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A universal velocity transformation for boundary layers with pressure gradients

Published online by Cambridge University Press:  25 August 2023

Peng E.S. Chen Open the ORCID record for Peng E.S. Chen [Opens in a new window] ,
Wen Wu Open the ORCID record for Wen Wu [Opens in a new window] ,
Kevin P. Griffin Open the ORCID record for Kevin P. Griffin [Opens in a new window] ,
Yipeng Shi  and
Xiang I.A. Yang Open the ORCID record for Xiang I.A. Yang [Opens in a new window]
Peng E.S. Chen*
Affiliation:
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
Wen Wu
Affiliation:
Department of Mechanical Engineering, University of Mississippi, MS 38677, USA
Kevin P. Griffin
Affiliation:
Center for Turbulence Research, Stanford University, CA 94305, USA National Renewable Energy Laboratory, CO 80401, USA
Yipeng Shi
Affiliation:
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China
Xiang I.A. Yang
Affiliation:
Mechanical Engineering, Pennsylvania State University, PA 16802, USA
*
†Email address for correspondence: chenpeng66@pku.edu.cn
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Abstract

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.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A3
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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