Flow of Turbulent Boundary Layers Over Low-Order Representations of Irregular Surface Roughness

Abstract

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 are generated using singular value decomposition (SVD) to decompose the complex topography into a set of topographical basis functions (383 total) of decreasing importance to the original (“full”) surface character. The low-order surface models are then formed by truncating the full set of basis functions at the first 5 and 16 modes (containing approximately 65% and 95% of the full surface content, respectively), so that only the most dominant, and large-scale, topographical features are included in the models while the finer-scale surface details are excluded. Physical replications of the full surface and the two low-order models are created using rapid prototyping methods to generate short and long streamwise fetches of roughness and particle-image velocimetry is 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 single-point 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 indicate 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, both low-order surface representations fail to reproduce important details of the Reynolds-shear-stress-producing events within the roughness sublayer, particularly the contributions of the most intense ejection and sweep events.