Direct measurements of turbulent boundary layer wall pressure wavenumber-frequency spectra on smooth and riblet-coated plates

Measurements of the fluctuating wall pressure space-time field were made with a linear array of 48 hydrophones beneath a fully developed turbulent boundary layer of water on a flat plate. Autospectra, cross-spectra, and wavenumber-frequency spectra were calculated from digitized hydrophone signals. Boundary layer parameters were estimated from streamwise velocity profiles that were measured with a laser doppler anemometry system and a pitot tube. The wall pressure measurements spanned an R&thetas; range of 3,000 to 16,800. ^ The estimated wall pressure spectra were scaled using boundary layer parameters and compared with other experimental data. Scaling laws were established for wavenumber-frequency spectra such that the data collapse over the widest possible range of Reynolds numbers, nondimensional frequencies, and nondimensional wavenumbers. Scaling results for the wavenumber-frequency spectra were consistent with those already established for wall pressure autospectra. An empirical model of the wall pressure streamwise wavenumber-frequency spectrum was developed based on normalized data. Because the model was based on the measured data, it predicts the asymmetric distribution in wavenumber of the wall pressure fluctuations that existing analytical and semi-empirical models do not. ^ Vinyl riblet material, consisting of a multitude of parallel, symmetric, “V” grooves with a peak-to-peak spacing and height of 0.1143-mm, was applied to the flat plate such that the grooves were aligned with the free-stream direction. Boundary layer parameters and wall pressure spectra were measured to assess the effect of the riblets on the turbulent boundary layer flow. The riblets had a minor effect on the wall pressure spectra (approximately 1dB attenuation or amplification), although there was a consistent decrease in the autospectrum levels at lower measured frequencies. Mean wall shear stresses were estimated using mean streamwise velocity profiles and also from attenuations of the wall pressure autospectra at low frequencies. The former method was very sensitive to the chosen wall-normal coordinate origin while the latter yielded maximum estimated skin friction drag reductions of 8.5% at a nondimensional riblet spacing of s+ = 14. These reductions were consistent with the results of other investigations that directly measured the drag on similar riblet materials using a force balance.