Begell House Inc.
Journal of Porous Media
JPM
1091-028X
12
7
2009
Conduction-Natural Convection in a Partitioned Triangular Enclosure Filled with Fluid Saturated Porous Media
593-611
10.1615/JPorMedia.v12.i7.10
Yasin
Varol
Vanderbilt University
Hakan Fehmi
Oztop
Mechanical Engineering Department, Firat University, Elazig, 23279, Turkey
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Numerical analysis has been performed to examine the conduction-natural convection in a partitioned triangular enclosure filled with a fluid-saturated porous medium. The enclosure is heated from the vertical wall and cooled from the inclined wall, while the bottom wall is adiabatic. In addition, the enclosure has a solid partition with finite thermal conductivity and thickness. The finite difference method is used to solve the governing partial differential equations which are written using the Darcy flow model. The parameters which affect heat transfer, flow field, and temperature distribution are the Rayleigh number, thickness of the partition, location of the center of the partition, and the thermal conductivity ratio. It is found that heat transfer is an increasing function of the Rayleigh number and thermal conductivity ratio and a decreasing function of partition thickness and partition location at the heated vertical wall.
Discretization and Solver Methods with Analytical Characteristic Methods for Advection-Diffusion Reaction Equations and 2D Applications
613-638
10.1615/JPorMedia.v12.i7.20
Juergen
Geiser
Univerity of Greifswald
Our studies are motivated by a desire to model long-time simulations of possible scenarios for waste disposal. We present transport of pollutants through ground water flowing through rocks or sand regarded as porous media. The models, including the conservation of mass and momentum for velocity and the porous media, are in accordance with Darcy's law. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion reaction equations, and the received results of several discretization methods are presented. In the numerical methods, we use large time steps to achieve long simulation times of about 10,000 years. We propose higher-order discretization methods, which allow us to use large time steps without losing accuracy. Operator splitting methods allow the decomposition of the multiphysical and multidimensional equation. Simpler physical and one-dimensional equations are obtained and can be discretized with higher-order methods. We obtain more effective solver methods with an underlying physical operator-splitting method. In the numerical example we simulate a radioactive waste disposal with underlying flowing groundwater that is solved by a density-driven flow model. The transport and reaction simulations for the decay chains are presented in 2D realistic domains, and we discuss the received results. Finally we present our conclusions and discuss possible further work.
Modeling Heat and Mass Transfer during Superheated Steam Drying of a Fixed Bed of Porous Particles
639-656
10.1615/JPorMedia.v12.i7.30
Jalila
Sghaier
Département d'Energétique, Ecole Nationale d'Ingénieurs de Monastir, Avenue Ibn Eljazzar, 5019 Monastir, Tunisie
Souad
Messai
Laboratoire d'Energétique et des Transferts Thermiques et Massiques, Faculté des Sciences de Tunis, Campus Universitaire 1060, Tunis, Tunisie
Wahbi
Jomaa
Laboratoire TREFLE-UMR 8508, Site ENSAM, Esplanade des Arts et Métiers, 33405 Talence Cedex, France
Ali
Belghith
Faculte des Sciences de Tunis, Laboratoire des Transferts de Chaleur et de Masse, Campus Universitaire, 1060 Tunis, Tunisia
Heat and mass transfer during drying of a fixed bed of wet porous particles in superheated steam is modeled. The mathematical model is based on the averaging approach using two changes of scale. Convective heat transfer is assumed between the granular bed and steam. To take into account the thermal nonequilibrium between the porous particle and fluid phase, a two-temperature macroscopic model is used to describe heat transfer. The mass transfer is introduced in the form of drying kinetics deduced from a single-particle model describing superheated steam drying. This model was developed in a previous paper. In this work, correlations of mass flux deduced from the single-particle model are presented and incorporated in the fixed-bed model. The set of partial equations describing the steam drying of a fixed bed is solved using the finite volume method, which was achieved by the computer program written in FORTRAN language. To validate this model, the predicted results are compared with the experimental results from the literature and good agreement was obtained.
Forced Convection with Counterflow in a Circular Tube Occupied by a Porous Medium
657-666
10.1615/JPorMedia.v12.i7.40
D A
Nield
University of Auckland
Auckland, New Zealand
An analytical solution is obtained for forced convection with counterflow in the core and sheath of a circular tube occupied by a saturated porous medium. The Brinkman model is employed for the porous medium. It is found that the effect of counterflow (in contrast to flow in one direction) is to reduce the value of the Nusselt number for large values of the core-sheath coordinate ξ, but to increase it for small values of ξ. In particular, Nu takes a zero minimum value when the mean velocity is zero.
A Nonlinear Stability Analysis for Thermoconvective Magnetized Ferrofluid with Magnetic-Field-Dependent Viscosity Saturating a Porous Medium
667-682
10.1615/JPorMedia.v12.i7.50
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
Poonam
Sharma
Department of Applied Sciences, National Institute of Technology, Hamirpur, 177 005, India
Amit
Mahajan
Department of Applied Sciences, National Institute of Technology, Hamirpur, 177 005, India; Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, N9B3P4, Canada
A nonlinear stability analysis of a magnetized ferrofluid with magnetic-field-dependent (MFD) viscosity heated from below, saturating a porous medium for the case of stress-free boundaries, is studied by a generalized energy method. A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of the linear one, thus indicating that subcritical instabilities are possible. It is also observed that a subcritical region of instability can be induced by a magnetic mechanism alone. However, the global nonlinear stability Rayleigh number is found to be exactly the same as that for linear instability in the case of a non-ferrofluid. For lower magnetic parameter values, this coincidence is immediately lost. The effect of the magnetic parameter (M3), medium permeability (Da), and MFD viscosity (δ) on the subcritical instability region has also been analyzed. It is shown that with the increase of the magnetic parameter (M3) and Darcy number (Da), the subcritical instability region obtained by the two theories decreases, whereas with the increase of MFD viscosity δ, the subcritical instability region expands.
Numerical Investigation of Nonaqueous Phase Liquid Behavior at Heterogeneous Sand Layers Using VODA Multiphase Flow Code
685-694
10.1615/JPorMedia.v12.i7.60
Jiri
Mikyska
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
Michal
Benes
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
Tissa H.
Illangasekare
Center for Experimental Study of Subsurface Environmental Processes, Colorado School of Mines, USA
Interplay between the gravitational and capillary pressure forces at the interfaces of sands with different capillarity properties determines the fate of nonaqueous phase liquids (NAPLs) in the subsurface. Competition of these two forces can be observed on inclined interfaces of homogeneous sand formations. We have developed a multiphase flow code that has been applied to the study of NAPL behavior at the inclined interfaces. This model provides two methods for numerical treatment of sharp interfaces between the sands with different capillarity properties. Numerical results are presented indicating domains of applicability of these methods and their ability to describe discontinuous saturation profiles across the interface. The model is applied for computation of two-phase flow in a layered medium containing an inclined interface between two homogeneous layers with different capillary pressure parameters. As another application of the model, we present results of simulation of NAPL flow in a random medium consisting of small inclined homogeneous blocks of sands. Numerical results are compared to the results of laboratory experiments.
Reduction and Solutions for Magnetohydrodynamic Flow of a Sisko Fluid in a Porous Medium
695-714
10.1615/JPorMedia.v12.i7.70
H.
Mambili-Mamboundou
Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational & Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
Fazal Mahmood
Mahomed
Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational & Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa
This work describes the exact analytic solutions for magnetohydrodynamic (MHD) unidirectional flow of a Sisko fluid in a semi-infinite porous medium. The governing nonlinear differential equation is obtained by employing reduction, and solutions have been developed using the similarity approach. We also present numerical solutions for the reduced equations. The influence of various parameters of interest is shown and discussed through several graphs. A comparison of the present analysis shows excellent agreement between analytic and numerical solutions.
Natural Convection from a Horizontal Annulus Filled with Porous Medium of Variable Permeability
715-724
10.1615/JPorMedia.v12.i7.80
Taha K.
Aldoss
Mechanical Engineering Department, Jordan University of Science and Technology, Irbid 22110, Jordan
Natural convection from a horizontal annulus filled with porous medium of variable permeability is investigated. Two cases are considered: variation of porous permeability in the radial direction and in the tangential direction. A numerical solution is obtained using a finite volume method. The effect of the permeability variation on the flow and heat transfer of the annulus is presented in terms of velocity and temperature profiles, Nusselt number, skin friction coefficient, and pressure coefficient at both the inner and outer walls of the annulus. Stream function distribution and isotherm contours are also shown for all considered cases. The calculation for the two reference cases, namely, free-fluid case and the uniform permeability case, are also calculated and presented for comparison. All calculations are performed at the same pertinent parameters, namely, Rayleigh number, Darcy number, and Prandtl number, with an annulus radius ratio of 2.0.