Experimental study of low-order models of highly-irregular roughness and their impact on turbulent boundary layers
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 2-D particle-image velocimetry (PIV) 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 followed by stereo PIV measurements in a wall-parallel plane deep in the roughness sublayer (y = 0.047δ). 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 from the 2-D PIV measurements 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. The stereo-PIV measurements deep within the roughness sublayer at y = 0.047δ reveal a wealth of information about roughness-induced effects, including the tendency of the roughness to promote ‘channeling’ of the flow in the form of low- and high-momentum pathways as noted in contour maps of the mean velocity defect. Similarly, enhanced turbulent and vortical activity is observed both between and along the spanwise boundaries of these streamwise-elongated large-scale pathways. Taken together, these observations support the idea that these persistent low-momentum pathways might represent the statistical imprint of trains of hairpin vortex packets that are channeled along preferred paths over the roughness. Conditional averaging and two-point correlations of velocity further support these structural observations, particularly clear large- scale streamwise coherence of these motions. Of interest, while the M = 5 results show important differences from the full-surface results, the M = 16 results are virtually indistinguishable from those of the full surface, including in the single-point turbulence statistics as well as the analysis of the average spatial structure. This consistency is not simply qualitative but is indeed quantitative as the magnitudes of the M = 16 model single-point statistics mirror those of the full surface as do the spatial locations of the low- and high-momentum pathways identified in the mean velocity defect results as well as the enhanced turbulent and vortical activity along the spanwise boundaries of these large-scale motions. Hence, these observations provide significant evidence supporting the importance of the intermediate topographical scales in setting the flow conditions within the roughness sublayer, not only in a statistical sense but also in a structural sense.
Turbulence, Boundary Layer, Rough-wall flow
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign