Characterizing the Roughness in Channel Flows Using Direct Numerical Simulations

Turbulent flows over bumpy walls are ubiquitous and pose a fundamental challenge to various engineering applications such as coastal boundary layers, drag on ships, hydraulic conveyance networks, and bluff body aerodynamics, to name a few. In this study, we used direct numerical simulations (DNS) along with a direct-forcing immersed boundary method (IBM) to understand the connection between the roughness geometry and the mean flow drag. A bumpy wall was constructed using an array of randomly oriented ellipsoids characterized by the Corey shape factor (Co). We found that our results exactly validated the experimental studies by Nikuradse for sand-grain type roughness (Co=1.0). Additionally, we observed that the mean flow drag increased for decreasing Co through an increase in the form-drag contribution and a decrease in the viscous drag. We also developed a relationship between the statistics of the bottom height distribution and the roughness parameter (z0) that may help explain the spread observed in the drag coefficient predicted when using conventional tools such as the Moody diagram.