Modeling isothermal and non-isothermal flows in porous media.

摘要

A complete understanding of the physics of flow and heat transfer phenomena in porous media is vital for accurate simulation of flow processes in industrial applications. In one such application pertaining to liquid composite molding (LCM) for manufacturing polymer composites, the fiber preforms used in LCM as reinforcements are limited not only to the single-scale porous media in the form of random fiber-mats, but also include dual-scale porous media in the form of woven or stitched fiber-mats. The conventional flow physics is not able to model the resin filling process in LCM involving the dual-scale porous media. In this study, the flow in dual-scale porous media is studied in order to predict the permeability of these fiber mats. The effect of aspect ratio of the fiber preform on the accuracy and flow during permeability estimation in single- and dual-scale porous media is analyzed experimentally and numerically.;Flow of liquid in a free channel bounded on one side by porous medium is studied next, and two well-known boundary conditions of stress continuity and stress jump at the interface of the two regions are evaluated numerically. A point-wise solution for Stokes flow through periodic and non periodic porous media (made of cylindrical particles) adjacent to the free channel is presented using the Imite element based CFD software COMSOL. The efficacy of the two interfacial conditions is evaluated after volume averaging the point-wise velocity using a long averaging volume, also called the representative elementary volume or REV, and then comparing such a volume-averaged velocity profile with the available analytical solution. The investigation is carried out for five different porosities at three different Reynolds numbers to cover a wide range of applications. The presence of randomly-placed cylinders during the creation of non-periodic porous media damps out spatial fluctuations in the averaged velocity observed in periodic porous media. The analytical solutions obtained after applying the stress-continuity and stress-jump boundary conditions are found to work well at low porosities, which is in contradiction with the results achieved earlier by other researchers.;The traditional approach of using averaged equations in the regions of sharp gradients in porous media to describe flow and transport is theoretically untenable and perhaps inaccurate. A novel ensemble averaging method is being proposed to test the accuracy of the volume averaged or smoothed description of flows in porous media in the regions of sharp gradients. In the new method, the flow in a certain arrangement of particles (called a realization) is averaged using a small unit cell, much smaller than the REV. Then such an averaged flow variable is further averaged over a whole gamut of randomly-generated particle realizations. First the accuracy of the ensemble averaging method was tested by comparing the permeability of an artificially generated porous medium obtained by the proposed method against the permeability predicted by some established theoretical models of permeability. The proposed method was found to be quite accurate. Later the ensemble average method was applied to the open-channel porous-medium interface region characterized by a sharp gradient in the flow velocities. It was discovered that the volume averaged description of such flows, characterized by the use of the Brinkman equation along with the stress-continuity and stress-jump conditions, is quite accurate for a range of Reynolds numbers.;The non-isothermal transport during flow in porous media is examined next. The main focus in this area of research is the thermal dispersion term found in the heat transfer equation for single- and dual-scale porous media. Most of the previous efforts on modeling the heat transfer phenomena in porous media were devoted to isotropic porous media. However, for the anisotropic porous media widely in many industrial applications, not much research on the dispersion tensor is available. A new combined experimental/numerical approach to estimating the dispersion tensor is introduced and applied for both isotropic (single-scale) and anisotropic (dual-scale) porous media. The equivalence between the heat and mass transfer is exploited and a 1-D flow experimental setup is employed to study the spreading of a dye. Later the mathematical model for such a spreading of concentration (equivalent to the temperature) around a point input in a constant velocity field is solved using the finite element based software COMSOL. Thus obtained numerical spreading pattern is fitted onto the experimentally observed one using the dispersion matrix (tensor) as a fitting parameter. A few cases of single- and dual-scale porous media are studied and the dispersion tensors are reported for each individual case. (Abstract shortened by UMI.)