Momentum transport and laminar friction in rough-wall duct flows

A large number of experiments and numerical simulations have proved that friction factors in laminar channel flows are roughness-dependent provided that the ratios between roughness and channel height (i.e., the relative roughness) exceed some threshold values. However, it is not yet clear what are the causes that lead to this anomalous behaviour. In order to shed light into this issue, this study presents results from two-dimensional Lattice-Boltzmann simulations of laminar flows in channels with rough walls. The Reynolds number, the geometry of the roughness elements and the relative roughness were varied extensively in order to provide a comprehensive set of data. The analysis and interpretation of the data were carried out within the framework of the Spatially Averaged Navier-Stokes equations, which are ideal to investigate momentum transfer mechanisms in flows over rough walls. The results show that for most of the investigated roughness geometries, the pressure gradient driving the flow is balanced by form-drag, viscous drag, and viscous shear stress whereas form-induced stresses remain largely negligible. Furthermore, it was observed that the higher the ratio between the drag acting upon the roughness elements and the total drag, the more friction factors deviate from classical theory. On the basis of these observations, we propose a formula, which predicts the shear stress partitioning and we discuss its relevance within the context of biomedical applications.