Modeling the wall pressure spectrum in turbulent pipe flows

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 wavenumber domain, the solution to the wavenumber-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.