Hexagonal roughness characterization in turbulent flow

Roughness characterization is important for modeling its effects in simulations and engineering tools. A common approximation is that the physical roughness height is equivalent to the sand grain height. However, this can lead to under- or over-prediction of flow quantities such as the wall shear stress and heat flux. In this work two rough surfaces were evaluated for flow modifications in a fully-developed turbulent channel flow. The first was a hexagonal, dimpled geometry meant to represent an ablated thermal protection system surface. The second surface was an unstructured granular surface with nominally the same roughness height as the dimpled surface. Differences from classical sand grain behavior were observed for both surfaces, with overall higher surface shear stress and larger shifts in the log-law when compared to smooth-wall cases. Conformance to Townsend’s hypothesis for the mean flow and velocity variance was only observed between the two rough surfaces in the outer layer for similar Reynolds numbers. An investigation into outer-layer flow structures using spectral maps indicated a significant decrease in larger-wavelength energy far from the wall for both rough surfaces. This departure from pure Townsend-like behavior in the outer-flow suggests that other roughness length scales are important for both surface geometries when modeling the transport and exchange of mass and energy between the surface and free-stream.