Modified log-wake law for turbulent flow in smooth pipes

Abstract

A modified log-wake law for turbulent flow in smooth pipes is developed and tested with laboratory data. The law consists of three terms: a log term, a sine-square term and a cubic term. The log term reflects the restriction of the wall, the sine-square term expresses the contribution of the pressure gradient, and the cubic term makes the standard log-wake law satisfy the axial symmetrical condition. The last two terms define the modified wake law. The proposed velocity profile model not only improves the standard log-wake law near the pipe axis but also provides a better eddy viscosity model for turbulent mixing studies. An explicit friction factor is also presented for practical applications. The velocity profile model and the friction factor equation agree very well with Nikuradse' and other recent data. The eddy viscosity model is consistent with Laufer's, Nunner's and Reichardt's experimental data. Finally, an equivalent polynomial version of the modified log-wake law is presented.

Keywords:

• Pipe flow
• turbulence
• logarithmic matching
• log law
• log-wake law
• velocity profile
• velocity distribution
• eddy viscosity
• friction factor