Convection In Anisotropic Porous Media Research Articles

Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

Abstract A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as R c ${R_c}$ increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c $Rc$ increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

Stability analysis of penetrative convection in anisotropic porous media with variable permeability

Abstract In this paper we study the penetrative convection in an anisotropic porous medium, for fluids with quadratic density law with the anisotropic permeability and thermal diffusivity effects. Both linear instability and global non-linear energy stability analyses are tested using a three-dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.

On the Nondimensionalization Process in Complex Problems: Application to Natural Convection in Anisotropic Porous Media

The nondimensionalization of the equations governing a given problem is a direct, relatively easy, and low-cost way to provide interesting information, the dimensionless groups that rule the problem and define its final patterns of solution. In complex problems, however, this technique frequently does not provide the precise and complete set of monomials we are looking for. The use of discrimination in the process of nondimensionalization, the detailed application of which is explained in this paper, always leads to a minimum set of parameters, which, separately, determine the solution of the problems. In addition, the physical meaning and order of magnitude of these discriminated monomials are also provided by the discrimination. The technique is applied to the coupled problem of natural convection between horizontal plates heated from below, containing an anisotropic porous medium.

Geothermal data analysis and optimization

The possibility of convective upwelling in the sedimentary Perth Basin, based on available data and simple models, was examined and its relative contribution to heat transport in a geothermal context assessed. The presence of such upwelling could greatly increase the viability of geothermal power extraction from the Basin. The onset of convection is determined by the Rayleigh number, which provides a measure for the balance between buoyancy driven upwelling and viscous resistance to flow. Being sedimentary, the porous aquifer system is layered and fractured so that the effects of anisotropy, especially that in permeability, need to be accounted for when determining the critical Rayleigh number. Variations in viscosity and the coefficient of thermal expansion also occur within the convection zone. Estimates were made for the relative size of the convective contribution to heat transport. The possibility of the surface detection of cellular convection and the effects of horizontal inflow into the convection zone were examined. References D. N. Smith, ``Cockburn No. 1 Well, Western Australia, Well Completion Report'', Western Australian Petroleum, Pty. Limited , October 1967. O. Kvernvold and P. A. Tyvand, ``Nonlinear thermal convection in anisotropic porous media'', J. Fluid Mech. , 90, pp.609--624, 1979. E. R. Lapwood, ``Convection of a fluid in a porous medium'', Proc. Camb. Phil. Soc. , 44, pp.508--521, 1948. R. McKibbin, ``Convection in an aquifer above a layer of heated impermeable bedrock'', NZ J. Sci., 26, pp.49--64, 1983. R. McKibbin, ``Thermal convection in layered and anisotropic porous media: a review'', In: Wooding, R. A. and I. White, (eds) ``Convective Flows in Porous Media'', Dept. Sci. Indust. Res., Wellington, New Zealand, pp.113--127, 1985. R. McKibbin, N. Hale, R. W. Style, and N. Walters, ``Convection and heat transport in layered sloping warm-water aquifers'', Journal of Porous Media, In press. D. A. Nield and A. Bejan, Convection in porous media , 3rd Edition, Springer, 2006. R. C. Ransom, Practical formation evaluation , Wiley, 1995. K. Regenauer-Lieb, H. T. Chua, X. Wang, F. G. Horowitz and J. Wellman, ``Direct heat geothermal applications in the Perth Basin of Western Australia'', Proc. 34th Annual Stanford Workshop on Geothermal Engineering , Chapter 14, Stanford University, California, 2009.

Penetrative convection in anisotropic porous media with variable permeability

The onset of penetrative convection in an anisotropic porous medium, for fluids with quadratic density law, is studied. In particular, the effects of anisotropic permeability and thermal diffusivity have been taken into account.

Lattice Boltzmann Method for Natural Convection in Anisotropic Porous Media

A lattice Boltzmann method (LBM) is proposed for the simulation of natural convection in anisotropic porous media with the generalized non-Darcy model. The Brinkman-Forchheimer momentum equation is recovered from a kinetic equation for the distribution function, which has a forcing term to introduce anisotropy of permeability. The LBM can analytically calculate fluid velocity using the inverse matrix for the Brinkman equation. The simulation results for a Poiseuille flow of anisotropic porous media demonstrate that the proposed LBM for the Brinkman equation has second-order accuracy in space for any permeability ratio. Since the forcing term of the generalized equation contains a nonlinear (Forchheimer) term containing the quadratic form of the velocity and the permeability tensor, the LBM must use a free-derivative optimization method. In the numerical simulation of natural convection, the streamlines and isotherms obtained by the LBM agree well with those of the finite difference method (FDM), as well as with those of previous investigations of various fundamental parameters, such as the Rayleigh number, the inclination of the principal permeability direction, and the permeability ratio. The numerical results of the LBM show good agreement with the reference solutions for the value of the stream function at the center of the primary vortex and the average Nusselt number.

Double diffusive convection in a vertical enclosure filled with anisotropic porous media

This paper summarises a numerical study of double-diffusive natural convection in a rectangular cavity filled with a saturated anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, while the horizontal walls are adiabatic and impermeable. The buoyancy forces that induce the fluid motion are assumed to be cooperative. Numerical results are presented for 10 2≤ R T≤10 4, 0≤ N≤30, 10 −5≤ K≤10 3, 1≤ Le≤10, and A=1, where R T, N, K, Le and A denote the thermal Rayleigh number, buoyancy ratio, permeability ratio, Lewis number and the aspect ratio. In the two extreme cases of heat-driven ( N≪1) and solute-driven ( N≫1) natural convection, scale analysis is applied to predict the order of magnitudes involved in the boundary layer regime. Also, based on the numerical results, correlations for the average Nusselt and Sherwood numbers are proposed for the range of parameters considered in this study. It is demonstrated that the anisotropic properties of the porous medium considerably modify the heat and mass transfer rates from that expected under isotropic conditions. The Brinkman's extension of Darcy's law is also used in this study to investigate double-diffusive convection in anisotropic porous media with high porosity.

Influence of heat dispersion on steady convection in anisotropic porous media

The influence of heat dispersion on steady buoyancy-driven convection is theoretically investigated. The motion takes place in an anisotropic porous layer with a uniform basic flow and being uniformly heated from below. The fluid-saturated layer is horizontally isotropic with respect to permeability and thermal diffusivity. It is of infinite horizontal extent and bounded by two horizontal perfectly heat-conducting planes. Dispersion effects at small Péclet numbers on the amplitude of the motion and on the heat transport are analytically studied.

Heat dispersion effect on thermal convection in anisotropic porous media

The effect of hydrodynamic dispersion on the onset of thermal convection in flows through anisotropic porous media is studied theoretically. The porous layer is homogeneous and bounded by two infinite perfectly-heat-conducting impermeable horizontal planes kept at constant temperatures. Horizontal isotropy with respect to permeability and thermal diffusivity is assumed. A pressure-driven basic flow is considered in the limits of small and large Peclet numbers. The analysis shows that the onset of convection in both cases is independent of longitudinal dispersion, while dispersion in lateral directions has stabilizing effects. The preferred mode of disturbance consists of stationary rolls with axes aligned in the direction of the basic flow.