Theoretical modeling of unsaturated flow in fibrous dual-scale porous media using the volume averaging method

Proper understanding of the physics of resin flow in liquid composite molding (LCM) processes is important for accurate simulation of the mold-filling process. This thesis seeks to present a new mathematical model for the unsaturated flow witnessed in woven, stitched or braided fiber mats during the mold-filling process in LCM. Mathematically rigorous phase-averaging method is employed to develop a new set of gap-averaged temperature and cure equations in these types of dual-scale porous media. These equations, in conjunction with the mass and momentum balance equations derived earlier, constitute a complete set of governing equations for the gap-averaged variables. The process of volume averaging of flow equations also gives rise to several new terms in the mass, energy and cure equations, namely the effective thermal conductivity tensor, the interfacial kinetic-effect force, the Brinkman force, and several source and sink terms. These terms are often complex and become difficult to estimate without invoking some kind of empiricism or simplification. To facilitate the simplification of these terms, finite element simulations of a steady-state Newtonian flow in the unit cells of some idealized dual-scale porous media were conducted. These studies revealed how the effective thermal conductivity responds to changes in the inlet velocity, interfacial mass flux from the inter-tow gaps into tows, interfacial energy flux from tows into gaps, and spacing between the tows. With the help of a non-isothermal flow simulation in an idealized porous medium consisting of aligned cylinders, it was discovered that neither the resin absorption rate nor the energy flux across the tow-gap interface seem to have a significant effect on the effective thermal conductivity of resin in the gap phase. This implies that the effective thermal conductivity measured for the saturated flow in a dual-scale porous medium can perhaps be applied to the unsaturated region behind the flow-front as well. Numerical studies were also conducted to estimate the two non-Darcian terms of the new momentum equation for dual-scale porous media, the interfacial kinetic-effect force and the Brinkman force. Flow simulation in an ideal dual-scale porous medium consisting of parallel slits separated by the resin absorbing tows revealed that steep sink gradients behind the flow front can make these extra non-Darcian terms quite significant in the momentum equation. However changes in the slip velocity at the tow-gap interface does not seem to have any significant effect on these two forces. It was also found that these forces become important at low Reynolds numbers. No such dependence of the two forces on sink gradient was observed for flow across cylindrical tows as very steep sink gradients could not be imposed. However they are expected to become important at higher sink gradients and lower Reynolds numbers.