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A study of wall shear stress in turbulent channel flow with hemispherical roughness

Published online by Cambridge University Press:  20 December 2019

Sicong Wu Open the ORCID record for Sicong Wu [Opens in a new window] ,
Kenneth T. Christensen Open the ORCID record for Kenneth T. Christensen [Opens in a new window]  and
Carlos Pantano Open the ORCID record for Carlos Pantano [Opens in a new window]
Sicong Wu*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL61801, USA
Kenneth T. Christensen
Affiliation:
Department of Aerospace and Mechanical Engineering, and Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN46556, USA International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka819-0385, Japan
Carlos Pantano
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL61801, USA Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA90089, USA
*
†Email address for correspondence: swu52@illinois.edu
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Abstract

Direct numerical simulations (DNS) of turbulent channel flow over hexagonally packed hemispheres were performed for friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}=200{-}600$. For cases at $Re_{\unicode[STIX]{x1D70F}}=400$, the inner-scaled roughness height $k^{+}=20$ was maintained while the spacing between roughness elements was varied from $d/k=2$ to 4. Two additional rough-wall cases were performed at $Re_{\unicode[STIX]{x1D70F}}=200$ and $600$, where $k^{+}=20$ and $d/k=4$ were fixed to investigate the $Re$ trends. For each case, wall shear stress was extracted from DNS by integrating the stress tensor over the rough surfaces. Spherical harmonics were employed to investigate the detailed spectral behaviour of the wall shear stress. Flow visualization near roughness elements was used to assist physical interpretations of the dominant flow features observed for various roughness characteristics. Analysis of amplitude modulation was applied to investigate the interactions between the ‘cell-averaged’ wall shear stress and outer, large-scale structures. A universal signal was obtained by removing the effects of outer, large-scale motions, based on the model proposed by Mathis et al. (J. Fluid Mech., vol. 715, 2013, pp. 163–180). Pre-multiplied spectra of the universal wall shear stress showed distinct behaviours at smaller scales for the ‘k-type’ roughness ($d/k=3{-}4$) compared to ‘d-type’ roughness ($d/k=2$), whereas the spectra at larger scales appeared similar for both types of roughness. A scaling relation between the variance of universal wall shear stress and averaging cell dimensions was found for both ‘k-type’ and ‘d-type’ roughness, which can be useful in designing candidate wall models used in large-eddy simulation.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A16
Copyright
© 2019 Cambridge University Press

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