Comparison of theoretical and experimental wall pressure wavenumber-frequency spectra for axisymmetric and flat-plate turbulent boundary layers

The measurement and analysis of turbulent boundary layer wall pressure fluctuations using a wavenumber filter of sensors provide quantitative knowledge of turbulence physics. In addition, the sources of flow-induced noise and vibration for towed SONAR arrays can be determined. An axisymmetric turbulent boundary layer can have significantly different features than those of a comparable flat-plate boundary layer. Here, a detailed comparison of the distribution of wall pressure energy in both wavenumber and frequency between flat-plate and thick axisymmetric boundary layers is presented. The background theory of wavenumber-frequency spectra and state-of-the-art models for flat-plate boundary layers are discussed. The widely used model of Chase (1987), valid for flat-plate boundary layers over a wide range of Reynolds numbers, is used and combined with a sensor response function to allow the effects of spatial averaging to be considered. It is demonstrated that when measured boundary layer parameters for the axisymmetric case are used in the Chase flat-plate model, the results accurately predict the axisymmetric boundary layer wall pressure measurements.