Geometric Porosity Research Articles

Hard convex body fluids in random porous media: Scaled particle theory

The scaled particle theory (SPT) is applied to describe thermodynamic properties of hard convex body (HCB) fluid in random porous media. To this purpose we extended the SPT2 approach, which has been developed previously for a hard sphere fluid in random porous matrices. The analytical expressions for the chemical potential and the pressure of an HCB fluid in an HCB or an overlapping hard convex body (OHCB) matrix are obtained and analyzed. Within the SPT2 approach a series of new approximations are proposed. The grand canonical Monte Carlo (GCMC) simulations are performed to verify an accuracy of the SPT2 and the developed approaches. The obtained analytical expressions include three types of porosity: the geometrical porosity ϕ0, the probe particle porosity ϕ and the porosity ϕ⁎ defined by the maximum packing fraction of a fluid in a given matrix. The effect of nonsphericity parameters of matrix and fluid particles on the thermodynamic properties of a fluid is discussed.

Experimental Investigation of Parachute Canopies with Rectangular Parallelepiped Geometries

A series of wind-tunnel experiments were conducted in which the drag characteristics and inflated geometry of model parachute canopies with rectangular parallelepiped geometries (polyhedron) were examined. The model-canopy layouts were the same as cross canopies with the adjacent sides completely attached together. All models had a base dimension of 0.2 m, and aspect ratios ranged from 0.2 to 1.2. The models did not have a central vent or any other geometric porosity. The data show the inflated geometry of the canopy differs from the constructed geometry with the smallest change occurring at a constructed aspect of 0.8 and the variation becomes larger for increasing or decreasing constructed aspect ratios. The data also indicate the aerodynamic drag coefficient, based on the projected area, has a maximum value of approximately one for the constructed aspect ratio of 0.3 corresponding to an inflated aspect ratio of 0.53. The drag coefficient is less for smaller and larger aspect-ratio models. If scaled by the canopy surface area drag of the rectangular parallelepiped canopies is lower than flat circular canopy designs. These findings are consistent with the past findings on other flexible parachute canopies and rigid bluff bodies.

Tracer tests to evaluate hydraulic residence time in limestone drains: Case study of the Lorraine site, Latulipe, Québec, Canada

Acid mine drainage (AMD) remains one of the major environmental problems for the mining industry. When AMD is produced on a mine site, passive treatment techniques such as limestone drains (LDs) can be used to improve water quality, particularly when the effluent is relatively small. In 1999, LDs were installed in combination with a cover with capillary barrier effects to rehabilitate the abandoned acid-generating Lorraine mine site in Quebéc, Canada. However, the quality of the water exiting the LD does not meet the local regulations (even if a significant improvement has been observed). To better understand the behaviour of the drains, the hydraulic residence time (HRT) was evaluated using various tracer tests. Tests’ results indicate that the HRT in the Lorraine LDs is close to the minimum value targeted at the design stage but is significantly different than those estimated from the geometrical characteristics and porosity of the drains and the water flow discharge.

Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity

Fluid---structure interaction (FSI) modeling of parachutes poses a number of computational challenges. These include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of ringsail parachutes the geometric porosity created by the construction of the canopy from "rings" and "sails" with hundreds of "ring gaps" and "sail slits," in the case of parachute clusters the contact between the parachutes, and "disreefing" from one stage to another when the parachute is used in multiple stages. The Team for Advanced Flow Simulation and Modeling (T?AFSM) has been successfully addressing these computational challenges with the Stabilized Space---Time FSI (SSTFSI) technique, which was developed and improved over the years by the T?AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T?AFSM, which are applicable to cases with nonmatching fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light. The special technique used in dealing with the geometric complexities of the rings and sails is the homogenized modeling of geometric porosity (HMGP), which was developed and improved in recent years by the T?AFSM. The surface-edge-node contact tracking (SENCT) technique was introduced by the T?AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T?AFSM. As an additional computational challenge, the parachute canopy might, by design, have some of its panels and sails removed. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the HMGP and needs to be actually resolved during the FSI computation. In this paper we focus on parachute disreefing, including the disreefing of parachute clusters, and parachutes with modified geometric porosity, including the reefed stages of such parachutes. We describe the additional special techniques we have developed to address the challenges involved and report FSI computations for parachutes and parachute clusters with disreefing and modified geometric porosity.

One-dimensional hard rod fluid in a disordered porous medium: scaled particle theory

The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical expressions are obtained for the chemical potential and pressure of a hard-rod fluid in hard rod and overlapping hard rod matrices. A series of new approximations for SPT2 are proposed. It is shown that apart from two well known porosities such as geometrical porosity and specific probe particle porosity, a new type of porosity defined by the maximum value of packing fraction of fluid particles in porous medium should be taken into account. The grand canonical Monte-Carlo simulations are performed to verify the accuracy of the SPT2 approach in combination with the new approximations. It is observed that the theoretical description proposed in this study essentially improves the results up to the highest values of fluid densities.

A Geometric Analysis of the Loop Form of a Tricot Stitch Knitted Fabric

A tricot stitch knitted fabric has been used in medical stents, such as tracheal stents and external stents. Both geometric form and porosity of the stent are key factors in clinical use. One loop of the tricot stitch knitted fabric was divided into seven parts, and the loop form was analyzed. The geometric characteristics under extreme condition for both latitudinal and longitudinal extension were given. The relationships between geometrical parameters of a tricot stitch knitted fabric were obtained.

Computational Methods for Parachute Fluid–Structure Interactions

The computational challenges posed by fluid–structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of “ringsail” parachutes the geometric complexities created by the construction of the canopy from “rings” and “sails” with hundreds of ring “gaps” and sail “slits”, and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling ( ) has successfully addressed these computational challenges with the Stabilized Space–Time FSI (SSTFSI) technique, which was developed and improved over the years by the and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the , which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the . The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the . We provide an overview of the core and special techniques developed by the , present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters.

Effect of a Bottom Gap on the Flow Characteristics behind Non-Planar Porous Fence

The flow field behind non-planar porous fence of geometric porosity ε=0.273 with various bottom gaps (G) has been investigated by hot-wire anemometer velocity field measurement technique in a wind tunnel experiment. Seven gap ratios G/H=0.000, 0.025, 0.075, 0.125, 0.150, 0.175, 0.200 of non-planar porous fence were tested in this study with the free-stream velocity fixed at 10m/s. The experimental data were analyzed and the turbulence intensity and wind reduction ratios for different gaps of the porous fence were calculated to estimate the shelter effect of a non-planar porous fence model. The results show that the gap ratio G/H=0.150 gives the best shelter effect among the seven gaps of the non-planar porous fence tested in this study, having a better mean velocity and turbulence intensity as well as wind reduction ratio in a large area behind the non-planar porous fence.

Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes

AbstractWe focus on fluid–structure interaction (FSI) modeling and performance analysis of the ringsail parachutes to be used with the Orion spacecraft. We address the computational challenges with the latest techniques developed by the T★AFSM (Team for Advanced Flow Simulation and Modeling) in conjunction with the SSTFSI (Stabilized Space–Time Fluid–Structure Interaction) technique. The challenges involved in FSI modeling include the geometric porosity of the ringsail parachutes with ring gaps and sail slits. We investigate the performance of three possible design configurations of the parachute canopy. We also describe the techniques developed recently for building a consistent starting condition for the FSI computations, discuss rotational periodicity techniques for improving the geometric‐porosity modeling, and introduce a new version of the HMGP (Homogenized Modeling of Geometric Porosity). Copyright © 2010 John Wiley & Sons, Ltd.

Fluid–structure interaction modeling of parachute clusters

AbstractWe address some of the computational challenges involved in fluid–structure interaction (FSI) modeling of clusters of ringsail parachutes. The geometric complexity created by the construction of the parachute from ‘rings’ and ‘sails’ with hundreds of gaps and slits makes this class of FSI modeling inherently challenging. There is still much room for advancing the computational technology for FSI modeling of a single raingsail parachute, such as improving the Homogenized Modeling of Geometric Porosity (HMGP) and developing special techniques for computing the reefed stages of the parachute and its disreefing. While we continue working on that, we are also developing special techniques targeting cluster modeling, so that the computational technology goes beyond the single parachute and the challenges specific to parachute clusters are addressed. The rotational‐periodicity technique we describe here is one of such special techniques, and we use that for computing good starting conditions for FSI modeling of parachute clusters. In addition to reporting our preliminary FSI computations for parachute clusters, we present results from those starting‐condition computations. In the category of more fundamental computational technologies, we discuss how we are improving the HMGP by increasing the resolution of the fluid mechanics mesh used in the HMGP computation and also by increasing the number of gores used. Also in that category, we describe how we use the multiscale sequentially coupled FSI techniques to improve the accuracy in computing the structural stresses in parts of the structure where we want to report more accurate values. All these special techniques are used in conjunction with the Stabilized Space–Time Fluid–Structure Interaction (SSTFSI) technique. Therefore, we also present in this paper a brief stability and accuracy analysis for the Deforming‐Spatial‐Domain/Stabilized Space–Time (DSD/SST) formulation, which is the core numerical technology of the SSTFSI technique. Copyright © 2010 John Wiley & Sons, Ltd.

Space–time finite element computation of complex fluid–structure interactions

AbstractNew special fluid–structure interaction (FSI) techniques, supplementing the ones developed earlier, are employed with the Stabilized Space–Time FSI (SSTFSI) technique. The new special techniques include improved ways of calculating the equivalent fabric porosity in Homogenized Modeling of Geometric Porosity (HMGP), improved ways of building a starting point in FSI computations, ways of accounting for fluid forces acting on structural components that are not expected to influence the flow, adaptive HMGP, and multiscale sequentially coupled FSI techniques. While FSI modeling of complex parachutes was the motivation behind developing some of these techniques, they are also applicable to other classes of complex FSI problems. We also present new ideas to increase the scope of our FSI and CFD techniques. Copyright © 2009 John Wiley & Sons, Ltd.

Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.

Fluid–structure interaction modeling of ringsail parachutes

In this paper, we focus on fluid–structure interaction (FSI) modeling of ringsail parachutes, where the geometric complexity created by the “rings” and “sails” used in the construction of the parachute canopy poses a significant computational challenge. It is expected that NASA will be using a cluster of three ringsail parachutes, referred to as the “mains”, during the terminal descent of the Orion space vehicle. Our FSI modeling of ringsail parachutes is based on the stabilized space–time FSI (SSTFSI) technique and the interface projection techniques that address the computational challenges posed by the geometric complexities of the fluid–structure interface. Two of these interface projection techniques are the FSI Geometric Smoothing Technique and the Homogenized Modeling of Geometric Porosity. We describe the details of how we use these two supplementary techniques in FSI modeling of ringsail parachutes. In the simulations we report here, we consider a single main parachute, carrying one third of the total weight of the space vehicle. We present results from FSI modeling of offloading, which includes as a special case dropping the heat shield, and drifting under the influence of side winds.

Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods

The stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) was applied to a number of 3D examples, including arterial fluid mechanics and parachute aerodynamics. Here we focus on the interface projection techniques that were developed as supplementary methods targeting the computational challenges associated with the geometric complexities of the fluid–structure interface. Although these supplementary techniques were developed in conjunction with the SSTFSI method and in the context of air–fabric interactions, they can also be used in conjunction with other moving-mesh methods, such as the Arbitrary Lagrangian–Eulerian (ALE) method, and in the context of other classes of FSI applications. The supplementary techniques currently consist of using split nodal values for pressure at the edges of the fabric and incompatible meshes at the air–fabric interfaces, the FSI Geometric Smoothing Technique (FSI-GST), and the Homogenized Modeling of Geometric Porosity (HMGP). Using split nodal values for pressure at the edges and incompatible meshes at the interfaces stabilizes the structural response at the edges of the membrane used in modeling the fabric. With the FSI-GST, the fluid mechanics mesh is sheltered from the consequences of the geometric complexity of the structure. With the HMGP, we bypass the intractable complexities of the geometric porosity by approximating it with an “equivalent”, locally-varying fabric porosity. As test cases demonstrating how the interface projection techniques work, we compute the air–fabric interactions of windsocks, sails and ringsail parachutes.

Inferring fractal dimension of rough/porous surfaces - a comparison of SEM image analysis and electrochemical impedance

There are many methods for analysis and description of surface topographies that rely on analysis of surface images obtained by various methods such as SEM or AFM. However, they can seldom provide quantitative topographical information. Such information can be obtained by fractal analysis of the images resulting in a characteristic fractal dimensions. The advantage of fractal approach to surface characterization is that it is insensitive to the structural details, and the structure is characterized by single descriptor, the fractal dimension D. On the other hand, it is well established that electrochemical impedance spectroscopy (EIS) is convenient method often used to infer the fractal dimension of porous or rough surfaces-electrodes. Here we present and discuss the results of comparison of two methods for determination of topological fractal properties of porous/rough surfaces: electrochemical impedance spectroscopy and (SEM) grey-scale image analysis. We have established that in most cases there is a good correlation between the fractal dimensions inferred from EIS measurements (DEIS) and those obtained from fractal analysis of gray scale SEM images (Dg). However, the fractal dimension inferred from gray scale SEM images Dg seems to be a better descriptor of surface topology than the fractal dimension inferred from CPE exponent   of EIS measurements, since the latter may be influenced by other parameters beside pure geometrical surface roughness or porosity. This conclusion is supported with recent finding of good correlation of Dg and relevant different profilometric parameters.

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.

The effect of moisture on physical properties of sorghum and millet

Knowledge of how the physical properties of grain vary with changes in moisture content is one of the prerequisites for the design and development of efficient processing and handling machines for the grains. Physical properties of two varieties of sorghum (Dionje and Jumbo) and one variety of pearl millet (IM) were investigated at different moisture levels within the moisture range 12 to 25% dry basis. Grain samples with different moisture levels were obtained by adding calculated amounts of distilled water to the grain, mix thoroughly and seal the samples in polythene bags and keep them in refrigerator at 5°C for fourteen days to allow moisture to distribute uniformly within the sample. The results showed that within this moisture range, all the physical properties studied varied linearly with moisture content. Linear dimensions (length, width and thickness), geometrical mean diameter, sphericity, surface area, volume, kernel density and porosity increased with increase in moisture content of the grain. On the other hand, bulk density decreased with increase in moisture content of the grain. Journal of Agriculture, Science and Technology Vol. 7(1) 2005: 30-40

Structural Features of Biomass in a Hybrid MBBR Reactor

The structural features of biomass present in the hybrid MBBR (Moving Bed Biofilm Reactor) aeration tank were studied in two subsequent periods, which differed in hydraulic and substrate loads. The physical characteristics of attached-growth biomass, such as, biofilm thickness, density, porosity, inner and surface fractal dimensions, and those of suspended-growth biomass, such as, floc size distribution, density, porosity, inner and surface fractal dimensions, were investigated in each study period and then compared. The results indicated that biofilm always had a higher density, geometric porosity, and a larger boundary fractal dimension than flocs. Both types of biomass were found to exhibit at least two distinct Sierpinski fractal dimensions, indicating two major different pore space populations. With the increasing wastewater flow, both types of biomass were found to shift their structural properties to larger values, except porosity and surface roughness, which decreased. Floc density and biomass Sierpinski fractals were not affected much by the system loadings.

THE STRUCTURE OF TURBULENT SHEAR FLOW AROUND A TWO-DIMENSIONAL POROUS FENCE HAVING A BOTTOM GAP

The flow field behind porous fences of geometric porosity ε=38·5% with various bottom gaps (G) has been investigated using a hybrid PTV velocity field measurement technique. Four gap ratiosG /H=0·0, 0·1, 0·2 and 0·3 were tested in this study. One thousand instantaneous velocity vector fields in the x–y plane were consecutively measured for each gap ratio. The free-stream velocity was fixed at 10cm/s and the corresponding Reynolds number based on the fence height (H) was Re=2985. The results show that the gap ratio G/H=0·1 gives the best shelter effect among the four gap ratios tested in this study, having a small shelter parameter ψ in a large area behind the fence. As the gap ratio increases, the region of mean velocity reduction decreases and the lower shear layer developed from the bottom gap expands upward. From the spatial distributions of turbulence statistics including turbulence intensities, Reynolds shear stress and turbulent kinetic energy, the wake characteristics can be divided into two categories depending on the gap ratio. When the gap ratio is aboveG /H=0·2, the turbulence statistics have large values in the lower shear layer. For the gap ratio G/H≤0·1, however, the lower shear layer displays small turbulence-statistics values and approach those of the no-gap case (G/H=0) with increasing distance downstream. In the upper shear layer separated from the fence top, the turbulence statistics are nearly independent of the gap ratio.

Fractal Analysis of Pore Distributions in Alum Coagulation and Activated Sludge Flocs

Abstract The information on floc porosity is essential for estimation of the permeability of the aggregate. The average porosity of alum and activated sludge flocs determined in this study on thin sections of the aggregates was similar, varying in the range from 8 to 9%. Similar porosity of the two different types of aggregates suggested that the permeability of these flocs could also be similar. However, the experimental observations of floc settling rates and floc shape factors did not support this expectation and led to a conclusion that the permeability of an aggregate cannot be estimated based on the average geometric porosity of a floc only. When the size distributions of pores on flocs' sections were analyzed using the concept of fractal geometry, different characteristic values for alum coagulation and activated sludge flocs were found. Larger pore size found in activated sludge flocs allows for more flow through these flocs. Therefore, the size of characteristic pores rather than the average total porosity determines the permeability of an aggregate.