Modeling the Wall Pressure Spectrum in Turbulent Pipe Flows

Abstract

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.

Fetch‐limited growth of wind waves

“…The dots in Figure 5 are experimental results, the lines represent Hwang's analytical expressions, and the hollow squares and triangles are the new theoretical results, obtained from and . The fit obtained in Figure 5 strengthens our confidence in the relevance of the turbulent pressure spectrum proposed by Lysak [2006], for the modeling of the lower part of the marine boundary layer.…”

“…The novelty of this note is in the application of Lysak 's [2006] theoretical result for P 3 to the wind‐wave generation problem. Note that neither Sobey [1986], nor anybody else known to us, provide theoretically based expressions for P 3 .…”

“…A model for the wall pressure spectrum in turbulent pipe flow is given by (31) of Lysak [2006] where χ is the wave number in the direction perpendicular to the ( x , z ) plane; ϑ is the root mean square turbulent velocity; and k e represents the wave number of the energy containing eddies.…”

“…Using and in the work by Lysak [2006], with the mixing length L = 0.4 z , gives …”

“…The connection between the deterministic and stochastic formulations, which is needed in order to discuss the spectra of the free surface in terms of the air pressure spectrum, is given in section 4. For the turbulent air pressure spectrum, we build on a recent paper by Lysak [2006], whose results are adapted to our needs and presented in section 5.…”