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The mean wall-normal velocity in turbulent boundary layer flows under pressure gradient

Published online by Cambridge University Press:  16 November 2023

Tie Wei Open the ORCID record for Tie Wei [Opens in a new window] ,
Zhaorui Li Open the ORCID record for Zhaorui Li [Opens in a new window] ,
Tobias Knopp Open the ORCID record for Tobias Knopp [Opens in a new window]  and
Ricardo Vinuesa Open the ORCID record for Ricardo Vinuesa [Opens in a new window]
Tie Wei*
Affiliation:
Department of Mechanical Engineering, New Mexico Tech, Socorro, NM 87801, USA
Zhaorui Li
Affiliation:
Department of Engineering, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USA
Tobias Knopp
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR (German Aerospace Center), Bunsenstr. 10, 37073 Gottingen, Germany
Ricardo Vinuesa
Affiliation:
FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden
*
†Email address for correspondence: tie.wei@nmt.edu
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Abstract

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.

JFM classification

Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A27
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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