Modeling the nonlinear permeability of porous composite structures with non-Newtonian fluids

Abstract

Abstract This work is related to the modelling filtration flow of an incompressible non-Newtonian viscous fluid in porous composite structures. A physical mathematical model of an incompressible non-Newtonian fluid flowing in a porous composite structure has been proposed. The pore–scale description of flow in a reinforced composite is obtained using asymptotic homogenization method. Then, the nonlinear filtration law is investigated theoretically using the anisotropic tensor function representation of the tensor independent variable. The finite element method was used to calculate the local problem, and the distribution of single hole velocity, pressure and non-Newtonian viscosity was obtained. Based on the numerical results verified by the famous Darcy’s law, the nonlinear filtration law of Carreau viscosity fluid was explored and the effective permeability under different parameters was obtained.