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

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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.

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Authors and Affiliations

  1. College of Chemical Engineering, Xiangtan University, Xiangtan, 411105, China

    Xiao Luo  (罗 潇), Ping-le Liu  (刘平乐) & He-an Luo  (罗和安)

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  1. Xiao Luo  (罗 潇)
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  2. Ping-le Liu  (刘平乐)
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  3. He-an Luo  (罗和安)
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Corresponding author

Correspondence to Ping-le Liu  (刘平乐).

Additional information

Foundation item: Project(20736009) supported by the National Natural Science Foundation of China; Project(07JJ6017) supported by the Natural Science Foundation of Hunan Province, China

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Luo, X., Liu, Pl. & Luo, Ha. Improvement of Prandtl mixing length theory and application in modeling of turbulent flow in circular tubes. J. Cent. South Univ. Technol. 15, 774–778 (2008). https://doi.org/10.1007/s11771-008-0143-3

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  • DOI: https://doi.org/10.1007/s11771-008-0143-3

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