Begell House Inc.
Journal of Porous Media
JPM
1091-028X
8
1
2005
Numerical Study of the Effects of Geometric Dimensions on Liquid-Vapor Phase Change and Free Convection in a Rectangular Porous Cavity
1-12
10.1615/JPorMedia.v8.i1.10
Mustapha
Najjari
Laboratoire d'Etudes des Systemes Thermiques et Energetiques, Cite Riadh, Zirig 6072 Gabes, Tunisia
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
By using an enthalpic method (two-phase mixture model), we have studied numerically liquid-vapor phase change with free convection in a rectangular porous cavity heated from below, cooled from above, and initially saturated with liquid phase. A finite-volume method is used for the numerical resolution of the volumetric enthalpy and pressure equations. Results giving evolution of temperature, velocities of the liquid and vapor, and evaporated volume are presented and analyzed. Parametric studies to assess the effects of aspect ratio of cavity are carried out. Special attention is paid to studying the complex interaction between free convection and liquid-vapor phase-change intensity.
Numerical Solution of Turbulent Channel Flow Past a Backward-Facing Step with a Porous Insert Using Linear and Nonlinear k-ε Models
13-30
10.1615/JPorMedia.v8.i1.20
Marcelo
Assato
Instituto de Aeronáutica e Espaço - IAE, Departamento de Ciência e Tecnologia Aeroespacial - DCTA, São José dos Campos – SP, 1228-904, Brazil
Marcos H. J.
Pedras
Instituto de Pesquisa e Desenvolvimento—IP&D, Universidade do Vale do Paraiba—UNIVAP, 12244-000—Sao Jose dos Campos—SP, Brazil
Marcelo J. S.
de Lemos
Departamento de Energia – IEME, Instituto Tecnológico de Aeronáutica – ITA,12228-900 São José dos Campos SP, Brazil
This work presents a numerical investigation of turbulent flow past a backward-facing-step channel with a porous insert using linear and nonlinear eddy viscosity macroscopic models. The nonlinear turbulence models are known to perform better than classical eddy-diffusivity models due to their ability to simulate important characteristics of the flow. Turbulence-driven secondary motion and the effects of streamline curvature on turbulence cannot be fully accounted for with simpler isotropic models. Parameters such as porosity, permeability, and thickness of the porous insert are varied in order to analyze their effects on the flow pattern, particularly on the damping of the recirculating bubble after the porous insertion. The numerical technique employed for discretizing the governing equations is the control-volume method. The SIMPLE algorithm is used to correct the pressure field. The classical wall function is utilized in order to handle flow calculation near the wall. Comparisons of results simulated with both linear and nonlinear turbulence models are shown.
Experimental Study of Non-Fourier Thermal Response in Porous Media
31-44
10.1615/JPorMedia.v8.i1.30
A. G. Agwu
Nnanna
Department of Engineering, Purdue University Calumet, Hammond, IN 46323-2094
A
Haji-Sheikh
Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX
K. T.
Harris
Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX
An experimental study of the non-Fourier behavior in porous media due to short time thermal perturbation is presented. The governing energy equation is formulated based on the two-equation model and the non-Fourier heat conduction model. This formulation leads to the emergence of three thermal lag times. These parameters account for the thermal interaction between the fluid and the neighboring solid matrix, as well as the delay time needed for both phases to approach thermal equilibrium. An experimental verification of this theoretical model was performed under standard laboratory conditions. The values of the aforementioned thermal parameters were determined from the measured solid temperature at different locations. The results indicate a satisfactory agreement between the experimental data and the non-Fourier conduction model, whereas the deviation from a prediction based on the Fourier conduction is significant.
Effect of Fouling on Stability of Bioconvection of Gyrotactic Microorganisms in a Porous Medium
45-53
10.1615/JPorMedia.v8.i1.40
A. A.
Avramenko
Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine
The main objective of this article is to investigate the effect of fouling on the stability of a uniform suspension of gyrotactic motile microorganisms in a fluid-saturated porous medium. Fouling occurs because of the deposition of microorganisms on a porous matrix. This deposition decreases porosity and permeability of the porous medium. Stability analysis carried out in this article reveals that there is a critical porosity of the porous medium. If the porous medium utilized for this process has a smaller porosity than critical, the uniform suspension of gyrotactic microorganisms is stable and bioconvection does not develop. If the porous medium has larger porosity than critical, the uniform suspension is unstable and bioconvection develops. In this article, a combination of analytical and numerical methods is utilized to solve this problem. First, a linear stability analysis is carried out analytically. Then, at the final stage of the research, numerical methods are utilized to compute the critical Darcy number.
Natural Convection from a Discrete Heater in a Square Cavity Filled with a Porous Medium
55-64
10.1615/JPorMedia.v8.i1.50
Nawaf H.
Saeid
Flow Modeling and Simulation Research Cluster, Universiti Teknologi Brunei, Tungku Link,
Gadong, BE 1410, Brunei Darussalam
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
A numerical study of the natural convection in a square porous cavity with one of its vertical walls heated differentially is carried out in the present paper. It is assumed that an isoflux or isothermal discrete heater is mounted on one of the vertical walls and the other vertical wall is at constant temperature, while the horizontal walls are adiabatic. The finite-volume method is used to solve the non-dimensional governing equations. The effect of location of the discrete heater is investigated for values of Rayleigh number (Ra) in the range 10 ≤ Ra ≤ 103 and heater length 0.1−0.5 of the cavity height. It is shown that the location of the discrete heater has important influence on the flow and heat transfer characteristics. It is also found that the maximum average Nusselt number takes place when the heater is placed near the bottom of the vertical wall for high values of Ra and relatively higher location for relatively low values of Ra for both isoflux and isothermal discrete heaters. The average Nusselt number increases with increasing length of both isothermal and isoflux heaters for a constant Ra.
Laminar Natural Convection Heat and Mass Transfer from a Horizontal Surface in Non-Darcy Porous Media
65-72
10.1615/JPorMedia.v8.i1.60
Virendra
Bansod
Department of Mathematics, Dr. B. A. Technological University, Lonere, India
P.
Singh
Department of Mathematics, Indian Institute of Technology, Kanpur, India
B. V.
Rathishkumar
Institute of Physical and Chemical Research Hirosawa 2-1, Wako-shi, Saitama, 351-0198, Japan; and Department of Mathematics, Indian Institute of Technology, Kanpur, India
In this paper, the series method is exploited to solve the problem of nonlinear convection in porous a plate with Forchheimer-Boussinesq approximations. The conservation equations that govern the problem are transformed into an infinite number of nonlinear ordinary differential equations in terms of perturbation function. These coupled nonlinear equations are solved numerically using the fourth-order Runge-Kutta method and Newton-Raphson technique. The numerical results of the physical parameters are presented in x-y plots. The validity of our series solution is verified with the heat transfer results of Cheng and Chang [Int. J. Heat Mass Transfer, vol. 19, pp. 1267-1272, 1976] for Darcy flow.
Uniform Lateral Mass Flux on Natural-Convection Flow over a Vertical Cone Embedded in a Porous Medium Saturated with a Non-Newtonian Fluid
73-84
10.1615/JPorMedia.v8.i1.70
Mahesh
Kumari
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
S.
Jayanthi
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
A boundary-layer analysis for uniform lateral mass flux effect on the natural convection flow of a non-Darcy, non-Newtonian power-law fluid, along an isothermal cone embedded in a saturated porous medium is investigated. Numerical solutions are obtained for the nonlinear coupled partial differential equations governing the flow using a Keller's box method. Results for the velocity and temperature profiles as well as the local Nusselt number and velocity at the wall are presented for various values of the mass flux parameter, power-law index, Ergun number, and Rayleigh number. Results are compared with the existing results.
Validity of the Local Thermal Equilibrium Assumption in Natural Convection from a Vertical Plate Embedded in a Porous Medium
85-95
10.1615/JPorMedia.v8.i1.80
O. M.
Haddad
Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
A. N.
Al-Khateeb
Department of Mechanical Engineering, Jordan University of Science & Technology, P.O. Box 3030, Irbid 22110, Jordan
The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in a porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Darcy model (slip condition) to govern the flow. It is found that there are three dimensionless parameters controlling the local thermal equilibrium assumption: the Biot number (Bi), the modified Rayleigh number (Ram), and the Darcy number (Da). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.