Equivalent Permeability of Adjacent Porous Regions

Fibrous reinforcements used in the manufacturing of composite structures have multiscale nature with varying permeability depending on the local porosity. Here, we discuss a formulation for homogenization of such multiscale regions using the analogy of electrical resistance in series and parallel. Using this analogy, we have developed relationship for computing the equivalent permeability of three adjacent porous regions. The equivalent permeability is the arithmetic mean of the permeabilities of the individual regions in case of parallel arrangement whereas the harmonic mean in the series case. Using numerical simulations, the model has been validated. In case of adjacent parallel regions where permeabilities differ by more than three orders of magnitude, the model does not perform very well. Nevertheless, the models presented here are applicable in the homogenization of multiscale porous regions encountered in manufacturing of fiber reinforced composite materials.