Turbulent flow over low-order models of highly irregular surface roughness

Low-order representations of surface roughness replicated from a turbine blade damaged by spallation (denoted as "full surface") are devised using singular value decomposition, and the impact of these low-order surface models is assessed in turbulent channel flow. The intent of this effort is to determine the level of topographical detail of the full surface that is required to reproduce the statistical character of turbulent flow over the full surface. Particle-image velocimetry measurements of flow at a fixed Reynolds number over a smooth surface, the full surface, and four low-order representations of the full surface reveal that a surface model based on the first 20 basis functions of the decomposition (9% of the total number of modes) yields an accurate reproduction of the statistics of flow over the full surface. In particular, the mean velocity profile, profiles of the Reynolds normal and shear stresses, and even the instantaneous turbulent events that contribute heavily to the generation of turbulent shear stress as assessed via quadrant analysis show consistency for flow over this low-order model as well as the full surface. Because the low-order modes included in these models reflect only the large-scale topographical features of the full surface (meaning finer-scale topographical details are excluded), these observations indicate that the larger-scale features of the full surface predominantly dictate its impact on the flow.