A universal velocity transformation for boundary layers with pressure gradients

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge...

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Bibliographic Details
Published in:Journal of fluid mechanics 2023-08, Vol.970, Article A3
Main Authors: Chen, Peng E.S., Wu, Wen, Griffin, Kevin P., Shi, Yipeng, Yang, Xiang I.A.
Format: Article
Language:English
Subjects:
Boundary layer flow
Boundary layers
Channel flow
Equilibrium
Flow mapping
Fluid mechanics
JFM Papers
Laminar flow
Law of the wall
MATHEMATICS AND COMPUTING
Navier-Stokes equations
Pressure
Pressure gradients
Reynolds number
Scaling
Shear stress
Transformations
turbulence theory
turbulent boundary layers
Velocity
Velocity distribution
Velocity profiles
Viscosity
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Summary:The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2023.570