Flow at the interface of a model fibrous porous medium

2001 ◽  
Vol 426 ◽  
pp. 47-72 ◽  
Author(s):  
DAVID F. JAMES ◽  
ANTHONY M. J. DAVIS
Keyword(s):  
Porous Medium ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Circular Cylinders ◽  
Interfacial Region ◽  
Filling Fraction ◽  
Apparent Slip ◽  
Square Array ◽  
Pressure Driven Flow

Planar flow in the interfacial region of an open porous medium is investigated by finding solutions for Stokes flow in a channel partially filled with an array of circular cylinders beside one wall. The cylinders are in a square array oriented across the flow and are widely spaced, so that the solid volume fraction ϕ is 0.1 or less. For this spacing, singularity methods are appropriate and so they are used to find solutions for both planar Couette flow and Poiseuille flow in the open portion of the channel. The solutions, accurate to O(ϕ), are used to calculate the apparent slip velocity at the interface, Us, and results obtained for Us are presented in terms of a dimensionless slip velocity. For shear-driven flow, this dimensionless quantity is found to depend only weakly on ϕ and to be independent of the height of the array relative to the height of the channel and independent of the cylinder size relative to the height of the channel. For pressure-driven flow, Us is found to be less than that under comparable shear-flow conditions, and dependent on cylinder size and filling fraction in this case. Calculations also show that the external flow penetrates the porous medium very little, even for sparse arrays, and that Us is about one quarter of the velocity predicted by the Brinkman model.

scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

An Efficient Immersed Boundary Method Based on Penalized Direct Forcing for Simulating Flows Through Real Porous Media

2012 ◽  
Author(s):  
Wim-Paul Breugem ◽  
Vincent van Dijk ◽  
René Delfos
Keyword(s):  
Porous Medium ◽  
Ct Scan ◽  
Immersed Boundary Method ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Particle Diameter ◽  
Immersed Boundary ◽  
Average Particle ◽  
Boundary Method ◽  
Direct Forcing

A computationally efficient Immersed Boundary Method (IBM) based on penalized direct forcing was employed to determine the permeability of a real porous medium. The porous medium was composed of about 9000 glass beads with an average particle diameter of 1.93 mm and a porosity of 0.367. The forcing of the IBM depends on the local solid volume fraction within a computational grid cell. The latter could be obtained from a high-resolution X-ray Computed Tomography (CT) scan of the packing. An experimental facility was built to determine the permeability of the packing experimentally. Numerical simulations were performed for the same packing based on the data from the CT scan. For a scan resolution of 0.1 mm the numerical value for the permeability was nearly 70% larger than the experimental value. An error analysis indicated that the scan resolution of 0.1 mm was too coarse for this packing.

Numerical treatment for Casson liquid flow in a microchannel due to porous medium: A hybrid nanoparticles aspects

2021 ◽  
pp. 095440622110089
Author(s):  
Gombi Rachappa Manohar ◽  
Puttaswamy Venkatesh ◽  
Bijjanal Jayanna Gireesha ◽  
Gosikere Kenchappa Ramesh
Keyword(s):  
Porous Medium ◽  
Volume Fraction ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Hybrid Nanoparticles ◽  
Hybrid Nanofluid ◽  
Current Investigation ◽  
Numerical Treatment

In the current investigation a mathematical model is simplified to explore the numerical treatment for the thermal and flow behavior in a magneto hydrodynamics Casson fluid through a micro channel by taking [Formula: see text] nanoparticles. The combined effects of temperature jump, porous medium and velocity slip are incorporated. Using the dimensionless variables one can obtain the governing differential equations thereafter resolved numerically using RKF45 method. The velocity, temperature, skin friction and Nusselt number coefficient are addressed for different pertaining parameter. The upshots of the current investigation are visualized through graphically elucidation. Out comes shows that larger values of solid volume fraction decreases both velocity and temperature field. Furthermore drag coefficient is increases for increase in magnetic parameter, also hybrid nanofluid gives more impact than nanofluid.

Flows Through Real Porous Media: X-Ray Computed Tomography, Experiments, and Numerical Simulations

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Wim-Paul Breugem ◽  
Vincent van Dijk ◽  
René Delfos
Keyword(s):  
Computed Tomography ◽  
Porous Medium ◽  
Ct Scan ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
X Ray ◽  
X Ray Computed

Two different direct-forcing immersed boundary methods (IBMs) were applied for the purpose of simulating slow flow through a real porous medium: the volume penalization IBM and the stress IBM. The porous medium was a random close packing of about 9000 glass beads in a round tube. The packing geometry was determined from an X-ray computed tomography (CT) scan in terms of the distribution of the truncated solid volume fraction (either 0 or 1) on a three-dimensional Cartesian grid. The scan resolution corresponded to 19.3 grid cells over the mean bead diameter. A facility was built to experimentally determine the permeability of the packing. Numerical simulations were performed for the same packing based on the CT scan data. For both IBMs the numerically determined permeability based on the Richardson extrapolation was just 10% lower than the experimentally found value. As expected, at finite grid resolution the stress IBM appeared to be the most accurate IBM.

scholarly journals Simulation and Analysis of Unbonded Nonwoven Fibrous Structures

2006 ◽  
Vol 1 (2) ◽  
pp. 155892500600100 ◽  
Author(s):  
Behnam Pourdeyhimi ◽  
Benoit Mazé ◽  
Hooman Vahedi Tafreshi
Keyword(s):  
Porous Medium ◽  
Volume Fraction ◽  
Fiber Diameter ◽  
Solid Volume Fraction ◽  
Fiber Properties ◽  
Nonwoven Materials ◽  
Potential Applications ◽  
Modeling Transport ◽  
Long Fibers ◽  
Virtual Structures

In this work we report on our algorithm for generating 3–D virtual structures resembling un-bonded fibrous webs. The paper discusses short and infinitely long fibers, each emulating a category of nonwoven fibrous medium. The structure Solid Volume Fraction (SVF), being the most important characteristic of a fibrous porous medium, is calculated for different fiberwebs and discussed in details. It is shown that the SVF of the fibrous structures generated by our algorithm is independent of the basis weight. In other words, the porosity of the medium is only a function of the fiber properties – this is as expected. It is also demonstrated that by decreasing the fiber diameter while keeping other properties of the virtual fiberweb constant causes the SVF to decrease almost linearly. The same is not observed for the fiber rigidity. The capability of our algorithm for generating fibrous webs made up of layers of different fibers is demonstrated and their properties are discussed. The application of such virtual fibrous structures in modeling transport phenomena in nonwoven materials and their potential applications in load-deformation studies are discussed.

scholarly journals Soret- Dufour Effect on Mixed Convection Past a Vertical Plate in Non-Darcy Porous Medium Saturated With Buongiorno Nanofluid in the Presence of Thermal Dispersion

2019 ◽  
Vol 35 (6) ◽  
pp. 851-862
Author(s):  
A. Aghbari ◽  
H. Ali Agha ◽  
D. Sadaoui
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Thermal Dispersion ◽  
Convective Boundary

ABSTRACTNumerical analysis was investigated for steady two-dimensional double diffusive mixed convection boundary layer flow over a semi-infinite vertical plate embedded non-Darcy porous medium filled with nanofluid, in presence of thermal dispersion and under convective boundary conditions. The Buongiorno nanofluid model is used, while the porous medium is described by the Darcy-Forchheimer extension. The governing partial differential equations are transformed into four coupled nonlinear ordinary differential equations using an appropriate similarity transformations and the resulting system of equations is then solved numerically by the finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature, concentration and solid volume fraction profiles. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of pertinent parameters.

scholarly journals Slip Microrotation Flow of Silver-Sodium Alginate Nanofluid via Mixed Convection in a Porous Medium

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3232
Author(s):  
Hossam A. Nabwey ◽  
Ahmed M. Rashad ◽  
Waqar A. Khan
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Skin Friction ◽  
Sodium Alginate ◽  
Volume Fraction ◽  
Colloidal Suspension ◽  
Solid Volume Fraction ◽  
Velocity Slip ◽  
Research Attention

In the previous decennium, considerable applications ofnanoparticles have been developed in the area of science. Nanoparticles with micropolar fluid suspended in conventional fluids can increase the heat transfer. Micropolar fluids have attracted much research attention because of their use in industrial processes. Exotic lubricants, liquid crystal solidification, cooling of a metallic plate in a bath, extrusion of metals and polymers, drawing of plastic films, manufacturing of glass and paper sheets, and colloidal suspension solutions are just a few examples. The primary goal of this studywas to see how radiation and velocity slip affect the mixed convection of sodium alginate nanofluid flow over a non-isothermal wedge in a saturated porous media.In this communication, theTiwari and Das model was employed to investigate the micropolarnanofluid flow via mixed convection over aradiated wedge in a saturated porous medium with the velocity slip condition. Nanoparticles of silver (Ag) wreused in asodium alginate base fluid. The intended system of governing equations is converted to a set of ordinary differential equations and then solved applying the finite difference method. Variousfluid flows, temperatures, and physical quantities of interest were examined. The effects of radiation on the skin friction are negligible in the case of forced and mixed convection, whereas radiation increases the skin friction in free convection. It is demonstrated that the pressure gradient, solid volume fraction, radiation, and slip parameters enhance the Nusselt number, whereas the micropolar parameter reduces the Nusselt number.

PIV measurements of flow through a model porous medium with varying boundary conditions

2009 ◽  
Vol 629 ◽  
pp. 343-374 ◽  
Author(s):  
JAMES K. ARTHUR ◽  
DOUGLAS W. RUTH ◽  
MARK F. TACHIE
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Porous Media ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Rectangular Channel ◽  
Solid Volume Fraction ◽  
Working Fluid ◽  
Free Zone ◽  
Flow Through

This paper reports an experimental investigation of pressure-driven flow through models of porous media. Each model porous medium is a square array of circular acrylic rods oriented across the flow in a rectangular channel. The solid volume fraction φ of the arrays ranged from 0.01 to 0.49. Three boundary conditions were studied. In the first boundary condition, the model porous medium was installed on the lower wall of the channel only and was bounded by a free zone. In the second and third boundary conditions, porous media of equal and unequal φ were arranged on the lower and upper channel walls so that the two media touched (second boundary condition), and did not touch (third boundary condition). Using water as the working fluid, the Reynolds number was kept low so that inertia was not a factor. Particle image velocimetry was used to obtain detailed velocity measurements in the streamwise-transverse plane of the test section. The velocity data were used to study the effects of φ and the different boundary conditions on the flow through and over the porous medium, and at the interface. For the first boundary condition, it was observed that at φ = 0.22, flow inside the porous medium was essentially zero, and the slip velocity at the porous medium and free zone interface decayed with permeability. In the second and third boundary conditions, flow communication between the porous media was observed to be dependent on the combinations of φ used, and the trends of the slip velocities at the interface between the two porous media obtained for that boundary condition were indicative of complicated interfacial flow.

Experimental Study of Turbulent Flow in Two-Dimensional Porous Media

2009 ◽  
Author(s):  
Sintia Bejatovic ◽  
Martin Agelinchaab ◽  
Mark F. Tachie
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Turbulent Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Channel Height ◽  
Two Dimensional ◽  
Clear Fluid ◽  
Test Channel ◽  
Flow Through

The paper reports on an experimental investigation of turbulent flow through model two-dimensional porous media. The porous media was bounded on one side by a solid plane wall and on the other side by a zone of clear fluid. The model porous media comprised of square arrays of circular acrylic rods that were inserted into precision holes drilled onto pairs of removable plates. The removable plates were then inserted into groves made in the side walls of the test channel. The rods fill about 59% of the channel height. Different combinations of rod diameter and center-to-center spacing were used to produce solid volume fractions that ranged from 0.11 to 0.44. The Reynolds number based on the bulk velocity of the approach flow and channel height was 16800. A high resolution particle image velocimetry (PIV) system was used to conduct detailed velocity measurements within the porous media and the adjacent clear fluid. The results demonstrate that permeability of the porous medium is more useful in correlating the flow characteristics than the porosity or solid volume fraction. Irrespective of rod diameter or spacing, a decrease in permeability of the porous medium produced a lower value of the dimensionless slip velocity. A decrease in permeability also produced higher resistance to the fluid flow through the porous medium. As a result, a larger fraction of the approach flow is channeled through the clear zone adjacent to a porous medium with lower permeability than those with relatively higher permeability. It was also observed that spatially averaged profiles of the mean velocities and turbulent quantities depend strongly on permeability.

Mixed Convection in an Inclined Nanofluid Filled-Cavity Saturated With a Partially Layered Porous Medium

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Abdelraheem M. Aly ◽  
Z. A. S. Raizah
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Particle Hydrodynamics ◽  
Medium Layer ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics ◽  
Inclined Cavity

The contribution of the current study is to investigate the mixed convection in an inclined nanofluid filled cavity saturated with a partially layered non-Darcy porous medium. Moreover, due to the advantage of the particle-based methods, we presented the improved version of an incompressible smoothed particle hydrodynamics (ISPH) method. The current ISPH method was improved in boundary conditions treatment using renormalization kernel function. In the current investigation, we assumed that the inclined cavity is filled with a Cu-water nanofluid. The upper half of the cavity is saturated with a non-Darcy porous medium. Here, one domain approach is used for coupling the nanofluid and the porous medium layer. The cooled top wall of the cavity is carrying a tangential unit velocity and the bottom wall is heated. The other two wall sides are adiabatic at zero velocity. Here, we investigated the effects of the Richardson parameter Ri0.0001–100, Darcy parameter Da 10−5–10−2, an inclination angle α0–90deg and a various solid volume fraction ϕ0–0.05 on the heat transfer of a Cu-water nanofluid. The obtained results showed that the average Nusselt number decreases as the Richardson number increases. An addition of 1–5% Cu nanoparticles slightly increased the overall heat transfer rate.

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