CFD prediction of flow and heat transfer in hollow fiber bundles for Membrane Distillation: a comparison of regular and random arrangements

Numerical simulations were conducted for steady, fully developed laminar flow with heat transfer in bundles of cylindrical rods representative of hollow-fiber Membrane Distillation units. Axial- and cross-flow configurations were investigated both for regular hexagonal arrays of fibers at different porosities (0.4, 0.5 and 0.6) and for several realizations of random distributions of 36 fibers at a fixed porosity of 0.5. In axial flow, due to channelling phenomena, random distributions exhibited a hydraulic permeability about twice larger and Nusselt numbers about one order of magnitude lower than in regular lattices. In cross-flow, a significant dependence of both the permeability and the Nusselt number on the forcing term orientation was observed for regular fiber arrangements, and a similar dependence on the specific realization was observed for random distributions. Once the results were averaged over all angles or realizations, the hexagonal regular lattices showed both the largest normal permeability and the highest mean Nusselt number in the whole range of Reynolds numbers investigated (similar to 10(-2) - 10(2)) with respect both to square lattices and to random fiber arrangements. For the regular hexagonal lattice, the influence of porosity was also assessed. CFD results showed that, as the porosity increases, the normal permeability increases while the mean Nusselt number decreases, suggesting that heat transfer attains a maximum at some porosity below the lowest one investigated (0.4)