Global and local transport properties of steady and unsteady flow in a symmetrical bronchial tree

The branching structures and bifurcation flows in human lung are crucial factors for the functioning of the respiratory system. In this paper, both steady and unsteady flow in a symmetrical bronchial tree have been investigated, and the global and local transport properties are explored by fractal geometry and computational fluid dynamics method, respectively. Firstly, total flow properties for steady laminar flow and pulsatile flow in a fractal tree-like network are derived, and the global fluid dynamics behavior under volume constrain is discussed accordingly. And then, a mathematical model is developed for the steady and unsteady gas flow as well as gas-particle two-phase flow in a four-generation bifurcation in order to study the local transport characteristics of bronchial tree. The results indicate that the critical successive diameter ratio for the first few generations is below the prediction of Murray's law while small airways follow Murray's law. It has been also shown that the asymmetrical and non-uniform flow distribution can be realized through a symmetric branching structure with increased Reynolds number. The asymmetric ratio is found to be scaled with the Reynolds number as χ ∼ Re0.00124 in the steady respiratory condition. The effect of Reynolds number and respiratory frequency on the flow distribution and particle deposit efficiency are studied for different respiratory conditions, which show that the particle deposit efficiency can be increased with increased Stokes number. The present work is important for the morphology of the bronchial tree and understanding the physical mechanism of the bifurcation flow.