The interaction of riblets with wall-bounded turbulence

The purpose of this thesis is to give answer to the question: why do riblets stop working for a certain size? Riblets are small surface grooves aligned in the mean direction of an overlying turbulent flow, designed specifically to reduce the friction between the flow and the surface. They were inspired by biological surfaces, like the oriented denticles in the skin of fastswimming sharks, and were the focus of a significant amount of research in the late eighties and nineties. Although it was found that the drag reduction depends on the riblet size scaled in wall units, the physical mechanisms implicated have not been completely understood up to now. It has been explained how riblets of vanishing size interact with the turbulent flow, producing a change in the drag proportional to their size, but that is not the regime of practical interest. The optimum performance is achieved for larger sizes, once that linear behavior has broken down, but before riblets begin adopting the character of regular roughness and increasing drag. This regime, which is the most relevant from a technological perspective, was precisely the less understood, so we have focused on it. Our efforts have followed three basic directions. First, we have re-assessed the available experimental data, seeking to identify common characteristics in the optimum regime across the different existing riblet geometries. This study has led to the proposal of a new length scale, the square root of the groove crosssection, to substitute the traditional peak-to-peak spacing. Scaling the riblet dimension with this length, the size of breakdown of the linear behavior becomes roughly universal. This suggests that the onset of the breakdown is related to a certain, fixed value of the cross-section of the groove. Second, we have conducted a set of direct numerical simulations of the turbulent flow over riblets, for sizes spanning the full drag reduction range. We have thus been able to reproduce the gradual transition between the different regimes. The spectral analysis of the flows has proven particularly fruitful, since it has made possible to identify spanwise rollers immediately above the riblets, which begin to appear when the riblet size is close to the optimum. This is a quite surprising feature of the flow, not because of the uniqueness of the phenomenon, which had been reported before for other types of complex and porous surfaces, but because most previous studies had focused on the detail of the flow above each riblet as a unit. Our novel approach has provided the adequate tools to capture coherent structures with an extended spanwise support, which interact with the riblets not individually, but collectively. We have also proven that those spanwise structures are responsible for the increase in drag past the viscous breakdown. Finally, we have analyzed the stability of the flow with a simplified model that connects the appearance of rollers to a Kelvin–Helmholtz-like instability, as is the case also for the flow over plant canopies and porous surfaces. In spite of the model emulating the presence of riblets only in an averaged, general fashion, it succeeds to capture the essential attributes of the breakdown, and provides a theoretical justification for the scaling with the groove cross-section.

Experimental study of surface roughness noise

A turbulent boundary-layer flow over a rough wall generates a dipole sound field as the near-field hydrodynamic disturbances in the turbulent boundary-layer scatter into radiated sound at small surface irregularities. In this paper, phased microphone arrays are applied to the experimental study of surface roughness noise. The radiated sound from two rough plates and one smooth plate in an open jet is measured at three streamwise locations, and the beamforming source maps demonstrate the dipole directivity. Higher source strengths can be observed in the rough plates than the smooth plate, and the rough plates also enhance the trailing-edge noise. A prediction scheme in previous theoretical work is used to describe the strength of a distribution of incoherent dipoles over the rigid plate and to simulate the sound detected by the microphone array. Source maps of measurement and simulation exhibit encouraging similarities in both source pattern and source strength, which confirms the dipole nature and the predicted magnitude of roughness noise. The simulations underestimate the streamwise gradient of the source strengths and overestimate the source strengths at the highest frequency. © 2007 by Yu Liu and Ann P. Dowling.