# On the hydrodynamic permeability of foamlike media

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006.

Thesis

This work entails the improvement of an existing three dimensional pore-scale model. Stagnant zones are included, the closure of the volume averaged pressure gradient is improved and an improved calculation of pore-scale averages, using the RUC, is done for the model to be a more realistic representative of the REV and thus of the foamlike material. Both the Darcy and the Forchheimer regimes are modelled and a general momentum transport equation is derived by means of an asymptotic matching technique. The RUC model is also extended to cover non-Newtonian flow. Since metallic foams are generally of porosities greater than 90%, emphasis is put on the accurate prediction of permeability for these porosities. In order to improve permeability predictions for these high porosity cases an adaptation to the RUC model was considered, whereby rectangular prisms were replaced by cylinders. Although this adaptation appears to give more accurate permeabilities at very high porosities, its implementation in a generalised model seems impractical. The prediction of the characteristic RUC side length is discussed and results of both the cylindrical strand model and the square strand model are compared to experimental work.