Effect of surface morphology on hydrodynamic drag and outer-layer similarity*

An experimental study was conducted on rough-wall, turbulent boundary layer (TBL) flow with regular and random roughness element arrangements. Varying planform densities of truncated cone roughness elements in a square staggered pattern were investigated. The same planform densities were also investigated in random arrangements. Element densities studied ranged from 10% to 79%. Detailed TBL velocity statistics were recorded with a two-component LDV system on a three-axis traverse. Important profile parameters were determined for all surfaces. In particular, hydrodynamic roughness length (z₀) was determined and compared with other studies. Additionally, a breakdown in outer-layer similarity was observed on the staggered element array similar to that reported by Placidi and Ganapathisubramani (2017) over regular arrays with varying planform density. However, outer-layer similarity was observed in spanwise-averaged profiles over the random arrangements even though individual profiles across the span varied significantly in both the inner and outer layers. This difference in outer-layer similarity over statistically similar surfaces adds interesting new evidence to the salient surface morphology parameters which generate or disrupt outer-layer similarity.