Begell House Inc.
Journal of Porous Media
JPM
1091-028X
10
2
2007
Analyzing Finite Volume for Single-Phase Flow in Porous Media
109-123
10.1615/JPorMedia.v10.i2.10
Sanjay Kumar
Khattri
Stord Haugesund University College, 0614 Oslo, Norway
Two-point finite volume methods (2P-FVMs) are extensively used for understanding porous media flow because these methods are fast and simple. In this article, we present numerical analysis of the two-point finite volume discretization of a pressure equation of a single-phase flowing in porous media. We present numerical problems with discontinuous permeability and diagonal permeability, together with Neumann and Dirichlet boundary conditions. An analysis of the effect of boundary conditions on the conditioning of the discrete systems is presented. We also analyze convergence of the 2P-FVM in various norms (L2 convergence for pressure and Darcy velocity and L∞ convergence for pressure) for problems with regularity H1+γ, for γ = 0.1, 0.2, ..., 0.9, 0.99.
Multigrid Solution of Modified Reynolds Equation Incorporating Poroelasticity and Couple Stresses
125-136
10.1615/JPorMedia.v10.i2.20
Nagendrappa
Bujurke
Karnatak University
Ramesh B.
Kudenatti
Department of Mathematics, Bangalore University, Central College Campus, Bangalore-560001, India
In this paper, theoretical analysis of effects of poroelasticity on the squeeze film behavior of poroelastic bearings with couple-stress fluid as lubricant is given. The modified form of Reynolds equation considering poroelasticity of the articular cartilage is derived. A finite difference-based multigrid method is used for its solution. It is observed that the poroelastic bearings with couple-stress fluid as lubricant provide increased pressure distribution and ensure significant load-carrying capacity compared to the classical case. Also, the role of elasticity is to enhance the load capacity of the poroelastic bearings. Predictions based on this simple model closely describe the salient features of the lubrication aspects of synovial joints.
Experimental Evaluation of Evaporation Enhancement with Porous Media in Liquid-Fueled Burners
137-150
10.1615/JPorMedia.v10.i2.30
Chendhil
Periasamy
Combustion and Flame Dynamics Laboratory, School of Aerospace and Mechanical Engineering, 865 Asp Ave, Room 212, The University of Oklahoma, Norman, OK 73019; and Now at Air Liquide R&D, Newark, DE 19702, USA
Sathish K.
Sankara-Chinthamony
Combustion and Flame Dynamics Laboratory, School of Aerospace and Mechanical Engineering, 865 Asp Ave, Room 212, The University of Oklahoma, Norman, OK 73019, USA
Subramanyam R.
Gollahalli
Combustion and Flame Dynamics Laboratory, School of Aerospace and Mechanical Engineering, 865 Asp Ave, Room 212, The University of Oklahoma, Norman, OK 73019, USA
Potential benefits of using a porous medium to enhance evaporation in liquid-fueled burners have been experimentally evaluated. An open-cell, silicon carbide-coated, carbon-carbon ceramic foam was used as a porous medium. Aviation-type kerosene was sprayed into a coflowing, preheated air environment using an air-blast atomizer, and the spray subsequently entered the porous medium. The minimum combustion heat feedback rate required for complete vaporization and the vapor concentration downstream of the porous medium were measured. Surface temperature measurements showed that the temperature of the porous medium was uniform within 10 K. The minimum heat feedback rate required for complete vaporization increased as the distance between the porous medium and the injector was decreased. Under the present conditions, with porous media and combustion heat feedback, complete vaporization was achieved at a coflow air temperature of 400 K. Without porous media, however, a minimum coflow air temperature of 500 K was required to achieve the same quality of evaporation. Measurements revealed that a combustion heat feedback rate of 1% produced average vapor concentrations of 63% and 43% more than that with no heat feedback at equivalence ratios of 0.3 and 0.6, respectively.
A Numerical Investigation of the Effects of Compositional and Thermal Buoyancy on Transient Plumes in a Porous Layer
151-173
10.1615/JPorMedia.v10.i2.40
J. E.
Milne
Department of Geological Sciences, University of Saskatchewan, 114 Science Place, Saskatoon, SK S7N 5E2, Canada
S. L.
Butler
Department of Geological Sciences, University of Saskatchewan, 114 Science Place, Saskatoon, SK S7N 5E2, Canada
We present a suite of high-resolution numerical model experiments conducted to investigate the effects of varying thermal and compositional buoyancy on the behavior and morphology of plumes in porous media. The calculations model the injection of fluid through a narrow opening into the base of a nonreactive, saturated, porous matrix with interstitial fluid of different temperature and/or solute concentration and are scaled to be comparable with previously published experimental results. Calculations are presented for the case of zero injection velocity (in which case heat and solute diffuse in from the boundary) and for small, nonzero injection velocity. Different combinations of thermal and compositional buoyancies result in various plume structures owing to the fact that solute and heat both diffuse and advect at different rates in porous media. Plumes with dominantly positive thermal buoyancy have large plume heads, while those with dominantly compositional buoyancy lack this feature and propagate more rapidly. When the injected fluid has positive compositional and negative thermal buoyancy, the initial flow spreads laterally along the base of the domain before a narrow straight-sided compositional plume emerges. For cases when the injected fluid has positive thermal buoyancy and negative compositional buoyancy, plumes initially rise upward before a dense solute “cap” forms, interrupting the flow. For sufficiently large positive thermal buoyancy, this cap breaks down and the flow becomes highly time dependent. The velocities and widths of the plumes are also presented in order to characterize the plumes formed in the different parameter regimes.
Thermal Modulation of Raleigh-Benard Convection in a Sparsely Packed Porous Medium
175-188
10.1615/JPorMedia.v10.i2.50
Beer S.
Bhadauria
Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India; Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
The linear stability of thermal convection in a horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation using the Brinkman model with effective viscosity larger than the fluid viscosity. The temperature field between the walls of the porous layer consists of two parts; a steady part and a time-dependent part that varies periodically. The combined effect of permeability and modulation of the walls' temperature on the stability of flow through a porous medium has been investigated using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of amplitude and frequency of modulation, porous parameter, viscosity ratio, and Prandtl number. It is found that the permeability has a stabilizing influence on the onset of thermal instability. Furthermore, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls' temperature. The effects of other parameters are also discussed.
Effective Emissivity Measurements of Powders and Their Mixtures
189-200
10.1615/JPorMedia.v10.i2.60
Fethi
Albouchi
ISIMM
Foued
Mzali
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Ecole Nationaled'Ingénieurs de Monastir, Tunisia
Fabrice
Rigollet
Aix Marseille Univ, CNRS, IUSTI
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
In this paper, an experimental measurement technique of the effective emissivity of powders is presented for a given spectral field, using the reflectance hemisphere method. This technique consists of heating a powder filled into a Teflon® cell, through a thin copper layer. The apparent temperature of the powder surface is then measured by an infrared camera, either directly or through an orifice arranged into the hemisphere. The effective emissivity is identified by comparing the flux emitted by the powder surface and that emitted by a specular hemisphere taken as a reference blackbody, for the same temperature and the same spectral wavelength field Δλ. The results are presented for a metallic and an insulating powder, and validated with literature values. The effective emissivities of powder mixtures are also presented in this paper.
Non-Darcian Forced Convection Heat Transfer over a Flat Plate in a Porous Medium with Variable Viscosity and Variable Prandtl Number
201-208
10.1615/JPorMedia.v10.i2.70
The steady laminar boundary layer flow in a non-Darcian porous medium over a flat plate with temperature-dependent viscosity is studied taking into account the variation of fluid viscosity and fluid Prandtl number with temperature. The results are obtained with the direct numerical solution of the boundary layer equations and concern the wall heat transfer, the wall shear stress and velocity, and temperature profiles across the boundary layer. The results of the present work are different from those existing in the literature, which have been obtained with the assumption of a constant Prandtl number.
Effect of Radiation on Non-Darcy Free Convection from a Vertical Cylinder Embedded in a Fluid-Saturated Porous Medium with a Temperature-Dependent Viscosity
209-218
10.1615/JPorMedia.v10.i2.80
M. A.
EL-Hakiem
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, Egypt
Ahmed M.
Rashad
Department of Mathematics, Aswan University, Faculty of Science, Aswan, 81528, Egypt
The effects of both radiation and the nonlinear Forchheimer terms on free convection from a vertical cylinder embedded in a fluid-saturated porous medium are examined. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The boundary-layer equations governing flow are solved numerically by using the second-level local nonsimilarity method, which is used to convert the nonsimilar equations into a system of ordinary differential equations. Numerical results for dimensionless velocity, temperature profiles, and the local Nusselt number are presented for Ergun number Er, viscosity/temperature θr, conduction radiation parameter Rd, surface temperature excess ratio H, and transverse curvature parameter ξ.