Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T01:30:25.414Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent channel flow over an anisotropic porous wall – drag increase and reduction

Published online by Cambridge University Press:  12 March 2018

Marco E. Rosti Open the ORCID record for Marco E. Rosti [Opens in a new window] ,
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]  and
Alfredo Pinelli
Marco E. Rosti*
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, Stockholm, Sweden
Luca Brandt
Affiliation:
Linné Flow Centre and SeRC, KTH Mechanics, Stockholm, Sweden
Alfredo Pinelli
Affiliation:
School of Mathematics, Computer Science and Engineering, City, University of London, UK
*
†Email address for correspondence: merosti@mech.kth.se
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than 20 % by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall-normal velocity at the interface while promoting an increase of the tangential slip velocity leading to an almost ‘one-component’ turbulence where the low- and high-speed streak coherence is strongly enhanced. On the other hand, strong drag increase is found when high wall-normal and low wall-parallel permeabilities are prescribed. In this condition, the enhancement of the wall-normal fluctuations due to the reduced wall-blocking effect triggers the onset of structures which are strongly correlated in the spanwise direction, a phenomenon observed by other authors in flows over isotropic porous layers or over ribletted walls with large protrusion heights. The use of anisotropic porous walls for drag reduction is particularly attractive since equal gains can be achieved at different Reynolds numbers by rescaling the magnitude of the permeability only.

JFM classification

Flow Control: Drag reduction Flow Control: Mixing enhancement Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , pp. 381 - 394
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abderrahaman-Elena, N. & García-Mayoral, R. 2017 Analysis of anisotropically permeable surfaces for turbulent drag reduction. Phys. Rev. Fluids 2 (11), 114609.CrossRefGoogle Scholar
Beavers, G. S., Sparrow, E. M. & Magnuson, R. A. 1970 Experiments on coupled parallel flows in a channel and a bounding porous medium. Trans. ASME J. Basic Engng 92, 843–848.Google Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
Carotenuto, C., Vananroye, A., Vermant, J. & Minale, M. 2015 Predicting the apparent wall slip when using roughened geometries: a porous medium approach. J. Rheol. 59 (5), 1131–1149.CrossRefGoogle Scholar
Deepu, P., Anand, P. & Basu, S. 2015 Stability of poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer. Phys. Rev. E 92 (2), 023009.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.Google Scholar
Gomez-de Segura, G., Sharma, A. & García-Mayoral, R. 2017 Turbulent drag reduction by anisotropic permeable coatings. In 10th International Symposium on Turbulence and Shear Flow Phenomena – TSFP10.Google Scholar
Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2016 Transport mechanism of interface turbulence over porous and rough walls. Flow Turbul. Combust. 97 (4), 1071–1093.Google Scholar
Kuwata, Y. & Suga, K. 2017 Direct numerical simulation of turbulence over anisotropic porous media. J. Fluid Mech. 831, 41–71.CrossRefGoogle Scholar
Minale, M. 2014a Momentum transfer within a porous medium. I. Theoretical derivation of the momentum balance on the solid skeleton. Phys. Fluids 26 (12), 123101.CrossRefGoogle Scholar
Minale, M. 2014b Momentum transfer within a porous medium. II. Stress boundary condition. Phys. Fluids 26 (12), 123102.Google Scholar
Ochoa-Tapia, J. A. & Whitaker, S. 1995 Momentum transfer at the boundary between a porous medium and a homogeneous fluid – I. Theoretical development. Intl J. Heat Mass Transfer 38 (14), 2635–2646.Google Scholar
Ochoa-Tapia, J. A. & Whitaker, S. 1998 Momentum jump condition at the boundary between a porous medium and a homogeneous fluid: inertial effects. J. Porous Media 1, 201–218.Google Scholar
Quintard, M. & Whitaker, S. 1994 Transport in ordered and disordered porous media ii: Generalized volume averaging. Trans. Porous Med. 14 (2), 179–206.Google Scholar
Rosti, M. E. & Brandt, L. 2017 Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall. J. Fluid Mech. 830, 708–735.CrossRefGoogle Scholar
Rosti, M. E., Cortelezzi, L. & Quadrio, M. 2015 Direct numerical simulation of turbulent channel flow over porous walls. J. Fluid Mech. 784, 396–442.Google Scholar
Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31, 974–984.Google Scholar
Tilton, N. & Cortelezzi, L. 2006 The destabilizing effects of wall permeability in channel flows: A linear stability analysis. Phys. Fluids 18 (5), 051702.CrossRefGoogle Scholar
Tilton, N. & Cortelezzi, L 2008 Linear stability analysis of pressure-driven flows in channels with porous walls. J. Fluid Mech. 604, 411–445.Google Scholar
Whitaker, S. 1969 Advances in theory of fluid motion in porous media. Ind. Engng Chem. 61 (12), 14–28.Google Scholar
Whitaker, S. 1986 Flow in porous media I: A theoretical derivation of Darcy’s law. Trans. Porous Med. 1 (1), 3–25.Google Scholar
Whitaker, S. 1996 The Forchheimer equation: a theoretical development. Trans. Porous Med. 25 (1), 27–61.Google Scholar