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Relaxation of turbulent pipe flow downstream of a square bar roughness element

Published online by Cambridge University Press:  19 July 2021

Liuyang Ding Open the ORCID record for Liuyang Ding [Opens in a new window]  and
Alexander J. Smits Open the ORCID record for Alexander J. Smits [Opens in a new window]
Liuyang Ding*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Alexander J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: liuyangd@princeton.edu
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Abstract

The relaxation of turbulent pipe flow downstream of a single square bar roughness element is studied at distances up to $120R$ ($R$ is the pipe radius). Three bar heights, $h/R = 0.04$, 0.1 and 0.2, are investigated. The data suggest three stages for the relaxing flow. Immediately following the square bar is the development of a separated shear layer, where we find that the peak Reynolds stress scales linearly with $h/R$ and the disturbance profile is characterised by $h$. The bulk shear stress and turbulence intensity in this stage scale as $(h/R)^{2}$ and reach their maximum near the reattachment point. The second stage features the redistribution of turbulence towards the pipe centre and a power law in the decay of turbulence. The extent of this region is characterised by a streamwise length scale, ${x_c}$, which measures the extent of the redistribution process. The final stage of recovery is found to be long-lasting and oscillatory owing to asynchronous recovery between the mean velocity and the Reynolds stress. The oscillation wavelength scales with ${x_c}$ and decreases with increasing $h/R$. In contrast, the deficits in the mean shear and the bulk shear stress increase with $h/R$. For all three bar sizes, the flow recovery is not complete until the streamwise distance exceeds 500$h$–1000$h$.

JFM classification

Turbulent Flows: Pipe flow Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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