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.
In order to determine empirically the wavenumber-frequency spectra of the wall pressure fluctuations beneath a turbulent boundary layer at nonconvective wavenumbers, a spatial filter with high wavenumber resolution is necessary. Such a filter can be realized by using a continuous system such as a flexible bar or by using a discrete array of finite-sized transducers. The bar offers the advantage that high wavenumber resolution can be achieved without the use of the elaborate equipment necessary for the transducer arrays. In order to use the bar as a spatial filter all that is required is a measurement of the modal displacement response at some spatial position. In this paper, the theoretical formulation of the bar as a continuous spatial filter is developed. Calibration procedures and measurement problems such as those associated with vibrational noise are discussed. Finally, measurements of the low-wavenumber (nonconvective) spectra of the wall pressure fluctuations obtained by using the bar as a spatial filter are reported. One important result of this study is that it demonstrates that the primary wavenumbers associated with the pressure fluctuations contributing to the bar response are not the convective wavenumbers. This implies that Corcos's model, which has been empirically verified only for wavenumbers near the convective wavenumbers [D. M. Chase, J. Acoust. Soc. Amer. 46, 1350–1365 (1969)], may not be adequate for predicting panel response. The measured low-wavenumber (nonconvective) spectra indicate the limitations of Corcos' model in this region. [Work supported by grant from the National Aeronautics and Space Administration.]
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