Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T23:10:32.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study on low-speed streaks in a turbulent boundary layer at low Reynolds number

Published online by Cambridge University Press:  18 September 2020

X. Y. Jiang Open the ORCID record for X. Y. Jiang [Opens in a new window] ,
C. B. Lee Open the ORCID record for C. B. Lee [Opens in a new window] ,
C. R. Smith ,
J. W. Chen  and
P. F. Linden
X. Y. Jiang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing100871, PR China
C. B. Lee*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing100871, PR China
C. R. Smith
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA18015, USA
J. W. Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing100871, PR China
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
*
†Email address for correspondence: cblee@mech.pku.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A study of low-speed streaks (LSSs) embedded in the near-wall region of a turbulent boundary layer is performed using selective visualization and analysis of time-resolved tomographic particle image velocimetry (tomo-PIV). First, a three-dimensional velocity field database is acquired using time-resolved tomo-PIV for an early turbulent boundary layer. Second, detailed time-line flow patterns are obtained from the low-order reconstructed database using ‘tomographic visualizations’ by Lagrangian tracking. These time-line patterns compare remarkably well with previously observed patterns using hydrogen bubble flow visualization, and allow local identification of LSSs within the database. Third, the flow behaviour in proximity to selected LSSs is examined at varying wall distances ($10 < y^+ < 100$) and assessed using time-line and material surface evolution, to reveal the flow structure and evolution of a streak, and the flow structure evolving from streak development. It is observed that three-dimensional wave behaviour of the detected LSSs appears to develop into associated near-wall vortex flow structures, in a process somewhat similar to transitional boundary layer behaviour. Fourth, the presence of Lagrangian coherent structures is assessed in proximity to the LSSs using a Lagrangian-averaged vorticity deviation process. It is observed that quasi-streamwise vortices, adjacent to the sides of the streak-associated three-dimensional wave, precipitate an interaction with the streak. Finally, a hypothesis based on the behaviour of soliton-like coherent structures is made which explains the process of LSS formation, bursting behaviour and the generation of hairpin vortices. Comparison with other models is also discussed.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A6
Check for updates
Copyright
© The Author(s), 2020. 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

REFERENCES

Acarlar, M. S. & Smith, C. R. 1987 a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.CrossRefGoogle Scholar
Acarlar, M. S. & Smith, C. R. 1987 b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
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, 1–54.CrossRefGoogle Scholar
Asai, M., Konishi, Y., Oizumi, Y. & Nishioka, M. 2007 Growth and breakdown of low-speed streaks leading to wall turbulence. J. Fluid Mech. 586, 371–396.CrossRefGoogle Scholar
Atkinson, C., Buchmann, N. A., Amili, O. & Soria, J. 2014 On the appropriate filtering of PIV measurements of turbulent shear flows. Exp. Fluids 55 (1), 1654.CrossRefGoogle Scholar
Bernard, P. S. 2013 Vortex dynamics in transitional and turbulent boundary layers. AIAA J. 51 (8), 1828–1842.CrossRefGoogle Scholar
Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Meyer, D. G. W., Rist, U., Lian, Q. X. & Lee, C. B. 2002 Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theor. Comput. Fluid Dyn. 15 (5), 317–337.CrossRefGoogle Scholar
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Chen, W. 2013 Numerical simulation of boundary layer transition by combined compact difference method. PhD thesis, Nanyang Technological University, Singapore.Google Scholar
Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544, 99–131.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids 2 (5), 765–777.CrossRefGoogle Scholar
Deng, S., Pan, C., Wang, J. J. & He, G. 2018 On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number. J. Fluid Mech. 844, 635–668.CrossRefGoogle Scholar
Dennis, D. J. C. & 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, 180–217.CrossRefGoogle Scholar
Elsinga, G. E., Kuik, D. J., van Oudheusden, B. W. & Scarano, F. 2007 Investigation of the three-dimensional coherent structures in a turbulent boundary layer with tomographic-PIV. AIAA Paper 2007–1305.CrossRefGoogle Scholar
Gao, Q., Ortiz-Dueñas, C. & Longmire, E. 2013 Evolution of coherent structures in turbulent boundary layers based on moving tomographic PIV. Exp. Fluids 54 (12), 1625.CrossRefGoogle Scholar
Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 110–120.CrossRefGoogle Scholar
Hack, M. J. & Moin, P. 2018 Coherent instability in wall-bounded shear. J. Fluid Mech. 844, 917–955.CrossRefGoogle Scholar
Haidari, A. H. & Smith, C. R. 1994 The generation and regeneration of single hairpin vortices. J. Fluid Mech. 277, 135–162.CrossRefGoogle Scholar
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 1–26.CrossRefGoogle Scholar
Haller, G. 2016 Dynamic rotation and stretch tensors from a dynamic polar decomposition. J. Mech. Phys. Solids 86, 70–93.CrossRefGoogle Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173.CrossRefGoogle Scholar
Hama, F. R. 1962 Streaklines in a perturbed shear flow. Phys. Fluids 5 (6), 644–650.CrossRefGoogle Scholar
Hama, F. R. & Nutant, J. 1963 Detailed flow-field observations in the transition process in a thick boundary layer. In Proceedings of the Heat Transfer and Fluid Mech. Inst., pp. 77–93. Stanford University Press.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research Report.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiang, X. Y., Lee, C. B., Chen, X., Smith, C. R. & Linden, P. F. 2020 Structure evolution at early stage of boundary-layer transition: simulation and experiment. J. Fluid Mech. 890, A11.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411–482.CrossRefGoogle Scholar
Kim, H., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–60.CrossRefGoogle Scholar
Kim, J. & Lim, J. 2000 A linear process in wall-bounded turbulent shear flows. Phys. Fluids 12 (8), 1885–1888.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339–363.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), 741–773.CrossRefGoogle Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243–251.CrossRefGoogle Scholar
Landahl, M. T. 1990 On sublayer streaks. J. Fluid Mech. 212, 593–614.CrossRefGoogle Scholar
Laurien, E. & Kleiser, L. 1989 Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech. 199, 403–440.CrossRefGoogle Scholar
Lee, C. B. 1998 New features of CS solitons and the formation of vortices. Phys. Lett. A 247 (6), 397–402.CrossRefGoogle Scholar
Lee, C. B. 2000 Possible universal transitional scenario in a flat plate boundary layer: measurement and visualization. Phys. Rev. E 62 (3), 3659–3670.CrossRefGoogle Scholar
Lee, C. B., Hong, Z. X., Kachanov, Y. S., Borodulin, V. I. & Gaponenko, V. V. 2000 A study in transitional flat plate boundary layers: measurement and visualization. Exp. Fluids 28 (3), 243–251.CrossRefGoogle Scholar
Lee, C. B & Li, R. Q. 2007 Dominant structure for turbulent production in a transitional boundary layer. J. Turbul. 8 (55), 1–34.CrossRefGoogle Scholar
Lee, C. B. & Wu, J. Z. 2008 Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802.CrossRefGoogle Scholar
Liu, C. Q., Wang, Y. Q., Yang, Y. & Duan, Z. W. 2016 New omega vortex identification method. Sci. China-Phys. Mech. Astron. 59 (8), 684711.CrossRefGoogle Scholar
Lu, L. J. & Smith, C. R. 1991 Use of flow visualization data to examine spatial-temporal velocity and burst-type characteristics in a turbulent boundary layer. J. Fluid Mech. 232, 303–340.CrossRefGoogle Scholar
Lynch, K. P. & Scarano, F. 2015 An efficient and accurate approach to MTE-mart for time-resolved tomographic PIV. Exp. Fluids 56 (3), 66.CrossRefGoogle Scholar
Mans, J., de Lange, H. C. & van Steenhoven, A. A. 2007 Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence. Phys. Fluids 19 (8), 088101.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.CrossRefGoogle Scholar
Matsuura, K. 2016 Direct numerical simulation of a straight vortex tube in a laminar boundary-layer flow. Intl J. Comput. Meth. Exp. Meas. 4 (4), 474–483.Google Scholar
Matsuura, K., Matsui, K. & Tani, N. 2018 Effects of free-stream turbulence on the global pressure fluctuation of compressible transitional flows in a low-pressure turbine cascade. Intl J. Numer. Meth. Heat Fluid Flow 28, 1187–1202.Google Scholar
Moin, P. & Moser, R. D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471–509.CrossRefGoogle Scholar
Musker, A. J. 1979 Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17 (6), 655–657.CrossRefGoogle Scholar
Naka, Y., Stanislas, M., Foucaut, J.-M., Coudert, S., Laval, J.-P. & Obi, S. 2015 Space-time pressure-velocity correlations in a turbulent boundary layer. J. Fluid Mech. 771, 624–675.CrossRefGoogle Scholar
Nishioka, M. & Asai, M. 1984 Evolution of Tollmien–Schlichting waves into wall turbulence. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 87–92. North-Holland.Google Scholar
Nishioka, M., Asai, M. & Iida, S. 1981 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Meyer), pp. 113–126. Academic Press.CrossRefGoogle Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802–811.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Sabatino, D. R., Praisner, T. J., Seal, C. V. & Smith, C. R. 2012 Hydrogen bubble visualization. In Flow Visualization: Techniques and Examples, 2nd edn (ed. A. J. Smith & T. T. Lim), pp. 27–45. Imperial College Press.CrossRefGoogle Scholar
Sabatino, D. R. & Rossmann, T. 2016 Tomographic piv measurements of a regenerating hairpin vortex. Exp. Fluids 57 (1), 1–13.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
Scarano, F 2013 Tomographic piv: principles and practice. Meas. Sci. Technol. 24 (1), 012001.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F. & Dierksheide, U. 2008 Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 44 (2), 305–316.CrossRefGoogle Scholar
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18 (4), 047105.CrossRefGoogle Scholar
Shalev-Shwartz, S. & Ben-David, S. 2014 Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press.CrossRefGoogle Scholar
Smith, C. R. 1984 A synthesized model of the near-wall behavior in turbulent boundary layers. In Proceedings of the 8th Symposium of Turbulence (ed. G. K. Pattersonand & J. L. Zakin), pp. 1–27. University of Missouri-Rolla.Google Scholar
Smith, C. R. 1998 Vortex development and interactions in turbulent boundary layers: implications for surface drag reduction. In Proceedings of the International Symposium on Seawater Drag Reduction, pp. 39–45. Office of Naval Research.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336 (1641), 131–175.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to $Re_\theta = 1410$. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Spalding, D. B. 1961 A single formula for the ‘law of the wall’. J. Appl. Mech. 28 (3), 455–458.CrossRefGoogle Scholar
Stanislas, M. 2017 Near wall turbulence: an experimental view. Phys. Rev. Fluids 2, 100506.CrossRefGoogle Scholar
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Tian, S. L., Gao, Y. S., Dong, X. R. & Liu, C. Q. 2018 Definitions of vortex vector and vortex. J. Fluid Mech. 849, 312–339.CrossRefGoogle Scholar
Titchener, N., Colliss, S. & Babinsky, H. 2015 On the calculation of boundary-layer parameters from discrete data. Exp. Fluids 56 (8), 159.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Wieneke, B. 2008 Volume self-calibration for 3d particle image velocimetry. Exp. Fluids 45 (4), 549–556.CrossRefGoogle Scholar
Wortmann, F. X. 1981 Boundary-layer waves and transition. In Advances in Fluid Mechanics (ed. E. Krause), pp. 268–279. Springer.CrossRefGoogle Scholar
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2015 Vortical structures in transitional and turbulent shear flows. In Vortical Flows, pp. 361–404. Springer.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22 (8), 085105.CrossRefGoogle Scholar
Wu, X., Moin, P., Wallace, J. M., Skarda, J., Lozano-Durán, A. & Hickey, J.-P. 2017 Transitional–turbulent spots and turbulent–turbulent spots in boundary layers. Proc. Natl Acad. Sci. USA 114 (27), E5292–E5299.CrossRefGoogle ScholarPubMed
Wu, Y. 2014 A study of energetic large-scale structures in turbulent boundary layer. Phys. Fluids 26 (4), 045113.CrossRefGoogle Scholar
Zhao, Y., Yang, Y. & Chen, S. 2016 Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech. 793, 840–876.CrossRefGoogle Scholar
Zhao, Y. M., Xiong, S. Y., Yang, Y. & Chen, S. Y. 2018 Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Phys. Rev. Fluids 3 (7), 074701.CrossRefGoogle Scholar