal elastic lamina (IEL) and a decrease in the diffusive permeability of a thin layer of endothelial surface glycocalyx (ESG) lead to a notable rise in the NO concentration in the vascular wall. The alterations in pore count in IEL and the viscosity of ESG are considered to be involved in the physiological and pathological regulation of NO concentrations. Full article

This study introduces a novel mathematical model tailored to the unique fluid dynamics of paper-based microfluidic devices (PBMDs), focusing specifically on the transport behavior of human blood plasma, albumin, and heat. Unlike previous models that depend on generic commercial software, our custom-developed computational incorporates the Richards equation to extend Darcy’s law for more accurately capturing capillary-driven flow and thermal transport in porous paper substrates. The model’s predictions were validated through experimental data and demonstrated high accuracy in both two- and three-dimensional simulations. Key findings include new analytical expressions for uniform paper wetting after sudden geometric expansions and the discovery that plasma and albumin preferentially migrate along paper edges—a phenomenon driven by surface tension and capillary effects that varies with paper type. Additionally, heat transfer analysis indicates that a one-minute equilibration period is necessary for the reaction zone to reach ambient temperature, an important parameter for assay timing. These insights provide a deeper physical understanding of PBMD operation and establish a robust modeling tool that bridges experimental and computational approaches, offering a foundation for the optimized design of next-generation diagnostic devices for biomedical applications. Full article

The non-Darcy seepage characteristics of broken rock mass is important for analyzing the seepage and stability of rock and soil mass. At present, the research on non-Darcy seepage models considering hydraulic conditions and medium void structures has considerable room for improvement. In this study, non-Darcy seepage tests were conducted on broken rock mass under the influence of different hydraulic pressures, sample gradations, and porosities. The influence of sample gradation and porosity on the linear and nonlinear term coefficients of Forchheimer’s law, the critical criterion of non-Darcy seepage, and the seepage flow regime was clarified. The influence of hydraulic gradient on the value of traditional hydraulic conductivity was revealed. A non-Darcy equivalent hydraulic conductivity, which changed with pressure gradient, was defined, then Forchheimer’s law and Darcy’s law were modified. Results showed that the relationship between pressure gradient and flow rate highly obeyed Forchheimer’s law. The minimum value of Forchheimer number was 9.4 times the critical value. Owing to the influence of inertial force and variable seepage channels, the linear and nonlinear term coefficients of Forchheimer’s law decreased while the Forchheimer number increased with the increase of pressure gradient, sample gradation, and porosity. With high hydraulic gradient, the non-Darcy equivalent hydraulic conductivity decreased nonlinearly, causing Darcy’s law to overestimate the seepage flow in this study by 2.47–13.40 times. Finally, Forchheimer’s law and Darcy’s law were modified to consider the influence of hydraulic gradient, sample gradation, and porosity. The modified Darcy’s law does not require the determination of the seepage flow regime and can accommodate the mutual transformation and coexistence between Darcy and non-Darcy seepage. Full article

To address the hydrogeological parameters of polluted sites at the site scale, a series of physical and numerical simulation experiments were conducted to investigate seepage and solute transport under the influence of various physical fields. These experiments utilized an experimental platform designed for the acquisition of pollutant transport and transformation data, which incorporated three-dimensional multifield coupling, alongside a numerical model that also accounted for multiphysical field interactions. The numerical simulations employed Darcy’s law, the heat conduction equation, and convective–dispersive equations to analyze the seepage field, heat transfer, and solute transport processes, respectively. The findings from both physical and numerical tests indicate that variations in groundwater temperature and solute concentration significantly influence solute transport dynamics. Specifically, an increase in groundwater temperature correlates with an accelerated migration rate of sodium chloride (NaCl) solute, resulting in a reduced time for the solute to achieve equivalent concentrations in observation wells. Conversely, when the concentration of NaCl in groundwater rises, the temperature of the groundwater also increases when the solute reaches the same concentration in the observation wells. This phenomenon can be attributed to the decrease in the specific heat capacity of groundwater with higher solute concentrations. Moreover, as the concentration of sodium chloride in groundwater increases, the rate of temperature elevation in the groundwater accelerates due to a decrease in specific heat capacity associated with higher solute concentrations, thereby requiring less thermal energy for the groundwater to attain the same temperature. The results further reveal that the hydraulic conductivity of the target aquifer, specifically the pulverized clay layer, ranges from 6.72 to 8.52 × 10⁻⁶ m/s, with an effective thermal conductivity of 2.2 W/(m·K), a longitudinal dispersion of 0.554 m, and a transverse dispersion of 0.05 m. Full article

Geometric properties of fractures, such as aperture and width, among others, significantly affect the fluid flow behaviors in fractured media. Previous studies have shown that fractures exhibit fractal properties. In this study, we examine the impact of nonlinear flow regimes and aperture and width fractal distributions on the flow behavior through fractal fractures. Both the aperture and width are treated independently following fractal distribution, but with distinct fractal dimensions. We explicitly examine the flow features without using Darcy’s law concept, which relies on the linear flow assumption with an effective permeability of fractal fractures. We directly consider the flow rate in a fracture with average aperture, average flow rate, and flow rate of linear flow in all the fractures, and nonlinear flow rate in all the fractures, and more realistically, the average flow rate when linear and nonlinear flows may coexist in different fractures and their differences. The results demonstrate that the nonlinear flow regime significantly reduces the flow rate through the fractal fractures, which could be quantified by the ratio of critical aperture to the minimum aperture in the fractal fractures. A large ratio of the maximum over the minimum apertures results in a large average flow rate in the fractal fractures. The increase in the minimum aperture also enhances the average flow rate. When the minimum aperture is close to the critical aperture, however, the flow rate in the fractal fractures starts to turn into nonlinear flow in all the fractures, and the average flow rate decreases. The nonlinear effect is amplified in fractal fractures compared to that in a single fracture. A larger fractal dimension of aperture leads to a lower average flow rate in the fractal fractures, as the average aperture decreases with the fractal dimension. However, the fraction of flow rate from the linear flow portion in the fractal fractures over the pure linear flow in all the fractures increases with the fractal dimension. Full article

The study examines the onset of magnetoconvection in a Casson fluid-saturated inclined porous layer. Oberbeck–Boussinesq approximation and Darcy law employed to characterize the fluid motion. The stability of the system is examined using both linear and nonlinear stability theories. A basic solution of the governing equation is determined. The linear instability is studied by employing disturbances to the basic flow. The nonlinear instability is analyzed utilizing the energy method. The solution to the eigenvalue problem is derived using the bvp4c routine in MATLAB R2023a. This study evaluates the influence of nondimensional parameters specifically, the Hartmann number, Casson parameter, and inclination angle on both linear and nonlinear instability. The Casson parameter destabilizes the system, whereas the Hartmann number and inclination angle stabilize it. Transverse rolls exhibit greater stability compared to longitudinal rolls. Changes in the Casson parameter significantly affect the presence or absence of transverse rolls; as its value changes, so does the disappearance of transverse rolls. Full article

A novel closed-form solution representing the fluid motion within a porous bushing was created to develop a recently patented bearing configuration with a self-contained lubrication system. The configuration has a lubricant reservoir surrounding the porous bushing that continuously supplies lubricant without an external pump. In regions of low pressure, the lubricant moves into the bearing clearance; where clearance pressure is high, the lubricant is transferred to the porous bushing and refills the supply reservoir. The porous bushing’s pressure distribution was used within Darcy’s law to determine the injection velocity into the bearing clearance. Selected cases were compared with previously published work for approach validation. The validity of assuming a linear distribution within the porous media was investigated, as was the variance of the attitude angle for eccentricity and the effects of porous medium thickness and bearing parameter on bearing load capacity. It was concluded that increasing the feeding parameter increased the bearing load capacity. The porous bearing’s pressure distribution, commonly assumed to be linear, was discovered to be increasingly nonlinear near the bearing’s axial ends. The effect of nonlinearity on the bearing load capacity depended on the thickness of the porous bushing and the eccentricity of the bearing. Full article

This study focuses on understanding the bioconvection in Jeffery–Hamel (JH) flow, which has valuable applications in areas like converging dies, hydrology, and the automotive industry, which make it a topic of practical importance. This research aims to explore Homogeneous–Heterogeneous (HH) chemical reactions in a magnetic Darcy–Forchheimer model with bioconvection in convergent/divergent channels. To analyze the role of porosity, the Darcy–Forchheimer law is applied. The main system of equations is simplified through similarity transformation into ordinary differential equations solved numerically with the help of the NDSolve technique. The results, compared with previous studies for validation, are presented through graphs and tables. The study reveals that in divergent channels, the velocity decreases with higher solid volume fractions, while in convergent channels, it increases. Furthermore, various physical parameters, such as the Eckert number and porosity parameter, increase skin friction in divergent channels but decrease it in convergent channels. These findings suggest that the parameters investigated in this study can effectively enhance homogeneous reactions, providing valuable insights for practical applications. Full article

Determining the friction coefficients for uniform flows over very rough bottoms is a long-standing problem in open-channel hydraulics and river engineering. This experimental study presents measurements of the surface deformation as well as Darcy–Weisbach and Manning friction coefficients for steady, turbulent (6058 $\le \mathcal{R}e\le$ 28,502), and subcritical flows (0.14 $\le \mathcal{F}r\le$ 0.52) over large roughness elements, where $\mathcal{F}r$ and $\mathcal{R}e$ denote the Froude and Reynolds numbers, respectively. The experiments were conducted in a rectangular, inclined flume with a train of half-cylinders mounted on the bed, with radii in the range 20 mm $\le a\le$ 50 mm. These obstacles yield a relative submergence 1.45 $\le h_N/a\le$ 4.41 and a constant spacing ratio $e/a=12.8$ across all experimental runs, where $h_N$ and e denote the normal flow depth and the center-to-center spacing between cylinders, respectively. The relative amplitude of the surface profiles, ($\Delta h/a$), was analyzed and found to correlate strongly with $h_N/a$, $\mathcal{R}e$ and $\mathcal{F}r$. The results reveal very high values of the Darcy friction factor, f, which follows scaling laws of the form ${f\propto (h_N/a)}^{\widehat{n}}$, with $\widehat{n}<0$, independent of a, and ${f\propto \mathcal{R}e}^{\beta }$, where $\beta <0$ is closely linked to a. Scaling relationships for the Manning roughness coefficient, (n), were also investigated and are reported herein. Full article