The scaling of the wall pressure fluctuations in polymer-modified turbulent boundary layer flow

Wall pressure fluctuations and integrated skin friction were measured beneath a turbulent boundary layer that was modified by adding drag-reducing polymer to the pure water flow. The measurements were performed on an axisymmetric model, equipped with an isolated cylindrical drag balance section, and placed in the test section of the 0.3048-m-diam water tunnel at ARL Penn State. Data were acquired at a free-stream velocity of 10.7 m/s with pure water and with polymer added to the water at concentrations of 1, 5, 10, and 20 weight parts per million. Nondimensionalization of the wall pressure fluctuation frequency spectra with traditional outer, inner, and mixed flow variables failed to adequately collapse the data. The mean square wall pressure fluctuations were found to scale linearly with the wall shear stress. Polymer addition had little effect on the characteristic time scale of the flow. These properties were used to develop a novel form of the nondimensional wall pressure fluctuation spectrum that provided the best collapse of the measured data.