Journal of Central South University of Technology

, Volume 15, Issue 6, pp 774–778

# Improvement of Prandtl mixing length theory and application in modeling of turbulent flow in circular tubes

Article

## Abstract

In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.

## Key words

turbulent flow Prandtl mixing length time-smoothed velocity eddy viscosity friction factor

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© Central South University Press and Springer-Verlag GmbH 2008

## Authors and Affiliations

• Xiao Luo (罗 潇)
• 1
• Ping-le Liu (刘平乐)
• 1
Email author
• He-an Luo (罗和安)
• 1
1. 1.College of Chemical EngineeringXiangtan UniversityXiangtanChina