Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-11T19:18:27.909Z Has data issue: false hasContentIssue false

Wall-attached structures in a drag-reduced turbulent channel flow

Published online by Cambridge University Press:  06 June 2022

Min Yoon
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea Division of Mechanical Engineering, Korea Maritime and Ocean University, 727 Taejong-ro, Yeongdo-gu, Busan 49112, Korea
Hyung Jin Sung*
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
*
 Email address for correspondence: hjsung@kaist.ac.kr

Abstract

We explore wall-attached structures in a drag-reduced turbulent channel flow with the Navier slip boundary condition. Three-dimensional coherent structures of the streamwise velocity fluctuations (u) are examined in an effort to assess the influence of wall-attached u structures on drag reduction. We extract the u clusters from the direct numerical simulation (DNS) data; the DNS data for the no-slip condition are included for comparison. The wall-attached structures, which are physically adhered to the wall, in the logarithmic region are self-similar with their height and contribute to the presence of logarithmic behaviour. The influence of the streamwise slip on wall-attached structures is limited up to the lower bound of the logarithmic region. Although wall-attached self-similar structures (WASS) slide at the wall, the formation and hierarchy of WASS are sustained. Weakened mean shear by the streamwise slip results in a diminution in the population density of wall-attached structures within the buffer layer, leading to sparse population of WASS. In contrast, the space occupied by WASS in the fluid domain increases. The streamwise slip induces long tails in the near-wall part of WASS, reminiscent of the footprints of large-scale motions. Both a decrease in the population density of WASS and a reduction in the density of skin friction of WASS are responsible for the overall drag reduction.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by 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

Adrian, R.J., Meinhart, C.D. & Tomkins, C.D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.CrossRefGoogle Scholar
Ahn, J., Lee, J.H., Lee, J., Kang, J.H. & Sung, H.J. 2015 Direct numerical simulation of a 30R long turbulent pipe flow at Reτ = 3008. Phys. Fluids 27 (6), 065110.CrossRefGoogle Scholar
del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.CrossRefGoogle Scholar
Bae, H.J. & Lee, M. 2021 Life cycle of streaks in the buffer layer of wall-bounded turbulence. Phys. Rev. Fluids 6 (6), 064603.CrossRefGoogle Scholar
Chin, C., Philip, J., Klewicki, J., Ooi, A. & Marusic, I. 2014 Reynolds-number-dependent turbulent inertia and onset of log region in pipe flows. J. Fluid Mech. 757, 747769.CrossRefGoogle Scholar
Chung, D., Monty, J.P. & Ooi, A. 2014 An idealised assessment of Townsend's outer-layer similarity hypothesis for wall turbulence. J. Fluid Mech. 742, R3.CrossRefGoogle Scholar
Dennis, D.J. & Nickels, T.B. 2011 Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J. Fluid Mech. 673, 180217.CrossRefGoogle Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech. 816, 167208.CrossRefGoogle Scholar
Eyink, G.L. 2008 Turbulent flow in pipes and channels as cross-stream ‘inverse cascades’ of vorticity. Phys. Fluids 20 (12), 125101.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357376.CrossRefGoogle Scholar
Flores, O., Jiménez, J. & Del Álamo, J.C. 2007 Vorticity organization in the outer layer of turbulent channels with disturbed walls. J. Fluid Mech. 591, 145154.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73L76.CrossRefGoogle Scholar
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18 (5), 051703.CrossRefGoogle 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.CrossRefGoogle Scholar
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511538.CrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.CrossRefGoogle Scholar
Han, J., Hwang, J., Yoon, M., Ahn, J. & Sung, H.J. 2019 Azimuthal organization of large-scale motions in a turbulent minimal pipe flow. Phys. Fluids 31 (5), 055113.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S.C.C. & Smits, A.J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 094501.CrossRefGoogle ScholarPubMed
Hutchins, N., Chauhan, K., Marusic, I., Monty, J. & Klewicki, J. 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145 (2), 273306.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.CrossRefGoogle Scholar
Hutchins, N., Nickels, T.B., Marusic, I. & Chong, M.S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.CrossRefGoogle Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.CrossRefGoogle Scholar
Hwang, J., Lee, J.H. & Sung, H.J. 2020 Statistical behavior of self-similar structures in canonical wall turbulence. J. Fluid Mech. 905, A6.CrossRefGoogle Scholar
Hwang, J., Lee, J., Sung, H.J. & Zaki, T.A. 2016 Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128157.CrossRefGoogle Scholar
Hwang, J. & Sung, H.J. 2017 Influence of large-scale motions on the frictional drag in a turbulent boundary layer. J. Fluid Mech. 829, 751779.CrossRefGoogle Scholar
Hwang, J. & Sung, H.J. 2018 Wall-attached structures of velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 856, 958983.CrossRefGoogle Scholar
Hwang, J. & Sung, H.J. 2019 Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow. Phys. Fluids 31 (5), 055109.Google Scholar
Ibrahim, J.I., Gómez-de-Segura, G., Chung, D. & García-Mayoral, R. 2021 The smooth-wall-like behaviour of turbulence over drag-altering surfaces: a unifying virtual-origin framework. J. Fluid Mech. 915, A56.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215236.CrossRefGoogle Scholar
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 369 (1940), 13961411.CrossRefGoogle ScholarPubMed
Kim, K., Baek, S.J. & Sung, H.J. 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38 (2), 125138.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.CrossRefGoogle Scholar
Klewicki, J.C., Murray, J.A. & Falco, R.E. 1994 Vortical motion contributions to stress transport in turbulent boundary layers. Phys. Fluids 6 (1), 277286.CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741773.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200. J. Fluid Mech. 774, 395415.CrossRefGoogle Scholar
Lee, J.H. & Sung, H.J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101131.CrossRefGoogle Scholar
Lee, J.H. & Sung, H.J. 2013 Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations. Phys. Fluids 25 (4), 045103.CrossRefGoogle Scholar
Lozano-Durán, A. & Bae, H.J. 2019 Characteristic scales of Townsend's wall-attached eddies. J. Fluid Mech. 868, 698725.CrossRefGoogle ScholarPubMed
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100130.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432471.CrossRefGoogle Scholar
Maciel, Y., Gungor, A.G. & Simens, M. 2017 Structural differences between small and large momentum-defect turbulent boundary layers. Intl J. Heat Fluid Flow 67, 95110.CrossRefGoogle Scholar
Maciel, Y., Simens, M.P. & Gungor, A.G. 2017 Coherent structures in a non-equilibrium large-velocity-defect turbulent boundary layer. Flow Turbul. Combust. 98 (1), 120.CrossRefGoogle Scholar
Marusic, I., Baars, W.J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.CrossRefGoogle Scholar
Marusic, I. & Monty, J.P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 4974.CrossRefGoogle Scholar
Marusic, I., Monty, J.P., Hultmark, M. & Smits, A.J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16 (7), L55L58.CrossRefGoogle Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111133.CrossRefGoogle Scholar
Navier, C.L.M.H. 1823 Mémoire sur les lois du mouvement des fluids. Mém. Acad. R. Sci. Inst. France 6, 389440.Google Scholar
Nickels, T.B., Marusic, I., Hafez, S. & Chong, M.S. 2005 Evidence of the k 1−1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 074501.CrossRefGoogle Scholar
Osawa, K. & Jiménez, J. 2018 Intense structures of different momentum fluxes in turbulent channels. Phys. Rev. Fluids 3 (8), 084603.CrossRefGoogle Scholar
Perry, A.E. & Abell, C.J. 1977 Asymptotic similarity of turbulence structures in smooth-and rough-walled pipes. J. Fluid Mech. 79 (4), 785799.CrossRefGoogle Scholar
Perry, A.E. & Chong, M.S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.CrossRefGoogle Scholar
Perry, A.E., Henbest, S. & Chong, M.S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.CrossRefGoogle Scholar
Ryu, J., Byeon, H., Lee, S.J. & Sung, H.J. 2019 Flapping dynamics of a flexible plate with Navier slip. Phys. Fluids 31 (9), 091901.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Tomkins, C.D. & Adrian, R.J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.CrossRefGoogle Scholar
Wang, L.H., Xu, C.X., Sung, H.J. & Huang, W.X. 2021 Wall-attached structures over a traveling wavy boundary: turbulent velocity fluctuations. Phys. Rev. Fluids 6 (3), 034611.CrossRefGoogle Scholar
Yang, J., Hwang, J. & Sung, H.J. 2019 Influence of wall-attached structures on the boundary of quiescent core region in turbulent pipe flow. Phys. Rev. Fluids 4 (11), 114606.CrossRefGoogle Scholar
Yoon, M., Ahn, J., Hwang, J. & Sung, H.J. 2016 a Contribution of velocity-vorticity correlations to the frictional drag in wall-bounded turbulent flows. Phys. Fluids 28 (8), 081702.CrossRefGoogle Scholar
Yoon, M., Hwang, J., Lee, J., Sung, H.J. & Kim, J. 2016 b Large-scale motions in a turbulent channel flow with the slip boundary condition. Intl J. Heat Fluid Flow 61, 96107.CrossRefGoogle Scholar
Yoon, M., Hwang, J. & Sung, H.J. 2018 Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer. J. Fluid Mech. 848, 288311.CrossRefGoogle Scholar
Yoon, M., Hwang, J., Yang, J. & Sung, H.J. 2020 Wall-attached structures of streamwise velocity fluctuations in an adverse pressure gradient turbulent boundary layer. J. Fluid Mech. 885, A12.CrossRefGoogle Scholar