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An important source of vibration and noise in piping systems is the fluctuating wall pressure produced by the turbulent boundary layer. One approach to calculating the wall pressure fluctuations is to use a stochastic model based on the Poisson pressure equation. If the model is developed in the wave-number domain, the solution to the wave-number-frequency spectrum can be expressed as an integral of the turbulent sources over the boundary layer thickness. Models based on this formulation have been reported in the literature which show good agreement with measured pressure spectra, but they have relied on adjustable “tuning” constants to account for the unknown properties of the turbulent velocity fluctuations. A variation on this approach is presented in this paper, in which only well-known “universal” constants are used to model the turbulent velocity spectrum. The resulting pressure spectrum predictions are shown to be in good agreement with canonical data sets over a wide range of Reynolds numbers.

The unsteady lift spectrum for airfoils in turbulent flow has been measured in a water tunnel experiment. The results provide validation data for analytical models that account for the effect of airfoil thickness on the high frequency gust response. A series of four airfoils with elliptical leading edge profiles and thickness-to-chord ratios ranging from 8 to 16 percent were tested in grid-generated turbulence. The turbulent velocity spectrum was measured using Laser Doppler Velocimetry, and was found to be reasonably well approximated by an isotropic, homogeneous turbulence model. The unsteady force measurement setup and calibration procedure were designed to minimize the effect of system resonances, and contamination from facility vibration was reduced using a multiple coherence noise removal technique. Measurements of the unsteady lift spectrum were made at six speeds over the Reynolds number range 0.5 to 1.6 million, and the results were collapsed into a nondimensional force spectrum for the non-dimensional frequency range 1 < f c/U ∞ < 10. The experimental results agree very well with theory and confirm the importance of accounting for thickness to avoid overprediction of the forces in the high frequency range.

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