Effects of Roughness on Measured Wall-Pressure Fluctuations beneath a Turbulent Boundary Layer

Abstract

This paper reports measurements of the cross-spectral density of the wall-pressure fluctuations beneath a turbulent boundary layer for three different surface-roughness conditions. The roughness consisted of sparsely populated, uniformly distributed sand particles—each roughness being distinguished by the sand-particle size. Separate studies of the spectral density and of the lateral and longitudinal narrow-band normalized space-time correlations were made in order to determine the cross-spectral density of the wall-pressure fluctuations. The results indicate that only the spectral density is strongly dependent on roughness size, for the roughnesses examined. To relate quantitatively the spectral densities measured on each surface, the roughness was characterized in terms of Nikuradse's equivalent sand-roughness parameter. The spectral density was then normalized, using this roughness parameter, the shear velocity, and the local coefficient of skin friction. Also, for the roughest surface, the pressure fluctuations in the vicinity of a particle and the correlation of these fluctuations with pressure fluctuations at some distance from the particle were examined in order to determine any observable effects of the local flow about the particles. The results indicate that the local flow can be ignored, provided that the roughness size is not too large. The measurements do not reveal any direct relation between the cross-spectral densities measured on rough surfaces with those measured on smooth.

The Wall Pressure Spectrum of High Reynolds Number Rough-Wall Turbulent Boundary Layers

“…This was attributed to the difference in turbulence production near the wall, which was concluded to be dependent on roughness height over rough walls rather than the viscous lengths associated with smooth wall flows. In general Blake concluded that for rough walls, roughness had the largest influence on medium and small scale turbulence structures, while unlike the findings of Aupperle and Lambert (1970), roughness spacing was speculated to have mild influence on the larger turbulence structures.…”

“…The relevant results determined in Smith largely revolve around the collapse of the wall pressure spectra over rough walls. A moderate collapse of Smith's data was observed while using the scaling variables proposed by Aupperle and Lambert's (1970) and Blake (1970) for equivalent roughness configurations. When using different roughness configurations, these scaling variables were shown to exhibit a poor collapse for the entire range of roughness data.…”

“…The study by Aupperle and Lambert (1970) was one of the first investigations focusing on surface pressure fluctuations for fully rough flows. Measurements were taken in a continuous-flow subsonic wind tunnel at 50-m/s for one smooth and three roughness configurations.…”

“…Blake's data from 1970 was revisited in Blake's 1971 paper. During this symposium, Blake reviewed the data from both Blake (1970) and Aupperle and Lambert (1970). It was found that both data sets showed a measure of collapse when using the earlier scaling proposed in Blake (1970).…”

“…However, an overlap region was observed, though a mid-frequency collapse was not observed for either set of scaling parameters. Varano continued and applied both Aupperle and Lambert's (1970) proposed empirical scaling and Smith's (2008) proposed empirical scaling. These results both proved to show a poor collapse of Varano's data.…”