Homogenization and Numerical Simulation of Flow in Geometries with Textile Microstructures

The simulation of the Liquid Composite Moulding process is an important step for the manufacturing of composites with textile reinforcements. However, its fast direct numerical simulation is impossible on the microscale due to computational complexity reasons. We have to resort to the macroscale instead. Here, an essential task is the fast and accurate prediction of the permeability of textile microstructures. For textiles composed of impermeable yarns, we discuss the homogenisation of the Stokes equations. This leads to Darcy’s law on the macroscale and gives the permeability via the so-called unit cell problems. These equations are then discretised and solved numerically. For textiles composed of permeable yarns, their dual porosity is accounted for by a fictitious domain approach in form of the Stokes/Brinkman equations. The results of our permeability computations in textiles are validated and compared to experimental data.