Flow modeling of linear and nonlinear fluids in two and three scale fibrous fabrics

Abstract

A crucial step in many composites manufacturing processes is the impregnation of fibrous medium with the resin. The fundamental property needed to quantify the flow is the permeability of the fibrous medium. Process models require the permeability as input data to predict flow patterns and pressure fields. Image-based computation can offer a good alternative to provide input data for subsequent analysis. However, digital images contain a huge amount of information that is difficult to handle in numerical models. Then efficient numerical techniques are needed to solve homogenization problems with geometrical data coming from high-resolution images, involving two or three scales and linear and non-linear fluids. Within this framework, this work addresses three main questions: (i) how to define an equivalent macroscopic Darcy’s model from a microscopic description consisting of a viscous fluid flow model defined in a two and three scales porous medium?; (ii) the discussion on the existence of an intrinsic geometrical permeability tensor in the general case of non Newtonian rheothining fluid models, and (iii) the proposal of a constructive multi-scale strategy for performing micro-macro simulations in both the linear and the nonlinear case.