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Consistent outer scaling and analysis of adverse pressure gradient turbulent boundary layers

Published online by Cambridge University Press:  04 March 2024

Mingze Han Open the ORCID record for Mingze Han [Opens in a new window] ,
Mingze Ma Open the ORCID record for Mingze Ma [Opens in a new window]  and
Chao Yan Open the ORCID record for Chao Yan [Opens in a new window]
Mingze Han
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
Mingze Ma
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
Chao Yan*
Affiliation:
National Key Laboratory of Computational Fluid Dynamics, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: yanchao@buaa.edu.cn
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Abstract

Under adverse pressure gradient (APG) conditions, the outer regions of turbulent boundary layers (TBLs) are characterized by an increased velocity defect $U_{e}-U$, an outwards shift of the peak value of the Reynolds shear stress $-\langle uv\rangle$ and an appearance of the outer peak value of the Reynolds normal stress $\langle uu\rangle$. Here $U_{e}$ is the TBL edge velocity. Scaling APG TBLs is challenging due to the non-equilibrium effects caused by changes in the APG. To address this, the response distance of TBLs to non-equilibrium conditions is utilized to extend the Zagarola–Smits scaling $U_{zs} = U_{e}({\delta ^{*} }/{\delta })$ and ensure that the original properties of the Zagarola–Smits scaling are maintained as $Re \to \infty$. Here $\delta ^{*}$ is the displacement thickness and $\delta$ is the boundary layer thickness. Based on the established correlation between $U_{e}-U$ and $-\langle uv\rangle$, the scaling is extended to $-\langle uv\rangle$. Furthermore, considering the coupling relationship between Reynolds stress components, the scaling is extended to encompass each Reynolds stress component. The proposed consistent scaling is verified using five non-equilibrium databases and five near-equilibrium databases, successfully collapsing the data of the TBL outer region. The pressure gradient parameter $\beta =({\delta ^{*} }/{\rho u_{\tau }^{2} }) ({\mathrm {d} P_{e} }/{\mathrm {d}\kern0.7pt x})$ of these databases spans two orders of magnitude. Here $P_{e}$ is the boundary layer edge pressure, $u_{\tau }$ is the friction velocity and $\rho$ is the density. Finally, the influence of the APG on the inner and outer regions of TBLs is analysed using the mean momentum balance equation. The analysis suggests that the shift of the $-\langle uv\rangle$ peak to the outer region under APG conditions is due to an insufficient inertia term near the inner region to balance the APG. It is observed that the APG promotes interaction between the inner and outer regions of TBLs, but the inner and outer regions still retain distinctive properties.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 982 , 10 March 2024 , A17
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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