Bulk flow scaling for turbulent channel and pipe flows
1 State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics, College of Engineering, Peking University - Beijing 100871, China
2 Department of Mechanical Engineering, Texas Tech University - Lubbock, TX 79409-1021, USA
Received: 26 May 2016
Accepted: 5 August 2016
We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel vs. circular pipe) by a variational calculation for a large-scale energy length, which characterizes its bulk flow scaling by a simple exponent, i.e., m = 4 for the channel and 5 for the pipe. The predicted mean velocity shows excellent agreement with several dozen sets of quality empirical data for a wide range of the Reynolds number (Re), with a universal bulk flow constant . Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.
PACS: 47.27.eb – Statistical theories and models / 47.27.nb – Boundary layer turbulence / 47.27.nd – Channel flow
© EPLA, 2016