A novel fractal model for permeability of damaged tree-like branching networks

Damage of the tree-like branching networks in nature is a very prevalent phenomenon, which has attracted a great deal of attention in various fields ranging from animate to inanimate flow systems for several decades. In this study, a novel model for permeability is proposed for damaged tree-like branching networks based on the fractal characteristics of tree-like branching networks. It is found that the proposed model is a function of structure parameters of damaged tree-like branching networks, such as the numbers (p) of damaged channels, the diameter ratio (β), length ratio (α), branching number (n), branching level (k), and the total number of branching levels (m) in the network. The influence of the micro-structural parameters on the effective permeability of the networks is systematically studied. It is found that the numbers of damaged channels and branching levels have significant effect on its permeability and pressure drop. The present results are much different from the heat transfer in damaged tree-like branching networks. The model may have the potential in analysis and design of fluid flow systems.