The hydrodynamic properties of unconventional surface roughness

Surface roughness is characterized by its statistics such as the average height, k_a, the root-mean-square, k_rms, the skewness, Sk, etc. A survey of the roughness in the existing literature shows limited work on roughness with low Sk and high k_rms/k_a, which is the focus of this talk. By controlling the spacing, height, and arrangement of rectangular protrusions and pits, such rough walls are constructed. Direct numerical simulations (DNSs) are conducted to study their hydrodynamic properties. The data suggests that Sk has a minor effect on the equivalent sandgrain roughness height (k_s) as pits, that contribute to negative Sk, do not significantly contribute to drag. Furthermore, the roughness arrangement, which is not captured by single-point roughness statistics, has a significant effect on k_s. Attempts in developing correlation-type rough-wall models show that the predictive power of a rough-wall model depends on how well the input space distinguishes the rough walls in the calibration dataset. Moreover, the importance of roughness statistics depends on the rough walls under consideration. These findings suggest that a universal rough-wall model might not be possible, and models for specific types of roughness might be more practical.