Heat and Fluid Flow Within an Anisotropic Porous Medium

Abstract

A numerical experiment at a pore scale using a full set of Navier-Stokes and energy equations has been conducted to simulate laminar fluid flow and heat transfer through an anisotropic porous medium. A collection of square rods placed in an infinite two-dimensional space has been proposed as a numerical model of microscopic porous structure. The degree of anisotropy was varied by changing the transverse center-to-center distance with the longitudinal center-to-center distance being fixed. Extensive calculations were carried out for various sets of the macroscopic flow angle, Reynolds number and degree of anisotropy. The numerical results thus obtained were integrated over a space to determine the permeability tensor, Forchheimer tensor and directional interfacial heat transfer coefficient. It has been found that the principal axes of the permeability tensor (which controls the viscous drag in the low Reynolds number range) differ significantly from those of the Forchheimer tensor (which controls the form drag in the high Reynolds number range), The study also reveals that the variation of the directional interfacial heat transfer coefficient with respect to the macroscopic flow angle is analogous to that of the directional permeability. Simple subscale model equations for the permeability tensor, Forchheimer tensor and directional Nusselt number have been proposed for possible applications of VAT to investigate flow and heat transfer within complex heat and fluid flow equipment consisting of small scale elements.

Effects of thermal dispersion on heat transfer in cross-flow tubular heat exchangers

“…Aris [5], Koch and Brady [6], Han et al [7], and Vortmeyer [8]) were made to establish useful correlations for estimating the effective thermal conductivities due to thermal dispersion (See Kaviany [9]). Furthermore, Kuwahara et al [10] and Nakayama et al [11] conducted a series of numerical experiments by assuming a macroscopically uniform flow through a lattice of rods, so as to elucidate the effects of microscopic velocity and temperature fields on the thermal dispersion. It is also worthwhile to mention that Nakayama et al [12] derived a thermal dispersion heat flux transport equation from the volume averaged version of Navier-Stokes and energy equations and showed that it naturally reduces to an algebraic expression for the effective thermal conductivity based on a gradient-type diffusion hypothesis.…”

Simulating micorotransport in realistic porous media

“…By processing the results at the microscale, the effective hydrodynamic and thermodynamic parameters are computed as functions of the system properties (e.g., porosity, Reynolds number, flow direction, material properties). A drawback of the algorithm in [28,38,39] is, however, that it does not extend easily to porous media with very complex geometries (see for example Fig. 1.1), as building a "suitable" numerical grid of the flow domain is very difficult and time consuming.…”

“…Also, the proposed transport model does not include a true thermal coupling between the fluid and the solids, i.e., conjugate heat transfer, and therefore does not support the effects of thermal material properties on the macroscopic thermodynamics. In this thesis we will follow a similar strategy for the computation of effective parameters as in references [28,38,39], however, we will extend it in two key areas. In Chap.…”

“…Using the method of volume averaging as their upscaling strategy, Kuwahara et al [28] and Nakayama et al [38,39] proposed an alternate approach to computing the effective parameters, i.e., one based on calculations from first principles. Their algorithm simulates fully-developed flow of a fluid with heat transfer inside a spatially periodic model of a porous medium, and solves directly for the primitive field variables (velocity, pressure and temperature) at the pore scale.…”

“…A large part of this research has concentrated on porous media composed of cylinders or spheres [10,12,16,17,26,56,67]. Others have considered porous media composed of rectangular shapes [38,39]. A feature common to all of these studies is the use of a body-conforming grid.…”