Lattice Boltzmann Simulation of Flow through Three-Dimensional Random Fiber Network with Considering of Quadratic Velocity Term

Fiber web is modeled as a three-dimensional random cylindrical fiber network. Nonlinear behavior of fluid flowing through the fiber network is numerically simulated by using lattice Boltzmann (LB) method. Nonlinear relationship between the friction factor and the modified Reynolds number is clearly observed and analyzed by using Fochheimer equation, which includes the quadratic term of velocity. We obtain a transition from linear to nonlinear region when the Reynolds numbers are sufficiently high, reflecting inertial effects of flows. The simulated permeability of such fiber network has relatively good agreement with experiment results and finite element simulations.