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Turbulent Poiseuille flow modeling by modified Prandtl-van Driest mixing length

基于改进的Prandtl-van Driest混合长度的湍流Poiseuille流动模型

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Abstract

The turbulent Poiseuille flow between two parallel plates is one of the simplest possible physical situations, and it has been studied intensively. In this paper, we propose a modified Prandtl-van Driest mixing length that satisfies both boundary conditions and wall damping effects. With our new formulations, we numerically solve the problem and, moreover, propose an approximate analytical solution of mean velocity. As applications of our solution, an approximate analytical friction coefficient of turbulent Poiseuille flow is proposed.

摘要

两个平行板之间的湍流Poiseuille流是最简单的物理情况之一, 此问题已经被深入的研究. 本文提出了一种改进的Prandtl-van Driest混合长度模型, 本模型同时满足边界条件和壁面阻尼效应. 使用我们的新公式, 我们可以求得问题的数值解, 此外, 本文还提出了平均速度的近似解析解. 作为我们解决方案的应用, 推导了湍流Poiseuille流的近似解析摩擦系数.

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Acknowledgements

This work was supported by Xi’an University of Architecture and Technology (Grant No. 002/2040221134). The author wishes to express his appreciation to Prof. Y. Pomeau for private communication and introduction of his work [17], Prof. X. Chen and Prof. Yun Bao for providing some useful publications, and to Mr. Zhe Liu for extracting the DNS, modelling and experimental data from Ref. [18], which are used to draw Fig. 6. Special thanks goes to my student, Mr. Xuang-Ting Liu, who modified the Maple code provided in the Appendix. I also wish to express my deep gratitude to all anonymous reviewers for their high-level academic comments that helped me to enhance the quality of this paper.

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  1. School of Civil Engineering & Institute of Mechanics and Technology, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Bo-Hua Sun  (孙博华)

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  1. Bo-Hua Sun  (孙博华)
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Correspondence to Bo-Hua Sun  (孙博华).

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Sun, BH. Turbulent Poiseuille flow modeling by modified Prandtl-van Driest mixing length. Acta Mech. Sin. 39, 322066 (2023). https://doi.org/10.1007/s10409-022-22066-x

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