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

Abstract

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)).

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

References in corpus (13)

• Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
• Roughness-induced critical phenomena in a turbulent flow
• Macroscopic effects of the spectral structure in turbulent flows
• Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
• Intermittency and rough-pipe turbulence
• The friction factor of two-dimensional rough-boundary turbulent soap film flows
• Rough-conduit flows and the existence of fully developed turbulence
• Friction factor for turbulent flow in rough pipes from Heisenberg's closure hypothesis
• Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation
• Estimating von-Karman's constant from Homogeneous Turbulence
• Phenomenology of Wall Bounded Newtonian Turbulence
• Drag reduction by polymer additives from turbulent spectra
• Steady Homogeneous Turbulence in the Presence of an Average Velocity Gradient