Impact of the Wall-Parallel Length Scale of Roughness on the Development of Turbulent Boundary Layers in Turbines

Abstract

The detrimental effects of surface roughness on the growth of turbulent boundary layers in turbines, and compressors, are well known. However, robust prediction of these effects can be problematic, especially for surfaces which are not similar to sand grains. Several publications have proposed that additional parameters such as effective slope, skew, etc. can be used to augment a wall-normal measure such as Sa to correlate surface roughness. Here, we introduce a new roughness parameter, the mean feature separation, which explicitly measures the average separation between each local minima and its closest local maxima. Scans of turbine blade surfaces showed that they can have mean separations which are up to six times that of the sand grain surface which has the same wall-normal length scale. The availability of high resolution, typically < 0.1 µm, area scanning tools, and 3D printing techniques have enabled the development of a “Scan-Scale-Print-Measure” methodology. A surface scan is scaled-up, 3D printed, applied to a flat-plate, and then the turbulent boundary layer is measured. The surface roughness-loss is the additional momentum thickness, above that of the datum smooth surface. The Scan-Scale-Print-Measure methodology has enabled parametric studies to be undertaken where the mean separation was increased while keeping either the Sa value or the feature size constant. Both studies demonstrated a surface roughness-loss that was strongly dependent on the mean separation and different to a Schlichting-based sand grain correlation. It also showed that for large mean separations, the roughness-loss decreased to zero. A parametric study into pits-and-peaks surface features showed that, at the same wall-normal length scale, peaks generated a surface roughness-loss twice that of pits. An engine representative surface produced only half the roughness-loss that would be attributed to a sand grain surface. The measured surface roughness-loss could be estimated within 5% using the aforementioned parametric studies.