Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Turbulent Poiseuille Flow Modelling by an Enhanced Prandtl-Driest Mixing Length

Version 1 : Received: 15 January 2022 / Approved: 17 January 2022 / Online: 17 January 2022 (15:31:50 CET)
Version 2 : Received: 26 January 2022 / Approved: 27 January 2022 / Online: 27 January 2022 (12:36:58 CET)
Version 3 : Received: 13 December 2022 / Approved: 14 December 2022 / Online: 14 December 2022 (11:10:32 CET)

A peer-reviewed article of this Preprint also exists.

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 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

Abstract

The turbulent Poiseuille flow between two parallel plates is one of the simplest possible physical situations, and it has been studied intensively. Different mixing lengths are used, but no one, to the best of our knowledge, has simultaneously considered the boundary conditions of two walls together with damping effects from both walls. In this paper, we propose an enhanced Prandtl-Driest mixing length that not only satisfies all of the boundary conditions, but it also includes both walls' damping effects as well. With our new formulations, we numerically solve the problem and, moreover, propose an explicit approximate solution. As applications of our solutions, the total velocity, total shear stress, energy dissipation density, energy balance, Kolmogorov scale law, and friction of turbulent Poiseuille flow are studied in detail. The study discovers that the high heels profiles of both mean and total velocity are universal for all wall-bounded turbulent flows.

Keywords

Turbulent flow; Poiseuille flow; Prandtl mixing length; high heels velocity profile; Reynolds number

Subject

Physical Sciences, Fluids and Plasmas Physics

Comments (1)

Comment 1
Received: 27 January 2022
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: Abstract is rewritten, reviews are partly rewritten in the section of introduction, and Fig.18 is redraw
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 1


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.