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Eddy viscosity and complete log-law for turbulent pipe flow at high Reynolds numbers

Author(s): Junke Guo

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Keywords: Eddy viscosity; friction factor; log-law; pipe flow; velocity distribution; wall-bounded flow

Abstract: Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles' log-wake law for which the wake component is purely empirical. This research innovates Coles' wake law with another log-function, and thus combines the log- and the wake-laws into a single (complete) log-law, for which the von Kármán constant (0.39) is the only fit parameter. Specifically, the symmetrical velocity distribution about the centreline requires a symmetrical eddy viscosity model which is approximated by a quartic polynomial, leading to a complete log-law including the effects of the bottom and top walls as well as their interactions. The complete log-law is confirmed with data from both smooth and rough pipes; it also results in an accurate and explicit friction law for smooth pipe flow. Furthermore, the complete log-law is preliminarily tested with data from channels and boundary layers; the quartic eddy viscosity may be extended for ice-covered river flow in future studies.

DOI: https://doi.org/10.1080/00221686.2016.1212945

Year: 2017

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