The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

By M. Schultz, K. Flack. Journal of Fluid Mechanics, 2006

366 citations recorded by the source corpus.

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a three-dimensional rough surface geometrically similar to the honed pipe roughness used by Shockling, Allen & Smits (J. Fluid Mech. vol. 564, 2006, p. 267). The present work covers a wide Reynolds-number range (Re θ = 2180–27 100), spanning the hydraulically smooth to the fully rough flow regimes for a single surface, while maintaining a roughness height that is a small fraction of the boundary-layer thickness. In this investigation, the root-mean-square roughness height was at least three orders of magnitude smaller than the boundary-layer thickness, and the Kármán number (δ+), typifying the ratio of the largest to the smallest turbulent scales in the flow, was as high as 10100. The mean velocity profiles for the rough and smooth walls show remarkable similarity in the outer layer using velocity-defect scaling. The Reynolds stresses and higher-order turbulence statistics also show excellent agreement in the outer layer. The results lend strong support to the concept of outer layer similarity for rough walls in which there is a large separation between the roughness length scale and the largest turbulence scales in the flow.

Subfields: Aerospace Engineering, Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/dc4143e92bff7bd52d9bc2523cd957916a2b199e

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Citations in the corpus

Turbulence Structure in Rough and Smooth Wall Boundary Layers (2006, methodology): “This is in contrast to experimental studies by Flack, Schultz & Shapiro (2005), Kunkel & Marušić (2006), Shockling, Allen & Smits (2006), and Schultz & Flack (2007) which provide support for similarity in smooth- and rough-wall boundary layers in terms of both the mean flow and the Reynolds…”
Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall (2010, background): “Schultz & Flack (2007) performed experiments with honed pipe roughness, ranging from hydrodynamically smooth to fully rough and found excellent agreement between the Reynolds stress profiles of the outer layer.”
Turbulence structure in a boundary layer with two-dimensional roughness (2009, methodology): “Schultz & Flack (2007) critically tested this hypothesis for the conditions proposed by Townsend (k δ and high Reynolds numbers), experimentally studying the boundary layer over a sanded surface.”
REYNOLDS-NUMBER SCALING OF TURBULENT CHANNEL FLOW (2013, background): “Further details of the LDV system are given in Schultz and Flack (2007).”
Characterization of superhydrophobic surfaces for drag reduction in turbulent flow (2018, background): “Both the efficacy and mechanism of these potentially drag-reducing surfaces have been previously debated (Schultz & Flack 2007; Zhao et al. 2007; Ünal, Ünal & Atlar 2012; Aljallis et al. 2013; Golovin et al. 2016).”
Effects of coating roughness and biofouling on ship resistance and powering (2007, background): “The effect of increasing roughness Reynolds number, k + , on the mean velocity profile can be seen in the recent results of Schultz and Flack ( 2007 ) which were obtained in a zero pressure gradient, turbulent boundary layer using laser Doppler velocimetry on a rough surface consisting of diagona”
Review and comparison of methods to model ship hull roughness (2020, methodology): “The roughness function by Schultz and Flack [8,13] and Cebeci and Bradshaw [12] are implemented with the constants provided in association with Eq.”