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 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 a 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, but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model. © 2012 American Physical Society.