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Direct numerical simulation of turbulent channel flow over random rough surfaces

Published online by Cambridge University Press:  15 December 2020

Rong Ma Open the ORCID record for Rong Ma [Opens in a new window] ,
Karim Alamé Open the ORCID record for Karim Alamé [Opens in a new window]  and
Krishnan Mahesh Open the ORCID record for Krishnan Mahesh [Opens in a new window]
Rong Ma
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Karim Alamé
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Krishnan Mahesh*
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: kmahesh@umn.edu
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Abstract

Direct numerical simulation of flow in a turbulent channel with a random rough bottom wall is performed at friction Reynolds number $Re_{\tau }=400$ and $600$. The rough surface corresponds to the experiments of Flack et al. (Flow Turbul. Combust., vol. 104, 2020, pp. 317–329). The computed skin-friction coefficients and the roughness functions show good agreement with experimental results. The double-averaging methodology is used to investigate mean velocity, Reynolds stresses, dispersive flux and mean momentum balance. The roll-up of the shear layer on the roughness crests is identified as a primary contributor to the wall-normal momentum transfer. The mean-square pressure fluctuations increase in the roughness layer and collapse onto their smooth-wall levels away from the wall. The dominant source terms in the pressure Poisson equation are examined. The rapid term shows that high pressure fluctuations observed in front of and above the roughness elements are mainly due to the attached shear layer formed upstream of the protrusions. The contribution of the slow term is smaller. The slow term is primarily increased in the troughs and in front of the roughness elements, corresponding to the occurrence of quasi-streamwise vortices and secondary vortical structures. The mean wall shear on the rough surface is highly correlated with the roughness height, and depends on the local roughness topography. The probability distribution function of wall shear stress fluctuations is consistent with higher velocities at roughness crests and reverse flow in the valley regions. Extreme events are more probable due to the roughness. Events with comparable magnitudes of the streamwise and spanwise wall shear stress occur more frequently, corresponding to a more isotropic vorticity field in the roughness layer.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A40
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© The Author(s), 2020. Published by Cambridge University Press

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