Modification of the large-scale features of high Reynolds number wall turbulence by passive surface obtrusions

Abstract

A high Reynolds number boundary-layer wind-tunnel facility at New Mexico State University was fitted with a regularly distributed braille surface. The surface was such that braille dots were closely packed in the streamwise direction and sparsely spaced in the spanwise direction. This novel surface had an unexpected influence on the flow: the energy of the very large-scale features of wall turbulence (approximately six-times the boundary-layer thickness in length) became significantly attenuated, even into the logarithmic region. To the author’s knowledge, this is the first experimental study to report a modification of ‘superstructures’ in a rough-wall turbulent boundary layer. The result gives rise to the possibility that flow control through very small, passive surface roughness may be possible at high Reynolds numbers, without the prohibitive drag penalty anticipated heretofore. Evidence was also found for the uninhibited existence of the near-wall cycle, well known to smooth-wall-turbulence researchers, in the spanwise space between roughness elements.

Appendix: Re-scaling spectra at z + = 15

In Section 4.3, it was noted that the near-wall spectra appear similar in shape with increasing roughness. If this is so, a suitable re-scaling may bring about collapse of the spectra. To illustrate this point, the spectra have been re-scaled in this section using a modified friction velocity. The true, local, friction velocity in between elements is unknown due to the difficulty of determining this quantity (note that U _τ quoted throughout the text was based on statistical profiles and therefore represents a spanwise-averaged friction velocity). However, the conjecture is that the near-wall behaviour between elements is similar to that of a smooth-wall boundary layer. Hence, an illustrative way to re-scale the spectra is to use the smooth-wall equivalent U _τ at the global Reynolds number of the boundary layer (determined from the smooth-wall data of Hutchins et al. 2009). Figure 9 shows that such a simple re-scaling brings the spectra into better agreement. It is doubtful that this is the correct scaling; however, the result better illustrates the similarities in the shape of the energy distribution over the spectrum.

Fig. 9

Re-scaled spectra at z ⁺ = 15 for all roughness cases study. Spectra are re-scaled with the smooth-wall equivalent U _τ