Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer

The present effort explores the relative impact of various topographical scales present within irregular surface roughness on a turbulent boundary layer under both developing- and developed-flow conditions. Low-order representations of highly irregular surface roughness replicated from a turbine-blade damaged by deposition of foreign materials were generated using singular value decomposition to decompose the complex topography into a set of topographical basis functions of decreasing importance to the original ("full") surface character. The low-order surface models were then formed by truncating the full set of basis functions at the first 5 and 16 modes (containing approximately 71% and 95% of the full surface content, respectively) so that only the most dominant and large-scale topographical features were included in the models, while the finer-scale surface details are excluded. Physical replications of the full surface and the two low-order models were created using rapid prototyping methods to generate short and long streamwise fetches of roughness, and particle-image velocimetry was used to acquire ensembles of instantaneous velocity fields in the streamwise-wall-normal plane for developing- and developed-flow conditions at moderate Reynolds number. Comparison of both single- and multipoint statistics (mean velocity and Reynolds normal and shear stresses) as well as quadrant analysis of the instantaneous events contributing to the mean Reynolds shear stress indicates that a 16-mode model of the full surface faithfully reproduces the characteristics of flow over the full surface for both developing- and developed-flow conditions. For the latter scenario, both the 5- and 16-mode models reproduce the outer-layer characteristics for flow over the full surface in accordance with Townsend's wall similarity hypothesis. However, neither low-order surface representation fully reproduces important details of the Reynolds-shear-stress-producing events within the roughness sublayer, particularly the contributions of the most intense ejection and sweep events.