Begell House Inc.
Journal of Porous Media
JPM
1091-028X
11
6
2008
Investigation of a Stochastic Model for Multiscale Dispersion in Porous Media
507-524
10.1615/JPorMedia.v11.i6.10
Don
Kulasiri
Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand
Sean
Richards
Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Canterbury, New Zealand
In this paper we explain the underlying concepts and reasoning behind a stochastic solute transport model (SSTM) for porous media developed without resorting to Fickian assumptions. The behavior of the model is explored for the different scales of experiments, and is compared with that of a deterministic dispersion model through the dispersion coefficient. The computational analysis shows that the SSTM is capable of mimicking advection-dispersion of a solute in a given porous media, and with the same values in SSTM parameters, variance, and correlation coefficient, multiscale behavior can be simulated. Dispersivity estimated for the concentration profiles from the SSTM are in the same neighborhood as the experimental data in the literature. This model shows promise in modeling advection-dispersion using the concepts in stochastic calculus.
Flow and Heat Transfer in a Cylinder with a Porous Medium Insert along the Compression Stroke
525-540
10.1615/JPorMedia.v11.i6.20
Nessrine
Zahi
Ecole Nationale d'Ingenieur de Monastir, Laboratoire d'Etude des Systémes Thermiques et Energétiques, Rue Ibn, Eljazar, 5019 Monastir, Tunisie
A.
Boughamoura
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisie
Dhahri
Hacen
National school of Engineers Laboratory of Thermal and Energy Systems Studies Monastir University, Ibn Eljazzar Street, 5019 Monastir, Tunisia
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
A numerical study of a laminar piston-driven flow and heat transfer is made in a cylinder partially filled with a laterally heated saturated porous medium. The Brinkman-Lapwood-Forchheimer-extended Darcy model, with variable porosity, is used in the compressible momentum equations. For the energy equation, the local thermal equilibrium assumption is used between the fluid and the solid phases. Numerical solutions are obtained during the compression stroke. Flow and temperature fields are examined over ranges of the principal parameters, i.e., the Reynolds number, the Darcy number, the porous medium length, the heat capacity ratio, and the thermal conductivity ratio.
Natural Convection Heat Transfer in an Inclined Porous Cavity under Time-Periodic Boundary Conditions with Positive/Negative Inclined Angles
541-555
10.1615/JPorMedia.v11.i6.30
Gang
Wang
Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China; and School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, P. R. China
Qiu-Wang
Wang
Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P.R. China
Min
Zeng
Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
Hiroyuki
Ozoe
Institute of Advanced Material Study, Kyushu University, Kasuga, Japan; and Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China
The unsteady natural convection in an inclined porous cavity with positive or negative inclined angles is studied numerically for the sinusoidal oscillating wall temperature on one side wall and constant average temperature on the opposing side wall. This system has no temperature difference between the opposing two side walls in a time-averaged sense, as studied by Kalabin et al. for a square enclosure. The flow field is modeled using the Brinkman-extended Darcy model. The effects of positive/negative inclined angles of the enclosure and oscillation frequency of wall temperature are studied for Ra = 106, Da = 10−3, ε = 0.6, and Pr = 1. The results demonstrate that the direction of heat flux is always from the lower side wall toward the upper side wall irrespective of the angles of inclination being positive or negative.
Entropy Generation for Pulsating Flow in a Composite Fluid/Porous System
557-574
10.1615/JPorMedia.v11.i6.40
Dhahri
Hacen
National school of Engineers Laboratory of Thermal and Energy Systems Studies Monastir University, Ibn Eljazzar Street, 5019 Monastir, Tunisia
Khalifa
Slimi
ISTLS
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
A numerical study of entropy generation for pulsating flow within a cylinder partially filled with a porous medium and exposed to a constant heat flux at the wall was carried out in the laminar flow regime. The porous substrate is attached to the inner side of the cylinder axis, while the upper side is filled with a pure fluid phase. The flow within the porous domain is modeled by the Brinkman-Lapwood-Forchheimer-extended Darcy model. The mathematical model for energy transport is based on the local thermal equilibrium assumption. The control volume-based finite element method is used to solve the differential system equations with an unequal order velocity-pressure interpolation. The obtained numerical code was validated with the closest available published results. A good agreement was shown. The numerical results of the flow, heat transfer, and entropy generation are presented and discussed. A comprehensive analysis of the influence of the amplitude pulsation, the frequency pulsation, the thermal conductivity ratio, the Darcy number, the porous layer thickness, and the modified Brinkman number on the entropy generation rate, as well as on the Bejan number, is also investigated.
Rotation of a Solid Sphere in a Viscous Fluid Bounded by a Concentric Spherical Porous Medium
575-588
10.1615/JPorMedia.v11.i6.50
Parul
Saxena
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh
226007, India
A. C.
Srivastava
Department of Mathematics & Astronomy, Lucknow University, Lucknow - 226007, India
The flow of a viscous fluid in a spherical annulus formed by a solid sphere rotating with a constant angular velocity and a concentric spherical porous medium has been discussed for small Reynolds numbers. The porous medium is fully saturated with the viscous fluid. It is assumed that the flow in the annular region of the width d in which a clear fluid flows is governed by the Navier-Stokes equation and that in the porous medium by Brinkman equation. Two flows are matched at the interface by the conditions suggested by Ochoa-Tapia and Whitaker. It has been found that the rotational velocity in both the media increases with the increase of permeability and with the decrease of d. It is maximum at the interface and then decreases exponentially. The effects of the decrease of d and increase of the ratio of effective viscosity in the porous medium and the viscosity of the fluid are to increase the torque on the rotating sphere. The torque on the rotating sphere also increases with the decrease of the permeability of the porous medium.
An Analytic Solution of Water Transport in Unsaturated Porous Media
591-601
10.1615/JPorMedia.v11.i6.60
M.
Nasseri
Civil Engineering Department, Shiraz University, Shiraz, IR, Iran
M. R.
Shaghaghian
Civil Engineering Department, Shiraz University, Shiraz, IR, Iran
Y.
Daneshbod
Civil Engineering Department, Islamic Azad University of Arsenjan, Arsenjan, IR, Iran
H.
Seyyedian
Civil Engineering Department, Shiraz University, Shiraz, IR, Iran
One of the most well-known equations to describe the behavior of the infiltration of unsaturated zones in soil as a porous medium is known as Richards' equation. Although analytical approaches in simulating infiltration are few, there are many numerical researches to model this physical phenomenon. The Adomian decomposition method (ADM) is one of the most recent approaches used in solving nonlinear partial differential or algebraic equations, and is an easy way to achieve the analytic solution. In this article, two refined approaches in improving ADM are used to simulate volumetric water content via Richards' equation. The first modification was recently presented by Wazwaz using a new regrouping approach in Adomian series terms and the last is the Pade approximation. A comparison of the exact solution and (modified) ADM illustrate very good coverage and results.
Three-Dimensional Free Convection Flow of a Viscous Fluid through a Nonhomogeneous Porous Medium
603-615
10.1615/JPorMedia.v11.i6.70
The present study deals with the theoretical analysis of time-dependent periodic variation in suction velocity and permeability on free convection unsteady flow of a viscous incompressible fluid past an infinite vertical porous plate. The flow is three-dimensional because the variation of permeability and suction velocity is transverse to the potential flow. Considering the free stream velocity to be uniform, series solutions are obtained for the flow field and temperature field. Expressions for the skin friction and heat transfer are also derived. The effects of all parameters on velocity, temperature, skin friction, and heat transfer rate (Nusselt number) are presented graphically and in tabular form followed by a detailed discussion. The model finds applications in nuclear heat transfer processes, metallurgy, aerospace/naval propulsion, and energy systems.