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Turbulent drag reduction by anisotropic permeable substrates – analysis and direct numerical simulations

Published online by Cambridge University Press:  18 July 2019

G. Gómez-de-Segura Open the ORCID record for G. Gómez-de-Segura [Opens in a new window]  and
R. García-Mayoral Open the ORCID record for R. García-Mayoral [Opens in a new window]
G. Gómez-de-Segura
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
R. García-Mayoral*
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: r.gmayoral@eng.cam.ac.uk
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Abstract

We explore the ability of anisotropic permeable substrates to reduce turbulent skin friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform direct numerical simulations of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performance begins to degrade. We observe that the degradation is associated with the appearance of spanwise-coherent structures, attributed to a Kelvin–Helmholtz-like instability of the mean flow. This feature is common to a variety of obstructed flows, and linear stability analysis can be used to predict it. For large permeabilities, these structures become prevalent in the flow, outweighing the drag-reducing effect of slip and eventually leading to an increase of drag. For the substrate configurations considered, the largest drag reduction observed is ${\approx}$20–25 % at a friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}=180$.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 124 - 172
Copyright
© 2019 Cambridge University Press 

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References

Abderrahaman-Elena, N., Fairhall, C. T. & García-Mayoral, R. 2019 Modulation of near-wall turbulence in the transitionally rough regime. J. Fluid Mech. 865, 1042–1071.Google Scholar
Abderrahaman-Elena, N. & García-Mayoral, R. 2017 Analysis of anisotropic permeable surfaces for turbulent drag reduction. Phys. Rev. Fluids 2, 114609.Google Scholar
Auriault, J. L. 2009 On the domain of validity of Brinkman’s equation. Trans. Porous Med. 79 (2), 215–223.Google Scholar
Battiato, I. 2012 Self-similarity in coupled Brinkman/Navier–Stokes flows. J. Fluid Mech. 699, 94–114.Google Scholar
Battiato, I. 2014 Effective medium theory for drag-reducing micro-patterned surfaces in turbulent flows. Eur. Phys. J. E 37, 19.Google Scholar
Battiato, I. & Rubol, S. 2014 Single-parameter model of vegetated aquatic flows. Water Resour. Res. 50, 6358–6369.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (1), 197–207.Google Scholar
Bechert, D. W., Bruse, M., Hage, W., Van der Hoeven, J. G. T. & Hoppe, G. 1997 Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 59–87.Google Scholar
Bottaro, A. 2019 Flow over natural or engineered surfaces: an adjoint homogenization perspective. J. Fluid Mech. (submitted).Google Scholar
Breugem, W. P. & Boersma, B. J. 2005 Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys. Fluids 17, 025103.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.Google Scholar
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 27–34.Google Scholar
Busse, A. & Sandham, N. D. 2012 Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24, 055111.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1–51.Google Scholar
Darcy, H. 1856 Les Fontaines Publiques de la Ville de Dijon. Victor Dalmont.Google Scholar
Fairhall, C. T., Abderrahaman-Elena, N. & García-Mayoral, R. 2019 The effects of slip and surface texture on turbulence over superhydrophobic surfaces. J. Fluid Mech. 861, 88–118.Google Scholar
Fairhall, C. T. & García-Mayoral, R. 2018 Spectral analysis of slip-length model for turbulence over textured superhydrophobic surfaces. Flow Turb. Combust. 100 (4), 961–978.Google Scholar
Forchheimer, P. 1901 Wasserbewegung durch boden. Z. Ver. Deutsch. Ing. 45, 1782–1788.Google Scholar
García-Mayoral, R., Gómez-de-Segura, G. & Fairhall, C. T. 2019 The control of near-wall turbulence through surface texturing. Fluid Dyn. Res. 51 (1), 011410.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. A 369, 1412–1427.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
García-Mayoral, R. & Jiménez, J. 2012 Scaling of turbulent structures in riblet channels up to Re 𝜏 ≈ 550. Phys. Fluids 24, 105101.Google Scholar
Gatti, D. & Quadrio, M. 2016 Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–582.Google Scholar
Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 51–61.Google Scholar
Gómez-de-Segura, G., Fairhall, C. T., MacDonald, M., Chung, D. & García-Mayoral, R. 2018a Manipulation of near-wall turbulence by surface slip and permeability. J. Phys.: Conf. Ser. 1001, 012011.Google Scholar
Gómez-de-Segura, G., Sharma, A. & García-Mayoral, R. 2018b Turbulent drag reduction using anisotropic permeable substrates. Flow Turb. Combust. 100 (4), 995–1014.Google Scholar
Hahn, S., Je, J. & Choi, H. 2002 Direct numerical simulation of turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.Google Scholar
Itoh, M., Tamano, S., Iguchi, R., Yokota, K., Akino, N., Hino, R. & Kubo, S. 2006 Turbulent drag reduction by the seal fur surface. Phys. Fluids 18, 065102.Google Scholar
James, D. F. & Davis, A. M. J. 2001 Flow at the interface of a model fibrous porous medium. J. Fluid Mech. 426, 47–72.Google Scholar
Jiménez, J. 1994 On the structure and control of near wall turbulence. Phys. Fluids 6 (2), 944–953.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
Joseph, D. D., Nield, D. A. & Papanicolaou, G. 1982 Nonlinear equation governing flow in a saturated porous medium. Water Resour. Res. 18 (4), 1049–1052.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.Google Scholar
Kuwata, Y. & Suga, K. 2016 Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls. Intl J. Heat Fluid Flow 61 (A), 145–157.Google Scholar
Kuwata, Y. & Suga, K. 2017 Direct numerical simulation of turbulence over anisotropic porous media. J. Fluid Mech. 831, 41–71.Google Scholar
Lācis, U. & Bagheri, S. 2017 A framework for computing effective boundary conditions at the interface between free fluid and a porous medium. J. Fluid Mech. 812, 866–889.Google Scholar
Le, H. & Moin, P. 1991 An improvement of fractional step methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 92, 369–379.Google Scholar
Le Bars, M. & Worster, M. G. 2006 Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification. J. Fluid Mech. 550, 149–173.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 5200. J. Fluid Mech. 774 (1), 395–415.Google Scholar
Lévy, T. 1983 Fluid flow through an array of fixed particles. Intl J. Engng Sci. 21 (1), 11–23.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct numerical simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26, 011702.Google Scholar
Luchini, P. 1996 Reducing the turbulent skin friction. In Computational Methods in Applied Sciences, Proceedings 3rd ECCOMAS CFD Conference, pp. 466–470. Wiley.Google Scholar
Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel flow and cross-flow. J. Fluid Mech. 228, 87–109.Google Scholar
MacDonald, M., Chan, L., Chung, D., Hutchins, N. & Ooi, A. 2016 Turbulent flow over transitionally rough surfaces with varying roughness densities. J. Fluid Mech. 804, 130–161.Google Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16 (7), L55.Google Scholar
Neale, G. & Nader, W. 1974 Practical significance of Brinkman’s extension of Darcy’s Law. Can. J. Chem. Engng 52, 475–478.Google Scholar
Ochoa-Tapia, J. A. & Whitaker, S. 1995a 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. 1995b Momentum transfer at the boundary between a porous medium and a homogeneous fluid – II. Comparison with experiment. Intl J. Heat Mass Transfer 38 (14), 2647–2655.Google Scholar
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turb. 7, N73.Google Scholar
Perot, J. B. 1993 An analysis of the fractional step method. J. Comput. Phys. 108, 51–58.Google Scholar
Perot, J. B. 1995 Comments on the fractional step method. J. Comput. Phys. 121, 190.Google Scholar
Rosti, M. E., Brandt, L. & Pinelli, A. 2018 Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech. 842, 381–394.Google 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
Rubol, S., Ling, B. & Battiato, I. 2018 Universal scaling-law for flow resistance over canopies with complex morphology. Sci. Rep. 8, 4430.Google Scholar
Gómez-de Segura, G.2019 Turbulent drag reduction by anisotropic permeable substrates. PhD thesis, University of Cambridge.Google Scholar
Seo, J., Garcia-Mayoral, R. & Mani, A. 2018 Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces. J. Fluid Mech. 835, 45–85.Google Scholar
Spalart, P. R. & McLean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. A 369, 1556–1569.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 (6), 1–21.Google Scholar
Suga, K., Nakagawa, Y. & Kaneda, M. 2017 Spanwise turbulence structure over permeable walls. J. Fluid Mech. 822, 186–201.Google Scholar
Suga, K., Okazaki, Y., Ho, U. & Kuwata, Y. 2018 Anisotropic wall permeability effects on turbulent channel flows. J. Fluid Mech. 855, 983–1016.Google Scholar
Tam, C. K. W. 1969 The drag on a cloud of spherical particles in low Reynolds number flow. J. Fluid Mech. 38 (3), 537–546.Google 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
Vafai, K. & Kim, S. J. 1990 Fluid mechanics of the interface region between a porous medium and a fluid layer – an exact solution. Intl J. Heat Fluid Flow 11 (3), 254–256.Google Scholar
Whitaker, S. 1996 The Forchheimer equation: a theoretical development. Trans. Porous Med. 25, 27–61.Google Scholar
Zampogna, G. A. & Bottaro, A. 2016 Fluid flow over and through a regular bundle of rigid fibres. J. Fluid Mech. 792, 5–35.Google Scholar