Search Results (34)

The stability of rubble mound breakwaters is highly affected by extreme wave loading. While extensive research has been devoted to wave-induced scour and liquefaction around breakwaters, comprehensive stability evaluations of the rubble mound breakwater core remain limited. This study develops a numerical framework to investigate the stability of rubble mound breakwaters subjected to solitary wave loading. Wave motion is modeled using the Navier–Stokes equations, wave-induced pore pressure is computed based on Darcy’s law, and soil behavior is represented through the Mohr–Coulomb constitutive model. The numerical model is validated against experimental data. To assess structural stability, the strength reduction method is employed to calculate the Factor of Safety (FOS) during wave propagation, with the minimum FOS serving as the stability criterion. Furthermore, the influence of key parameters, including wave height, soil shear strength, wave–current interaction, berm dimensions, and slope gradient, on breakwater stability is systematically analyzed. 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

The moving particle semi-implicit method (MPS) has been employed to numerically simulate fluid flows. Further, some studies have used the MPS method to solve the Darcy–Brinkman equation, which also expresses fluid flow in porous media. However, these studies simulated flows only in porous media with high permeability, not in relatively low permeability. Thus, this study developed a numerical simulation method that employs Navier–Stokes equations to describe flow in surface water and the Richards equations, derived from the Darcy law and the law of conservation of mass, to describe water flow in porous media, and it uses the MPS method to discretize those equations. This numerical simulation method was then evaluated by comparing the numerical simulation results with previously obtained experimental results for fluid draining from the bottom of a column, which was first packed with silica sand saturated with water and then filled with water to 25 cm above the top surface of the sand, which had an intrinsic permeability of 1.737 × 10^–11 m², a porosity of 0.402, van Genuchten parameters of 0.231 kPa^–1 and 9.154, a residual gas saturation of 0.0, and a residual water saturation of 0.178. The numerical simulation was able to simulate the decrease in the level of the surface water above the silica sand in the column, similar to the column experimental results. However, the decrease in the saturated water in the silica sand obtained by the numerical simulation was almost consistent with the experimental results. Full article

This paper presents an efficient numerical method for the fractional-order generalization of the stochastic Stokes–Darcy model, which finds application in various engineering, biomedical and environmental problems involving interaction between free fluid flow and flows in porous media. Unlike the classical model, this model allows taking into account the hereditary properties of the process under uncertainty conditions. The proposed numerical method is based on the combined use of the sparse grid stochastic collocation method, finite element/finite difference discretization, a fast numerical algorithm for computing the Caputo fractional derivative, and a cost-effective ensemble strategy. The hydraulic conductivity tensor is assumed to be uncertain in this problem, which is modeled by the reduced Karhunen–Loève expansion. The stability and convergence of the deterministic numerical method have been rigorously proved and validated by numerical tests. Utilizing the ensemble strategy allowed us to solve the deterministic problem once for all samples of the hydraulic conductivity tensor, rather than solving it separately for each sample. The use of the algorithm for computing the fractional derivatives significantly reduced both computational cost and memory usage. This study also analyzes the influence of fractional derivatives on the fluid flow process within the fractional-order Stokes–Darcy model under uncertainty conditions. Full article

During tunnel development in metal mines, there are situations where a zone of contact between the ore and the surrounding rock is reached. Nevertheless, there is a notable disparity in the mechanical characteristics between the ore and the surrounding rock, leading to a specific response of grouting in the contact area between the ore and rock. This response differs from the typical diffusion and curtain formation effects observed when using grouting slurry. This study investigates the effects of grouting curtain creation when implementing highly advanced curtain grouting in a water-rich highway, utilizing the engineering conditions of Zhongjiu Iron Mine as a reference. At first, Darcy’s law and the Navier-Stokes equation are used to control the flow of fluid in the area where the ore-rock meets the rock around it. COMSOL, a multi-physical field coupled analysis software, is employed for the numerical simulation of slurry plane diffusion, single-hole, and group-hole curtain grouting. Two optimization strategies for group-hole grouting parameters are subsequently suggested and proven using numerical simulation. Finally, the project implements the research to assess the influence of curtain grouting by employing the water influx of the exploratory apertures as the standard of comparison before and after grouting; the results demonstrate that the slurry forms a highly efficient grouting curtain, effectively impeding water infiltration. The findings indicate that slurry diffusion in the contact zone between the ore and rock follows a spherical motion pattern, resulting in a considerable decrease in the flow rate compared to the previous stage. The force of gravity visibly affects the spreading of the slurry in the area where the ore and rock come into contact, causing the slurry to mostly spread downwards. This inclination intensifies as the rate of grouting is elevated. To successfully address the inadequate distribution of the slurry, one can either increase the rate at which grouting is performed or decrease the distance between the grouting holes. Full article

The Phase-Change Heat Exchanger Unit in Layered Porous Media (PCEU-LPM) is obtained through frozen pouring processing, and exhibits characteristics such as high thermal conductivity, high latent heat, and high permeability, making it suitable for dissipating heat in airborne electronic devices. This study numerically investigates the impact of aircraft speed acceleration conditions, which lead to weightlessness or overload, on the performance of the PCHEU-LPM, with a particular focus on the influence of natural convection in the liquid-phase region. Initially, a microscale thermal analysis model is established based on the Navier–Stokes equation scanning electron micrograph to calculate the effective thermal conductivity and permeability of the PCHEU-LPM under different porosities. Subsequently, these parameters are incorporated into a macroscale thermal analysis model based on Darcy’s law, employing an average parameter approach. Using the macroscale thermal analysis model, temperature and velocity fields are computed under various porosities, acceleration magnitudes, and directions. The calculation results indicate that as the acceleration increases from α = 0 to α = 10 g, the interface temperature of the PCHTU-LPM decreases by approximately 5.2 K, and the temperature fluctuation decreases by 2.4 K. If the porosity of the PCHTU-LPM is increased from ε = 70% to ε = 85%, the influence of acceleration change on natural convection will be further amplified, resulting in a decrease in the interface temperature of the PCHTU-LPM by approximately 10.2 K and a decrease in temperature fluctuation by 5.8 K. When the acceleration direction is +z, the interface temperature of the PCHTU-LPM is at its lowest, while it is highest when the acceleration direction is −z, with a maximum difference of 15.4 K between the two. When the acceleration direction is ±x and ±y, the interface temperature lies between the former two cases, with the interface temperature slightly higher for ±y compared to ±x, with a maximum difference of 3.9 K between them. Full article

Various researchers in the field of engineering have used porous media for many years. The present paper studies heat enhancement using two different types of porous media. In the first type, porous metal foam media was used experimentally and numerically for heat extraction. The porous medium was replaced with a porous structure using the Gyroid model and the triply periodic minimum surfaces technique in the second type. The Darcy–Brinkman model combined with the energy equation was used for the first type, whereas Navier–Stokes equations with the energy equation were implemented for the second type. The uniqueness of this approach was that it treated the Gyroid as a solid structure in the model. The two types were tested for different heat fluxes and different flow rates. A comparison between the experimental measurements and the numerical solution provided a good agreement. By comparing the performance of the two types of structure, the Gyroid structure outperformed the metal foam for heat extraction and uniformity of the temperature distribution. Despite an 18% increase in the pressure drop in the presence of the Gyroid structure, the performance evaluation criteria for the Gyroid are more significant when compared to metal foam. Full article

The problem of formulating variational models for irreversible processes of media deformation is considered in this paper. For reversible processes, the introduction of variational models actually comes down to defining functionals with a given list of arguments of various tensor dimensions. For irreversible processes, an algorithm based on the principle of stationarity of the functional is incorrect. In this paper, to formulate a variational model of irreversible deformation processes with an expanded range of coupled effects, an approach is developed based on the idea of the introduction of the non-integrable variational forms that clearly separate dissipative processes from reversible deformation processes. The fundamental nature of the properties of symmetry and anti-symmetry of tensors of physical properties in relation to multi-indices characterizing independent arguments of bilinear forms in the variational formulation of models of thermomechanical processes has been established. For reversible processes, physical property tensors must necessarily be symmetric with respect to multi-indices. On the contrary, for irreversible thermomechanical processes, the tensors of physical properties that determine non-integrable variational forms must be antisymmetric with respect to the permutation of multi-indices. As a result, an algorithm for obtaining variational models of dissipative irreversible processes is proposed. This algorithm is based on determining the required number of dissipative channels and adding them to the known model of a reversible process. Dissipation channels are introduced as non-integrable variational forms that are linear in the variations of the arguments. The hydrodynamic models of Darcy, Navier–Stokes, and Brinkman are considered, each of which is determined by a different set of dissipation channels. As another example, a variational model of heat transfer processes is presented. The equations of heat conduction laws are obtained as compatibility equations by excluding the introduced thermal potential from the constitutive equations for temperature and heat flux. The Fourier and Maxwell–Cattaneo equations and the generalized heat conduction laws of Gaer–Krumhansl and Jeffrey are formulated. Full article

Cement fractures represent preferential leakage pathways in abandoned wells upon exposure to a CO₂-rich fluid. Understanding fracture alteration resulting from geochemical reactions is critical for assessing well integrity in CO₂ storage. This paper describes a mathematical model used to investigate the physical and the chemical changes in cement properties when CO₂-saturated water is injected into a wellbore. This study examines the flow of a solution of CO₂-saturated water in a two-dimensional fractured cement. In this approach, a micro-continuum equation based on the Darcy–Brinkman–Stokes (DBS) equation is used as the momentum balance equation; in addition, reactive transport equations are used to study the coupled processes of reactant transport and geochemical reactions, and the model for cement porosity alteration and fracture enhancement. This paper focuses on the effects of cement porosity, fracture aperture size, and surface roughness. Mineral dissolution and precipitation mechanisms are also considered. Our simulations show that smaller initial fracture apertures tend to a high mineral precipitation self-sealing. However, a complete sealing of the fracture is not observed due to the continuous flow of CO₂-saturated water. The calcite precipitation mechanism of a rough fracture (random zigzag shape) differs from that of a smooth/flat fracture surface. Full article

Topology optimization (TO) is an effective approach to designing novel and efficient heat transfer devices. However, the TO of conjugate heat transfer has been essentially limited to laminar flow conditions only. The present study proposes a framework for TO involving turbulent conjugate heat transfer based on the variable density method. Different from the commonly used and oversimplified Darcy model, this approach is based on the more accurate and widely accepted k-ε model to optimize turbulent flow channels. We add penalty terms to the Navier–Stokes equation, turbulent kinetic energy equation, and turbulent energy dissipation equation, and use interpolation models for the thermal properties of materials. A multi-objective optimization function, aiming to minimize the pressure drop and the average temperature, is set up to balance the thermal and hydraulic performance. A case study is conducted to compare various optimization methods in the turbulent regime, and the results show that the present method has substantially higher optimization effectiveness while remaining computationally inexpensive. Full article

This paper is aimed at efficient numerical implementation of the fractional-order generalization of the stochastic Stokes–Darcy model, which has important scientific, applied, and economic significance in hydrology, the oil industry, and biomedicine. The essence of this generalization of the stochastic model is the introduction of fractional time derivatives in the sense of Caputo’s definition to take into account long-term changes in the properties of media. An efficient numerical method for the implementation of the fractional-order Stokes–Darcy model is proposed, which is based on the use of a higher-order approximation formula for the fractional derivative, higher-order finite difference relations, and a finite element approximation of the problem in the spatial direction. In the paper, a rigorous theoretical analysis of the stability and convergence of the proposed numerical method is carried out, which is confirmed by numerous computational experiments. Further, the proposed method is applied to the implementation of the fractional-order stochastic Stokes–Darcy model using an ensemble technique, in which the approximation is carried out in such a way that the resulting systems of linear equations have the same coefficient matrix for all realizations. Furthermore, evaluation of the discrete fractional derivatives is carried out with the use of parallel threads. The efficiency of applying both approaches has been demonstrated in numerical tests. Full article

To prevent CO₂ leakage and ensure the safety of long-term CO₂ storage, it is essential to investigate the flow mechanism of CO₂ in complex pore structures at the pore scale. This study focused on reviewing the experimental, theoretical, and numerical simulation studies on the microscopic flow of CO₂ in complex pore structures during the last decade. For example, advanced imaging techniques, such as X-ray computed tomography (CT) and nuclear magnetic resonance (NMR), have been used to reconstruct the complex pore structures of rocks. Mathematical methods, such as Darcy’s law, the Young–Laplace law, and the Navier-Stokes equation, have been used to describe the microscopic flow of CO₂. Numerical methods, such as the lattice Boltzmann method (LBM) and pore network (PN) model, have been used for numerical simulations. The application of these experimental and theoretical models and numerical simulation studies is discussed, considering the effect of complex pore structures. Finally, future research is suggested to focus on the following. (1) Conducting real-time CT scanning experiments of CO₂ displacement combined with the developed real-time CT scanning clamping device to achieve real-time visualization and provide a quantitative description of the flow behavior of CO₂ in complex pore structures. (2) The effect of pore structures changes on the CO₂ flow mechanism caused by the chemical reaction between CO₂ and the pore surface, i.e., the flow theory of CO₂ considering wettability and damage theory in a complex pore structures. (3) The flow mechanism of multi-phase CO₂ in complex pore structures. (4) The flow mechanism of CO₂ in pore structures at multiscale and the scale upgrade from microscopic to mesoscopic to macroscopic. Generally, this study focused on reviewing the research progress of CO₂ flow mechanisms in complex pore structures at the pore scale and provides an overview of the potential advanced developments for enhancing the current understanding of CO₂ microscopic flow mechanisms. Full article

This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape. Full article

In this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–Katchalsky equations, and the three-pore model to simulate plasma and substance flows across the endothelium. The behaviours of all substances in the arterial wall are modelled with convection–diffusion–reaction equations, and finally, plaque growth is calculated. We consider a 2D geometry of a carotid artery, but the model can be extrapolated to other geometries or arteries, such as the coronaries or the aorta. A mono-variant sensitivity analysis of the model parameters was performed, with values of $\pm 25\%$ and $\pm 10\%$, with respect to the values of the previous model. The results were analysed with respect to the volume in the plaque of foam cells (FC), synthetic smooth muscle cells (SSMC), and collagen fibre. It was observed that the volume in the plaque of the different substances (FC, SSMC, and collagen) has a strong influence on the results, so it could be used to analyse the vulnerability of plaque. The stenosis ratio of the plaque was also analysed, showing a strong influence on the results as well. Parameters that influence all the results considered when ranged $\pm 10\%$ are the rate of LDL degradation and the diffusion coefficients of LDL and monocytes in the arterial wall. Furthermore, it was observed that the change in the volume of foam cells in the plaque has a greater influence on the stenosis ratio than the change of synthetic smooth muscle cells or collagen fibre. Full article

The aim of this study is to examine the Darcy–Forchheimer flow = of $H_{2}O$-based $Al-A{l}_2{O}_3/$$Cu-A{l}_2{O}_3$ hybrid nanofluid past a heated stretchable plate including heat consumption/ generation and non-linear radiation impacts. The governing flow equations are formulated using the Naiver–Stokes equation. These flow equations are re-framed by using the befitted transformations. The MATLAB bvp4c scheme is utilized to compute the converted flow equations numerically. The graphs, tables, and charts display the vicissitudes in the hybrid nanofluid velocity, hybrid nanofluid temperature, skin friction coefficient, and local Nusselt number via relevant flow factors. It can be seen that the hybrid nanofluid velocity decreased as the magnetic field parameter was increased. The hybrid nanofluid temperature tended to rise as the heat absorption/generation, nanoparticle volume friction, and nonlinear radiation parameters were increased. The surface drag force decreased when the quantity of the magnetic parameter increased. The larger size of the radiation parameter led to enrichment of the heat transmission gradient. Full article