Permeable Walls Research Articles

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.

Three-dimensional simulation of cavitating flow in reciprocating positive displacement pumps with fluid-actuated valves

Abstract An in-house compressible three-dimensional (3D) finite volume Computational Fluid Dynamics (CFD) method, with statistical turbulence model and moving grid capabilities, is presented and applied to the suction stroke of a simplex plunger positive displacement pump. The approach utilizes a pressure-based implicit solution algorithm and a mass transfer cavitation model. Fluid-actuated valve dynamics are approximated using a fluid-structure interaction algorithm. The closed valve and early phase of valve opening are approximated by a permeable wall. A circular segment model is introduced, significantly reducing computing time. Experimental validation is performed by time-resolved pressure and flow rate measurements, as well as high-speed visualizations of the valve dynamics. A speed variation is conducted to investigate harmless advanced and erosive distinctive partial cavitation. The simulation reproduces the delay of cavity collapse, observed with increasing speed, and reveals distinctive void patterns related to the chamber pressure time progression. These void patterns are fundamental for understanding the cavitation dynamics and potential erosion risk in the system. Deviations from data remain in the flow phase subsequent to the collapse due to overestimated wave reflection at the inlet boundary in the suction pipe.

Establishing patterns of change in the coefficients of reflection, transmission, and dissipation of wave energy depending on parameters of a permeable vertical wall

The object of research is permeable vertical walls (breakwaters) with different degrees of permeability. This paper reports the results of experimental research into the interaction of gravity waves with models of permeable vertical walls (breakwaters), which were formed from cylindrical piles of circular cross-section. With the help of visual and instrumental studies, the features of interaction of surface gravity waves with permeable vertical walls of different permeability have been identified. The degree of wave transformation by these walls was also determined in the form of reflection, transmission, and dissipation coefficients of wave energy. It was established that with a decrease in the permeability of the vertical wall and an increase in the steepness of the initial wave and a decrease in its period, the height of the reflected wave increased. The pattern of the transmitted wave height had the opposite trend. It was determined that the wave reflection coefficient increased with a decrease in the permeability of the vertical wall and the steepness of the initial wave. The wave transmission coefficient had the opposite trend, namely, it increased with increasing wall permeability and with decreasing steepness of the initial wave. The gravity wave energy dissipation coefficient decreased with increasing vertical wall permeability, but for waves with a significant steepness hi/λ>0.038, a decrease in the wave energy dissipation coefficient was observed for walls with low permeability and the appearance of extreme values of this coefficient. Thus, features in the interaction of surface gravity waves with permeable vertical walls (breakwaters) of different permeability have been researched and the degree of wave transformation by these walls has been determined, which could make it possible to effectively design and operate permeable vertical walls as coastal protection structures

Effectiveness of different mixed physical barriers in controlling seawater intrusion in homogeneous and layered coastal aquifers

The intrusion of salt water into coastal regions threatens water resources, especially in arid and semi-arid regions. It damages large quantities of fresh water in these regions, and the productivity of the freshwater abstraction wells declines. Management of seawater intrusion (SWI) is therefore needed to improve fresh groundwater in these regions. This study investigated 12 different configurations of mixed physical subsurface barriers (MPBs) to control SWI in homogeneous and heterogeneous layered aquifers. The effectiveness of different MPB locations and configurations was tested, including (i) a barrier wall on the landward side and the subsurface dams on the seaward side, (ii) a barrier wall on the seaward side and a subsurface dam on the landward side, and (iii) the barrier wall was placed above the subsurface dam, both with different permeabilities. All simulations were based on the SEAWAT code. The numerical model was validated against experimental data. The results showed that a permeable cut-off wall above an impermeable subterranean dam (case MPB-3) with different permeabilities resulted in a reduction of the seawater wedge of 91% and 92% for homogeneous and heterogeneous layered aquifers, respectively. When the barrier wall was placed on the land side and the dam on the seaside (case MPB-1), the reduction of the seawater wedge reached 83% and 85% for homogeneous and heterogeneous layered aquifers, respectively. In contrast, when the dam was placed on the land side and the wall on the seaside (case MPB-2), the saltwater wedge was reduced by 73% for both homogeneous and heterogeneous layered aquifers. In addition, a case study was conducted on the Biscayne aquifer, southeast Florida, USA, with homogeneous conditions. Seawater intrusion was reduced by 36% and 44% in case MPB-1, 41% and 38% in case MPB-2, and 43% and 46% in case MPB-3. These seawater intrusion control methods offer numerous benefits, including improving freshwater storage, effectively controlling salinity during droughts, and potentially improving contaminant management.

Effects of Tapering and Electro-Osmosis on Copper-Suspended Nanofluid Through a Composite Stenosed Artery with Permeable Walls: Exact Solutions

Effects of Tapering and Electro-Osmosis on Copper-Suspended Nanofluid Through a Composite Stenosed Artery with Permeable Walls: Exact Solutions

The Implicit Euler Scheme for FSDEs with Stochastic Forcing: Existence and Uniqueness of the Solution

In this paper, we focus on fractional stochastic differential equations (FSDEs) with a stochastic forcing term, i.e., to FSDE, we add a stochastic forcing term. Using the implicit scheme of Euler’s approximation, the conditions for the existence and uniqueness of the solution of FSDEs with a stochastic forcing term are established. Such equations can be applied to considering FSDEs with a permeable wall.

Exploring the influence of morphology on magnetized Ree–Eyring tri‐hybrid nanofluid flow between orthogonally moving coaxial disks using artificial neural networks with Levenberg–Marquardt scheme

AbstractThe present study presents an analysis of Ree–Eyring tri‐hybrid nanofluid flow between two expanding/contracting disks with permeable walls by applying the computing power of Levenberg–Marquardt supervised neural networks (LM‐SNNs). The effects of thermal radiation, Brownian motion, and thermophoresis were also thoroughly examined. The results are presented for tri‐hybrid nanofluid with SWCNT and MWCNT and Fe2O3 and H2O base fluid. The coupled non‐linear PDE system is transformed into a system of ODE associated with convective boundary conditions by applying the appropriate transformations. This is then accomplished numerically by using the finite difference‐based BVP‐4c MATLAB code that implements the three‐stage Lobatto IIIA formula. The results are novel and have been validated with LM‐SNNs outcomes. It has been observed that both numerical outcomes and LM‐SNNs produce equivalent results, and both approaches exhibit a drop in the velocity profile for the magnetic field near the lower plate and a rise near the upper plate. The skin friction against the Prandtl number increases, whereas the Nusselt number decreases at the upper disc. Compared to BVP‐4c numerical approaches, the given LM‐SNNs model is more dependable, efficient, and time‐saving because it requires less work and produces results quickly.

Mathematical modeling of creeping electromagnetohydrodynamic peristaltic propulsion in an annular gap between sinusoidally deforming permeable and impermeable curved tubes

The present work investigates the creeping peristaltic propulsion of viscid fluid in an annular gap between sinusoidally deforming permeable and impermeable curved tubes of similar shape under the influence of an externally imposed electric and magnetic field. In this model, the outer tube with a permeable wall surface is supposed to satisfy the Saffman slip condition. The flow equations are simplified by the estimation of a large wavelength in comparison with the radius of the external tube. An analytical solution for the axial velocity is obtained in the computational software MATHEMATICA. Graphical analyses are conducted to explore the variations in wall shear stress, velocity, pressure rise, frictional force, and stream function with respect to different emergent parameters, providing insight into the underlying physics of the flow phenomena. An investigation of the effects of the Hartmann number and electric field strength on the flow through a gap between deformable tubes with curved structures has important implications for a variety of engineering applications, including mechanical and biomedical engineering. The streamlines are plotted to discuss fluid trapping and visualize the flow pattern of the viscid fluid inside the curved annular domain. A comparative analysis of fluid transport induced by sinusoidal, triangular, trapezoidal, and square wave shapes is encountered with the help of streamlined contour diagrams. The comparison of pressure gradients in three different models is also discussed to gain insight due to fluid–structure interaction. A gap in the body of recently published literature is filled by the results discussed in this paper.

Viscous fluid flow and heat transfer past a permeable wall jet with convective boundary conditions

PurposeThe steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered.Design/methodology/approachThe partial differential equations for mass, momentum and energy conservation are changed to the system of ordinary differential equations through similarity solution transformations. Solutions, both numerical and asymptotic, to these similarity equations are found in some new ranges of parameters in the governing equations.FindingsThe equations are solved both asymptotically and numerically for a range of the transpiration parameter S and the flow parameter λ given in Mahros et al. (2023), thus greatly extending the range of these previous solutions. Asymptotic solutions for both large and small values of the Prandtl number σ are derived, showing good agreement with additional numerical integrations. It should be noted that in Mahros et al. (2023), only the case when σ=1 was treated. A solution for large λ when S=1 is obtained, showing a different asymptotic form to the case when S>0 in Mahros et al. (2023). Multiple solutions were seen by them for S<0 and the nature of the lower solution branch as S→0 from below is discussed. The question as to whether the lower branch solutions join as λ>0 when S<0 is resolved through obtaining an asymptotic solution λ small.Originality/valueThe accuracy of the solutions has been checked through a detailed comparison between the solutions obtained numerically and analytically, where excellent agreement has been found. This study is important for scientists working in the area of jet flows to become familiar with the flow properties and behaviour of jets.

Dynamics of Gas Motion in Pipe with Permeable Wall

Dynamics of Gas Motion in Pipe with Permeable Wall

The analytical solutions of squeezing flow and heat transfer in an horizontal filtering channel

Flow and heat transfer dynamics inside different industrial chambers play a vital role in understanding momentum and heat transfer during industrial operations. Analysis of such flow and heat transfer helps operators to know how the system works. To better understand the filtration process, the current study analytically investigated the internal flow and heat transfer through a porous horizontal filter channel under the influence of a uniform magnetic field while removing unwanted contaminations from the fluid inside the filter chamber. Thus, the novelty of the current study is to advance the filtration process by investigating how the top moving wall, which aims to minimise filter cake formation, affects permeates outflow (the current design). The partial differential equations (PDEs) model representing the internal flow and heat transfer during filtration is transformed into a system of ordinary differential equations (ODEs) using Lie point symmetry reduction without changing the dynamics under investigation. After that, the transformed equations are solved analytically using the perturbation approximation technique. The comparative analysis between the obtained semi-analytical and NDSolve numerical solutions was used to show the correlation of internal flow, temperature, and pressure profiles. The obtained solutions are used to find the best combination of dimensionless parameters that arise from flow and heat transfer dynamics that lead to optimum outflow. Graphical analysis of flow and heat transfer dynamics are used to indicate the combination of parameters that leads to maximum outflow based on scientific evidence. It is observed that, on average, the velocity increases significantly by 122.55% across all cases of Re ranging from 0 to 3.2 at the top permeable wall y=1. This significant increase is due to the motion of the moving wall and fluid injection happening at y=1. The results show that more chamber volume, small pores size, weak injection, weak magnetic force, and less Joule heating are crucial to increase internal temperature and permeate outflow velocity during filtration.

Biochar reduces antibiotic transport by altering soil hydrology and enhancing antibiotic sorption

The performance of biochar (BC) in reducing the transport of antibiotics under field conditions has not been sufficiently explored. In repacked sloping boxes of a calcareous soil, the effects of different BC treatments on the discharge of three relatively weakly sorbing antibiotics (sulfadiazine, sulfamethazine, and florfenicol) via runoff and drainage were monitored for three natural rain events. Surface application of 1 % BC (1 %BC-SA) led to the most effective reduction in runoff discharge of the two sulfonamide antibiotics, which can be partly ascribed to the enhanced water infiltration. The construction of 5 % BC amended permeable reactive wall (5 %BC-PRW) at the lower end of soil box was more effective than the 1 %BC-SA treatment in reducing the leaching of the most weakly sorbing antibiotic (florfenicol), which can be mainly ascribed to the much higher plant available and drainable water contents in the 5 %BC-PRW soil than in the unamended soil. The results of this study highlight the importance of BC’s ability to regulate flow pattern by modifying soil hydraulic properties, which can make a significant contribution to the achieved reduction in the transport of antibiotics offsite or to groundwater.

Reinventing shake flask fermentation: The breathable flask.

Cultivating cells in shake flasks is a routine operation that is largely unchanged since its inception. A glass or plastic Erlenmeyer vessel with the primary gas exchange taking place across various porous plugs is used with media volumes typically ranging from 100 mL to 2 L. Oxygen limitation and carbon dioxide accumulation in the vessel is a major concern for studies involving shake flask cultures. In this study, we enhance mass transfer in a conventional shake flask by replacing the body wall with a permeable membrane. Naturally occurring concentration gradient across the permeable membrane walls facilitates the movement of oxygen and carbon dioxide between the flask and the external environment. The modified flask called the breathable flask, has shown a 40% improvement in mass transfer coefficient (kLa) determined using the static diffusion method. The prokaryotic cell culture studies performed with Escherichiacolishowed an improvement of 28%-66% in biomass and 41%-56% in recombinant product yield. The eukaryotic cell culture study performed with Pichia pastoris expressing proinsulin exhibited a 40% improvement in biomass and 115% improvement in protein yield. The study demonstrates a novel approach to addressing the mass transfer limitations in conventional shake flask cultures. The proposed flask amplifies its value by providing a membrane-diffusion-based sensing platform for the integration of low-cost, noninvasive sensing capabilities for real-time monitoring of critical cell culture parameters like dissolved oxygenand dissolved carbon dioxide.

Numerical study on altitude-compensating mechanism of a permeable nozzle

A conceptual adaptive altitude compensation nozzle with a permeable wall (permeable nozzle for short) is proposed in the present study. The typical operating states of the nozzle are demonstrated using numerical methods and the underlying mechanism of its altitude compensation is interpreted. The numerical results show that, at low nozzle pressure ratios, the external atmosphere enters the nozzle through its permeable wall section, which inhibits the backflow at the nozzle wall, weakens the strength of the separated oblique shock, thus improves the low-altitude thrust performance of the nozzle. However, at high nozzle pressure ratios, the exhaust gas leaves the nozzle through its permeable wall, which weakens the expansion of the exhaust gas and reduces the thrust performance. The permeable nozzle is considered to possess altitude compensation ability when the enhancement in its low-altitude thrust performance surpasses the deterioration in high-altitude thrust performance. The thrust composition analysis of the permeable nozzle reveals that its altitude compensation ability derives from the internal pressure rise due to the atmospheric air penetration into the nozzle at low nozzle pressure ratios.

Numerical investigation of LDL nanoparticle collision in coronary artery grafts with porous wall and different implantation angles and two state of inlet velocity.

This study aimed to reduce the risk of graft occlusion by evaluating the two-phase flow of blood and LDL nanoparticles in coronary artery grafts. The study considered blood as an incompressible Newtonian fluid, with the addition of LDL nanoparticles, and the artery wall as a porous medium. Two scenarios were compared, with constant inlet velocity (CIV) and other with pulsatile inlet velocity (PIV), with LDL nanoparticles experiencing drag, wall-induced lift, and induced Saffman lift forces, or drag force only. The study also evaluated the concentration polarization of LDLs (CP of LDLs) near the walls, by considering the artery wall with and without permeation. To model LDL nanoparticles, the study randomly injected 100, 500, and 1000 nanoparticles in three release states at each time step, using different geometries. Numerical simulations were performed using COMSOL software, and the results were presented as relative collision of nanoparticles to the walls in tables, diagrams, and shear stress contours. The study found that a graft implantation angle of 15° had the most desirable conditions compared to larger angles, in terms of nanoparticle collision with surfaces and occlusion. The nanoparticle release modes behaved similarly in terms of collision with the surfaces. A difference was observed between CIV and PIV. Saffman lift and wall-induced lift forces having no effect, possibly due to the assumption of a porous artery wall and perpendicular outlet flow. In case of permeable artery walls, relative collision of particles with the graft wall was larger, suggesting the effect of CP of LDLs.

“The Right Despair”: Kafka’s Nihilist Technique

Kafka’s drawing style, like his writing one, is abstemious in the extreme; the question is how to characterize his criterion of subtraction. Studying the diary drawings alongside the text in which they are embedded points toward a general dynamic of deactivation—an aesthetics of disillusion in the baroque tradition of desengaño—that can be seen more clearly than read. Kafka repeatedly draws and writes about thresholds. But while his diary writing tends to thematize a perceived failure to pass from one side to another, the accompanying drawings systematically eliminate this register, and with it, all sense of directional movement or striving. The drawings operate as emblems of a passage, and so also of metapherein, in all its most iconic shapes—ladders, gates, permeable walls—but of a passage suspended at the very apex of its arc, where failure is impossible to distinguish from success. The nihilistic thrust of an aestheticized despair is here in turn negated, and the result, like Wittgenstein’s duck rabbit example, is in principle ambiguous. The essay argues that such structural ambiguity becomes a crucial feature of the literary works, which are constructed, as the diary entries themselves usually are not, in accordance with a similarly emblematic technique of double negation or “right despair.”

An Analytical Study of Fluid Flow Through a Porous Filled Channel with Permeable Wall: Suction/Injection Wall Conditions

To depict fluid movement in a channel with a rectangle-shaped cross-section and porous walls, the twodimensional Darcy Brinkman equation of motion with uniform suction and injection is analytically solved using the perturbation method. The analytical expressions for non-dimensional axial velocity, normal velocity, skin friction coefficient and pressure drop are obtained using the perturbation method at a low Reynolds number. Graphical analysis has been done for the derived quantities for different Darcy and Reynolds numbers. At higher Reynolds numbers, the emergence of the velocity overshoots and the presence of an unfavourable pressure gradient zone are significantly less noticeable. The streamlines follow the same pattern since the flow is steady. When the Darcy number is large, the non-dimensional stream function expression reduces to the stream function expression available in the literature. Non-dimensional pressure drop increases up to a specific entry length. The skin friction coefficient decreases as the Reynolds number increases. Acceleration of the fluid in the porous region leads to lesser skin friction; hence, pressure drop rises.

Reynolds number dependence of turbulent flows over a highly permeable wall

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$ , and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$ . Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

New in the hydraulics of channels with permeable walls: indicator of the relative value of the dissipation

The factors that have led to the creation of the scientific direction “hydraulics of variable mass” to study the fluid movement laws in channels with permeable walls are indicated. The results of applying of the dynamics of a variable mass point for describing the flow in such pipelines are presented. It is noted unjustifiability of the second Newton’s law generalization to the case of motion of a variable mass point for hydrodynamics problems. The functionality of one-dimensional and multidimensional models of fluid motion in permeable channels based on the classical equations of fluid and gas mechanics is characterized. It is substantiated the dominance of one-dimensional models in engineering computational practice, and a number of contradictions in the description of fluid dynamics are shown (with the flow visualization). On the base of the new kinematic image (instead of the generally accepted “solid jet”, when fluid particles are separated or joined), it has been obtained a one-dimensional equation of fluid motion in a permeable channel in which the friction coefficient is an indicator of the relative magnitude of the energy dissipation of the flow. The dependence of the Coriolis coefficient on the flow regime is constructed. The structure of the friction drag coefficient of a permeable channel has been studied using the vector dimension of length. It is shown that the dissipation of the flow energy in a permeable channel is higher both during outflow and inflow of liquid than in channels with solid walls at the same flow rates. The results are in demand in the development of chemical technology devices, nuclear reactors with microfuel elements, filters and heat exchangers containing channels with permeable walls.

Darcy-Forchheimer hybrid nanofluid flow in an asymmetric channel with an exponential heat source, variable thermal conductivity, and activation energy

Background Heat transfer in nanofluid flows plays a vital role in many industrial, medical, and manufacturing industries. Hybrid nanofluid (HNF) has a significant potential to enhance the thermal characteristics of several fluids employed in a wide range of thermal systems and thus uses reduced energy and provides increased sustainability. Also, the thermal conductivity of nanofluid depends on the mobility of nanoparticles and that can be improved by activation energy (AE) besides the latent micro convection. Literature reveals that the research works available on the enhanced heat transfer due to the appropriate combination of nanoparticles along with AE in an asymmetric channel is very limited. Aim This study aims to explore the impact of the AE and the variable thermal conductivity (VTC) on the HNF flow in an asymmetric channel with permeable walls. The effects of radiation, thermal conductivity, and exponential heat sources are also considered. Method An effective similarity transformation is used to convert the governing equations into a system of nonlinear ordinary differential equations (ODEs). The nonlinear ODEs with appropriate boundary conditions are solved numerically by a shooting method. Results The consequences of the physical parameters on the axial velocity, temperature, and species concentration are explained and are presented through graphs. In comparison to viscous fluid, the dual nanofluids have a 5.8% higher heat transfer rate with VTC parameter at the lower wall. However, the species concentration rate of HNF is 20.0% higher than that of viscous fluid with AE parameter.