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On the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition

Published online by Cambridge University Press:  25 August 2020

F. Picella Open the ORCID record for F. Picella [Opens in a new window] ,
J.-Ch. Robinet Open the ORCID record for J.-Ch. Robinet [Opens in a new window]  and
S. Cherubini Open the ORCID record for S. Cherubini [Opens in a new window]
F. Picella
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013Paris, France
J.-Ch. Robinet
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013Paris, France
S. Cherubini*
Affiliation:
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Re David 200, 70126Bari, Italy
*
†Email address for correspondence: [email protected]
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Abstract

Superhydrophobic surfaces dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. Under wetting-stable conditions, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip–no-slip conditions taking into account or not the displacement of the gas–water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated yet. In this work we study, by means of numerical simulations and global stability analyses, the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition in a channel flow. For the K-type scenario, a strong transition delay is found using spatially homogeneous or heterogeneous slippery boundaries with flat, rigid liquid–gas interfaces. Whereas, when the interface dynamics is taken into account, the time to transition is reduced, approaching that of a no-slip channel flow. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown, reducing the transition delay effect with respect to flat slippery surfaces. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimating transition delay. Contrariwise, non-modal transition triggered by a broadband forcing is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on the interface dynamics and on the considered transition process.

JFM classification

Flow Control: Drag reduction Instability: Transition to turbulence Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Aghdam, S. K. & Ricco, P. 2016 Laminar and turbulent flows over hydrophobic surfaces with shear-dependent slip length. Phys. Fluids 28 (3), 035109.CrossRefGoogle Scholar
Alamé, K. & Mahesh, K. 2019 Wall-bounded flow over a realistically rough superhydrophobic surface. J. Fluid Mech. 873, 977–1019.CrossRefGoogle Scholar
Alinovi, E. & Bottaro, A. 2018 Apparent slip and drag reduction for the flow over superhydrophobic and lubricant-impregnated surfaces. Phys. Rev. Fluids 3 (12), 124002.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.CrossRefGoogle Scholar
Arnoldi, W. E. 1951 The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q. Appl. Maths 9 (1), 17–29.CrossRefGoogle Scholar
Barthlott, W., Mail, M., Bhushan, B. & Koch, K. 2017 Plant surfaces: structures and functions for biomimetic innovations. Nano-Micro Lett. 9 (2), 23.CrossRefGoogle ScholarPubMed
Barthlott, W. & Neinhuis, C. 1997 Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 202 (1), 1–8.CrossRefGoogle Scholar
Bidkar, R. A., Leblanc, L., Kulkarni, A. J., Bahadur, V., Ceccio, S. L. & Perlin, M. 2014 Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces. Phys. Fluids 26 (8), 085108.CrossRefGoogle Scholar
Bottaro, A. 2019 Flow over natural or engineered surfaces: an adjoint homogenization perspective. J. Fluid Mech. 877, P1.CrossRefGoogle Scholar
Brandt, L., Cossu, C., Chomaz, J.-M., Huerre, P. & Henningson, D. S. 2003 On the convectively unstable nature of optimal streaks in boundary layers. J. Fluid Mech. 485, 221–242.CrossRefGoogle 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.CrossRefGoogle Scholar
Cassie, A. B. D. & Baxter, S. 1944 Wettability of porous surfaces. Trans. Faraday Soc. 40, 546.CrossRefGoogle Scholar
Castagna, M., Mazellier, N. & Kourta, A. 2018 Wake of super-hydrophobic falling spheres: influence of the air layer deformation. J. Fluid Mech. 850, 646–673.CrossRefGoogle Scholar
Daniello, R. J., Waterhouse, N. E. & Rothstein, J. P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21 (8), 085103.CrossRefGoogle Scholar
Davis, A. M. J. & Lauga, E. 2010 Hydrodynamic friction of fakir-like superhydrophobic surfaces. J. Fluid Mech. 661, 402–411.CrossRefGoogle Scholar
Fairhall, C. T., Abderrahaman-Elena, N. & García-Mayoral, R. 2018 The effect of slip and surface texture on turbulence over superhydrophobic surfaces. J. Fluid Mech. 861, 88–118.CrossRefGoogle Scholar
Fairhall, C. T. & García-Mayoral, R. 2018 Spectral analysis of the slip-length model for turbulence over textured superhydrophobic surfaces. Flow Turbul. Combust. 100 (4), 961–978.CrossRefGoogle ScholarPubMed
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G. 2008 nek5000 Web Page. Available at: http://nek5000.mcs.anl.gov.Google Scholar
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1984 On the interaction of compliant coatings with boundary-layer flows. J. Fluid Mech. 140 (1), 257.CrossRefGoogle Scholar
García Cartagena, E. J., Arenas, I., Bernardini, M. & Leonardi, S. 2018 Dependence of the drag over super hydrophobic and liquid infused surfaces on the textured surface and weber number. Flow Turbul. Combust. 100 (4), 945–960.CrossRefGoogle Scholar
Gilbert, N. & Kleiser, L. 1990 Near-wall phenomena in transition to turbulence. In Near-Wall Turbulence, pp. 7–27. Hemisphere.Google Scholar
Gose, J. W., Golovin, K., Boban, M., Mabry, J. M., Tuteja, A., Perlin, M. & Ceccio, S. L. 2018 Characterization of superhydrophobic surfaces for drag reduction in turbulent flow. J. Fluid Mech. 845, 560–580.CrossRefGoogle Scholar
Guo, H., Borodulin, V. I., Kachanov, Y. S., Pan, C., Wang, J. J., Lian, Q. X. & Wang, S. F. 2010 Nature of sweep and ejection events in transitional and turbulent boundary layers. J. Turbul. 11, N34.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jelly, T. O., Jung, S. Y. & Zaki, T. A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26 (9), 095102.CrossRefGoogle Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411–482.CrossRefGoogle 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
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12 (1), 1.CrossRefGoogle Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23 (1), 495–537.CrossRefGoogle Scholar
Lee, C., Choi, C.-H. & Kim, C.-J. 2016 Superhydrophobic drag reduction in laminar flows: a critical review. Exp. Fluids 57 (12), 176.CrossRefGoogle Scholar
Lee, J., Jelly, T. O. & Zaki, T. A. 2015 Effect of Reynolds number on turbulent drag reduction by superhydrophobic surface textures. Flow Turbul. Combust. 95 (2–3), 277–300.CrossRefGoogle Scholar
Lee-Wing, H. 1989 A legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows. PhD dissertation, Department of Mechanical Engineering, Massachusetts Institute of Technology.Google Scholar
Lee-Wing, H. & Patera, A. T. 1990 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Meth. Appl. Mech. Engng 80 (1–3), 355–366.CrossRefGoogle Scholar
Li, Y., Alame, K. & Mahesh, K. 2017 Feature-resolved computational and analytical study of laminar drag reduction by superhydrophobic surfaces. Phys. Rev. Fluids 2 (5), 054002.CrossRefGoogle Scholar
Ling, H., Srinivasan, S., Golovin, K., McKinley, G. H., Tuteja, A. & Katz, J. 2016 High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670–703.CrossRefGoogle Scholar
Lisi, E., Amabili, M., Meloni, S., Giacomello, A. & Casciola, C. Massimo 2017 Self-recovery superhydrophobic surfaces: modular design. ACS Nano 12 (1), 359–367.CrossRefGoogle ScholarPubMed
Loiseau, J.-C., Robinet, J.-C., Cherubini, S. & Leriche, E. 2014 Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations. J. Fluid Mech. 760, 175–211.CrossRefGoogle Scholar
Lucey, A. D. & Carpenter, P. W. 1995 Boundary layer instability over compliant walls: comparison between theory and experiment. Phys. Fluids 7 (10), 2355–2363.CrossRefGoogle Scholar
Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel flow and cross-flow. J. Fluid Mech. 228, 87.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415–441.CrossRefGoogle Scholar
Malm, J., Schlatter, P. & Sandham, N. D. 2011 A vorticity stretching diagnostic for turbulent and transitional flows. Theor. Comput. Fluid Dyn. 26 (6), 485–499.CrossRefGoogle Scholar
Martell, M. B., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.CrossRefGoogle Scholar
Martell, M. B., Rothstein, J. P. & Perot, J. B. 2010 An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation. Phys. Fluids 22 (6), 065102.CrossRefGoogle Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16 (7), L55–L58.CrossRefGoogle Scholar
Min, T. & Kim, J. 2005 Effects of hydrophobic surface on stability and transition. Phys. Fluids 17 (10), 108106.CrossRefGoogle Scholar
Navier, C. L. M. H. 1823 Mémoire sur les lois du mouvement des fluides. Mémoires de l'Académie Royale des Sciences de l'Institut de France.Google Scholar
Nishioka, M., Iid A, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane poiseuille flow. J. Fluid Mech. 72 (4), 731.CrossRefGoogle Scholar
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.CrossRefGoogle Scholar
Olsson, P. J. & Henningson, D. S. 1995 Optimal disturbance growth in watertable flow. Stud. Appl. Maths 94 (2), 183–210.CrossRefGoogle Scholar
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50 (04), 689.CrossRefGoogle Scholar
Ou, J., Perot, B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16 (12), 4635–4643.CrossRefGoogle Scholar
Park, H., Park, H. & Kim, J. 2013 A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25 (11), 110815.CrossRefGoogle Scholar
Park, H., Sun, G. & Kim, C.-J. 2014 Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722–734.CrossRefGoogle Scholar
Patankar, N. A. 2016 Thermodynamics of trapping gases for underwater superhydrophobicity. Langmuir 32 (27), 7023–7028.CrossRefGoogle ScholarPubMed
Philip, J. R. 1972 Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23 (3), 353–372.CrossRefGoogle Scholar
Picella, F., Bucci, M. A., Cherubini, S. & Robinet, J.-C. 2019 a A synthetic forcing to trigger laminar–turbulent transition in parallel wall bounded flows via receptivity. J. Comput. Phys. 393, 92–116.CrossRefGoogle Scholar
Picella, F., Loiseau, J.-C., Lusseyran, F., Robinet, J.-C., Cherubini, S. & Pastur, L. 2018 Successive bifurcations in a fully three-dimensional open cavity flow. J. Fluid Mech. 844, 855–877.CrossRefGoogle Scholar
Picella, F., Robinet, J. C. & Cherubini, S. 2019 b Laminar–turbulent transition in channel flow with superhydrophobic surfaces modelled as a partial slip wall. J. Fluid Mech. 881, 462–497.CrossRefGoogle Scholar
Pralits, J. O., Alinovi, E. & Bottaro, A. 2017 Stability of the flow in a plane microchannel with one or two superhydrophobic walls. Phys. Rev. Fluids 2 (1), 013901.CrossRefGoogle Scholar
Ramaswamy, B. & Kawahara, M. 1987 Arbitrary Lagrangian–Eulerian finite element method for unsteady, convective, incompressible viscous free surface fluid flow. Intl J. Numer. Meth. Fluids 7 (10), 1053–1075.CrossRefGoogle Scholar
Rastegari, A. & Akhavan, R. 2015 On the mechanism of turbulent drag reduction with super-hydrophobic surfaces. J. Fluid Mech. 773, R4.CrossRefGoogle 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
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42 (1), 89–109.CrossRefGoogle Scholar
Sandham, N. D. & Kleiser, L. 1992 The late stages of transition to turbulence in channel flow. J. Fluid Mech. 245 (1), 319.CrossRefGoogle Scholar
Sayadi, T., Hamman, C. W. & Moin, P. 2013 Direct numerical simulation of complete h-type and k-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480–509.CrossRefGoogle Scholar
Schellenberger, F., Encinas, N., Vollmer, D. & Butt, H.-J. 2016 How water advances on superhydrophobic surfaces. Phys. Rev. Lett. 116 (9), 096101.CrossRefGoogle ScholarPubMed
Schlatter, P., Stolz, S. & Kleiser, L. 2006 Large-eddy simulation of spatial transition in plane channel flow. J. Turbul. 7, N33.CrossRefGoogle Scholar
Schlatter, P. C. 2005 Large-eddy simulation of transition and turbulence in wall-bounded shear flow. PhD thesis, ETH Zurich.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schönecker, C., Baier, T. & Hardt, S. 2014 Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state. J. Fluid Mech. 740, 168–195.CrossRefGoogle Scholar
Seo, J., García-Mayoral, R. & Mani, A. 2015 Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 783, 448–473.CrossRefGoogle Scholar
Seo, J., García-Mayoral, R. & Mani, A. 2017 Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces. J. Fluid Mech. 835, 45–85.CrossRefGoogle Scholar
Seo, J. & Mani, A. 2016 On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces. Phys. Fluids 28 (2), 025110.CrossRefGoogle Scholar
Seo, J. & Mani, A. 2018 Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces. Phys. Rev. Fluids 3 (4), 044601.CrossRefGoogle Scholar
Steinberger, A., Cottin-Bizonne, C., Kleimann, P. & Charlaix, E. 2007 High friction on a bubble mattress. Nat. Mater. 6 (9), 665–668.CrossRefGoogle ScholarPubMed
Teo, C. J. & Khoo, B. C. 2010 Flow past superhydrophobic surfaces containing longitudinal grooves: effects of interface curvature. Microfluid Nanofluid 9 (2–3), 499–511.CrossRefGoogle Scholar
Theofilis, V. & Colonius, T. 2003 An algorithm for the recovery of 2- and 3d BiGlobal instabilities of compressible flow over 2d open cavities. In 33rd AIAA Fluid Dynamics Conference and Exhibit. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
van der Walt, S., Schönberger, J. L., Nunez-Iglesias, J., Boulogne, F., Warner, J. D., Yager, N., Gouillart, E., Yu, T.the scikit-image contributors 2014 scikit-image: image processing in Python. PeerJ 2, e453.CrossRefGoogle ScholarPubMed
Wang, Z., Bovik, A. C., Sheikh, H. R. & Simoncelli, E. P. 2004 Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13 (4), 600–612.CrossRefGoogle ScholarPubMed
Wenzel, R. N. 1936 Resistance of solid surfaces to wetting by water. Ind. Engng Chem. 28 (8), 988–994.CrossRefGoogle Scholar
Wexler, J. S., Jacobi, I. & Stone, H. A. 2015 Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 114 (16), 168301.CrossRefGoogle ScholarPubMed
Woolford, B., Prince, J., Maynes, D. & Webb, B. W. 2009 Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21 (8), 085106.CrossRefGoogle Scholar
Xiang, Y., Huang, S., Lv, P., Xue, Y., Su, Q. & Duan, H. 2017 Ultimate stable underwater superhydrophobic state. Phys. Rev. Lett. 119 (13), 134501.CrossRefGoogle ScholarPubMed
Ybert, C., Barentin, C., Cottin-Bizonne, C., Joseph, P. & Bocquet, L. 2007 Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries. Phys. Fluids 19 (12), 123601.CrossRefGoogle Scholar
Yu, K. H., Teo, C. J. & Khoo, B. C. 2016 Linear stability of pressure-driven flow over longitudinal superhydrophobic grooves. Phys. Fluids 28 (2), 022001.CrossRefGoogle Scholar
Zampogna, G. A., Magnaudet, J. & Bottaro, A. 2018 Generalized slip condition over rough surfaces. J. Fluid Mech. 858, 407–436.CrossRefGoogle Scholar
Zang, T. A. & Krist, S. E. 1989 Numerical experiments on stability and transition in plane channel flow. Theor. Comput. Fluid Dyn. 1 (1), 41–64.Google Scholar
Zhang, J., Tian, H., Yao, Z., Hao, P. & Jiang, N. 2015 Mechanisms of drag reduction of superhydrophobic surfaces in a turbulent boundary layer flow. Exp. Fluids 56 (9), 179.CrossRefGoogle Scholar
Zhang, C., Wang, J., Blake, W. & Katz, J. 2017 Deformation of a compliant wall in a turbulent channel flow. J. Fluid Mech. 823, 345–390.CrossRefGoogle Scholar
Zhang, J., Yao, Z. & Hao, P. 2016 Drag reductions and the air–water interface stability of superhydrophobic surfaces in rectangular channel flow. Phys. Rev. E 94 (5), 053117.CrossRefGoogle ScholarPubMed