An extension of the momentum transfer model to time-dependent pipe turbulence

Details An extension of the momentum transfer model to time-dependent pipe turbulence An extension of the momentum transfer model to time-dependent pipe turbulence

2011-09-20

arxiv.org/abs/1109.4401v4

Physics

Fluid Dynamics

15 pages. 2 figures (included) arXiv admin note: text overlap with arXiv:1005.0400

Scientific paper

We analyze a possible extension of Gioia and Chakraborty's momentum transfer model of friction in steady turbulent pipe flows (Phys. Rev. Lett. 96, 044502 (2006)) to the case of time and/or space dependent turbulent flows. The end result is an expression for the stress at the wall as the sum of an steady and a dynamic component. The steady part is obtained by using the instantaneous velocity in the expression for the stress at the wall of a stationary flow. The unsteady part is a weighted average over the history of the flow acceleration, with a weighting function similar to that proposed by Vardy and Brown (Journal of Sound and Vibration 259, 1011 (2003); ibid. 270, 233 (2004)), but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model (B. Brunone et al., J. of Water Resources Planning and Management 236 (2000)).

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