Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
13
12
2010
THE INSTABILITY OF A DEVELOPING THERMAL FRONT IN A POROUS MEDIUM. III SUBHARMONIC INSTABILITIES
In this paper we study the instability of the developing thermal boundary layer that is induced by suddenly raising the temperature of the lower horizontal boundary of a uniformly cold semi-infinite region of saturated porous medium. The basic state consists of no flow, but the evolving temperature field may be described by a similarity solution involving the complementary error function. In very recent papers, Selim and Rees (2007a) (Part I) have sought to determine when this evolving thermal boundary layer becomes unstable and then Selim and Rees (2007b) (Part II) followed the subsequent evolution of horizontally periodic disturbances well into the nonlinear regime. In this paper we investigate the secondary instability of the nonlinear cells by introducing subharmonic disturbances into the evolving flow. We consider three different types of subharmonic disturbance, namely, the 2:1, 3:2, and 4:3 types. Cellular disturbances are seeded into the evolving basic state, the primary mode having an amplitude that is greater than that of the subharmonic. In general, we find that the subharmonic decays at first, while the primary mode grows, but at a time that is dependent on the relative initial amplitudes, the subharmonic experiences an extremely rapid growth and quickly establishes itself as the dominant flow pattern. A fairly detailed account of the 2:1 case is given, including an indication of how the time of transition between the primary and the subharmonic varies with wave number and initial amplitudes. The other two types of subharmonic disturbance yield a richer variety of behaviors; therefore, we present some typical cases to indicate some of the ways in which the primary mode may be destabilized.
Asma
Selim
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
D. Andrew S.
Rees
Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
1039-1058
BUOYANCY OPPOSED MIXED CONVECTION IN A TWO-SIDED LID-DRIVEN DIFFERENTIALLY HEATED SQUARE CAVITY FILLED WITH A POROUS MEDIUM
Mixed convection flow in a two-dimensional square cavity filled with a Darcian fluid-saturated uniform porous medium is considered. The cold vertical wall at the left is moving up whereas the hot wall in the right is moving down. The fixed top and the bottom walls are thermally insulated. The normalized governing equations are solved numerically with appropriate boundary conditions by finite volume approach. The code has been validated with previously published work and the results are found to be in excellent agreement. The study is conducted by varying the Richardson number Ri = (Gr/Re2)[Ri =
(Gr/Re2)], Darcy number (Da = κ/H2κ, Grashof number Gr = (gβΔTH3/v2)[Gr = (gβΔTH3/v2)]. The Prandtl number is fixed at 0.71. A parametric study is conducted and a set of streamlines and isotherm plots are presented. A heat transfer correlation is also presented.
Elaprolu
Vishnuvardhanarao
Fluidyn Software and Consultancy Pvt Ltd. Bangalore-560 102, India
Manab Kumar
Das
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, India
1059-1072
LAMINAR AND TURBULENT FLOWTHROUGH AN ARRAY OF CYLINDERS
When modeling fluid flow through porous media it is necessary to know when to take inertia effects into account, as well as when to switch to a turbulent description of the flow. From an engineering point of view, the problem is often solved with the empirically derived Ergun equation or a recently upgraded version by Nemec and Levec [Chem. Eng. Sci., vol. 60, pp. 6947−6957, 2005]. The drawback with this approach is, however, that the mechanisms for the transitions between the three states of flow are not revealed and time-consuming experiments have to be performed. In order to increase knowledge of the detailed flow, numerical studies of flow through arrays of quadratically packed cylinders at a variety of Re values were carried out. One result is that the laminar and turbulent approaches used both mimic experimental results for low Re, while for higher Re only the turbulent approach resembles the empirically derived equations. The deviation from Darcy’s law for different porosities of the array can be defined by usage of Re based on the hydraulic radius and the average interstitial velocity. However, to find a common Re when turbulence need to be accounted for, another Re based solely on the averaged interstitial velocity and the diameter of the cylinders was used. It was found that at low Re the laminar and turbulent setups give practically the same velocity fields, while the turbulent dissipation at higher Re results in larger circulation zones and weaker jets.
T. Staffan
Lundstrom
Division of Fluid Mechanics, Luleå University of Technology, SE- 971 87, Luleå, Sweden
J. Gunnar I.
Hellstrom
Division of Fluid Mechanics, Lulea University of Technology, 971 87 Lulea, Sweden
P. Jonas P.
Jonsson
Division of Fluid Mechanics, Luleâ University of Technology; and Epsilon High Tech AB, Sweden
1073-1085
NEW MODELING APPROACH FOR HEAT AND MASS TRANSFERS DURING SORPTION PHENOMENA IN A PLANE ADSORBER
A model approach for heat and mass transfers during gas sorption by a zeolite bed is developed. The mathematical modeling is based on assuming the bed to be formed with three phases-solid, liquid, and gaseous. The classical finite volume method is used to numerically solve the differential set of governing macroscopic equations. Numerical results provide us the time-space evolutions of temperature and moisture content. A comparison between results obtained with a three-phase model versus those obtained with a two-phase model is performed and discussed. A comprehensive analysis of the influence of the bed porosity and the grain porosity on the average reduced moisture content and average reduced temperature is also investigated.
Abdelaziz
Zegnani
Ecole Nationale d'Ingénieurs de Monastir, 5000 Monastir, Tunisia
Abdallah
Mhimid
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
Hacen
Dhahri
Laboratoire d'Etudes des Systèmes Thermiques et Energétiques, Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia
Khalifa
Slimi
ISTLS
1087-1100
IMPLICATIONS OF EVOLUTIONARY EQUATIONS IN ELASTICITY OF POROUS MATERIALS
In this study we prove the existence and uniqueness of solutions for the mixed initial-boundary value problems in the context of the elasticity of micropolar porous bodies through an equation of evolution. In the same manner, the continuous dependence of the solutions upon initial data and supply terms is also proved.
Marin
Marin
Department of Mathematics, University of Brasov, Romania
1103-1109
A NOTE ON THE DARCY−FORCHHEIMER−BRINKMAN EQUATION FOR FULLY DEVELOPED FLOWTHROUGH A POROUS CHANNEL BOUNDED BY FLAT PLATES
We consider the fully developed flow through straight porous channels, where the flow entry profiles are Poiseulle−Couette combinations. In particular, we use the Darcy−Forchheimer−Brinkman equation as the model governing the plane parallel flow through the porous medium. In the past, this particular model has been solved using numerical methods due to its nonlinear nature. We present an analytical solution of the problem employing an emerging perturbation technique, which has been proven to be successful in tackling nonlinear problems. We offer various verifications of the solution by comparing to existing, documented results and also mathematically, through reduction to simpler problems.
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
A. R.
Ansari
Department of Mathematics & Statistics, College of Informatics & Electronics, University of Limerick, Limerick, Ireland
1111-1117