The structure and scaling of rough-wall turbulent boundary layers
Citations
Altmetric:
Altmetric::
Authors
Editor
Date
2017
Source Title
Publisher
Melbourne Authors
Affiliation
Mechanical Engineering
Document Type
PhD thesis
Subject Code
Citations
Access Status
Open Access
DOI
Access URL
Open Access URL
Open Access at PMC
Linked Resource URL
NHMRC Grant Code
ARC Grant Code
Description
© 2017 Dr. Dougal Thomas Squire
Abstract
Turbulent wall layers are a pervasive and influential feature in nature and engineering; common examples include the atmospheric and benthic layer, boundary layers developing on aerial, marine and terrestrial vehicles, and flows in piping networks. These flows are characterised by high Reynolds numbers and, more often than not, surface roughness that exerts a dynamical effect on the flow. The latter may result from manufacturing defects, erosion and/or deposition, including that of living organisms. In this thesis, rough-wall turbulent boundary layers are investigated experimentally across an unprecedented range of boundary layer and roughness parameters. The measurements presented herein were performed above a well-characterised sand grain roughness using four experimental techniques, including hot-wire anemometry and particle image velocimetry. A floating element drag balance was used to obtain accurate estimates of the wall drag and associated parameters. New and existing smooth-wall measurements using the same experimental arrangements have been obtained for comparative purposes.
Statistics and spectra of the streamwise velocity component reveal convincing support for Townsend's Reynolds number similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) when the friction Reynolds number, delta+ > 14,000. Wall-similarity is also observed at much lower friction Reynolds numbers when the roughness Reynolds number is high (i.e. the flow is fully rough). Subtraction of smooth- and rough-wall streamwise velocity spectra at matched friction Reynolds number demonstrates that the differences between the near-wall inner-normalised energy of these flows occurs predominantly for scales on the order of the boundary layer thickness (typically, several hundred times the characteristic roughness height). This is most apparent when the flow is fully rough. To the author's knowledge, outer-region flow dependence on the roughness Reynolds number has not been previously identified.
At high roughness Reynolds number, wall-similarity is also observed for the spatial structure of the outer region. This is true over the three orders of magnitude of streamwise scales resolved by the present PIV measurements. Remarkably, spatial similarity between smooth- and rough-wall flows is even observed at wall-normal locations where large scale differences are apparent in the respective energy spectra. Particular attention is given to the spanwise vorticity structure in the outer region of rough-wall flows. This is motivated by suggestions from previous rough-wall studies that the structure of vortical events in the outer regions may be particularly susceptible to changes to the wall boundary condition. Our data suggest, however, that the present sand grain roughness does not influence outer-region vorticity structure at high roughness Reynolds numbers beyond Townsend's hypothesis. Issues with applying Taylor's frozen turbulence hypothesis (Proceedings of the Royal Society of London A, vol. 164, 1938, pp. 476-490) in rough-wall flows are identified as a potential source of uncertainty in previous literature regarding the universality of outer-region spatial structure in rough-wall flows.
Interactions between the inner and outer regions of rough-wall turbulent boundary layers are examined within the framework of a model introduced by Marusic et al. (Science, vol. 329, 2010, pp. 193-196). The model is characterised by two empirically observed inner-outer interactions: superposition of energy from outer-region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale `universal' signal (u*), which in smooth-wall flows is Reynolds number invariant. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer-region similarity. The latter is explained by assuming that large scale fluctuations are quasi-steady from the perspective of small scale motions. Using the model parameters obtained from the two-point measurements, predictions of inner-region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u* signal does depend on roughness Reynolds number (ks+), but is robust to changes in friction Reynolds number (delta+). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number.
Notes
Terms of Use
Keywords
wall-bounded turbulence, boundary layer flows, rough walls