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Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall

Published online by Cambridge University Press:  08 February 2024

Kazuhiko Suga Open the ORCID record for Kazuhiko Suga [Opens in a new window]  and
Yusuke Kuwata Open the ORCID record for Yusuke Kuwata [Opens in a new window]
Kazuhiko Suga*
Affiliation:
Department of Mechanical Engineering, Osaka Metropolitan University, Osaka 599-8531, Japan
Yusuke Kuwata
Affiliation:
Department of Mechanical Engineering, Osaka Metropolitan University, Osaka 599-8531, Japan
*
†Email address for correspondence: suga@omu.ac.jp
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Abstract

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$. Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$, and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$. The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$. By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$.

JFM classification

Turbulent Flows: Turbulence simulation Low-Reynolds-number flows: Porous media Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 980 , 10 February 2024 , A51
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© The Author(s), 2024. Published by Cambridge University Press

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