Flow, Turbulence and Combustion

, Volume 100, Issue 2, pp 391–416 | Cite as

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

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Abstract

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e 𝜃 = 1000 based on the momentum thickness or R e τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.

Keywords

Turbulent boundary layer control Streamwise vortices Velocity streaks 

Nomenclature

Latin symbols

Ao

Peak-to-peak oscillation amplitude at the actuator tip

\(A_{\omega _{x} } \)

Size of streamwise vortex

Dyz

Velocity gradient tensor

fo

Oscillation frequency

Hc

Height of vortex center

H12

= δ /𝜃, Shape factor, where δ and 𝜃 are displacement and momentum thicknesses, respectively

Lc

Transverse spacing of adjacent vortex centers

Nc

Number of vortex center

Re𝜃

= U 𝜃/ν, Reynolds number based on momentum thickness

Reτ

= u τ δ/ν, Reynolds number based on friction velocity

S

Spacing of adjacent streaks

U, U

Local mean and free-stream streamwise velocities, respectively

u

Streamwise fluctuating velocity

uτ

\(= \sqrt {\overline \tau _{w} /\rho } ,\) friction velocity

W

Streak width

Wp

Perturbed spanwise velocity

w

Spanwise fluctuating velocity

x

Streamwise direction

y

Wall-normal direction

z

Spanwise direction

Greek symbols

δ99

Boundary layer thickness defined by the location where U = 99% U

𝜃

Momentum thickness

Λci

= (ω x / |ω x |)λ c i , signed swirling strength

λr

Real eigenvalue

λci

Vortex strength as indicated by eigenvalue of the local velocity gradient tensor

λz

Wavelength

v

Wall-normal fluctuating velocity

ρ

Flow density

\(\overline \tau _{w} \)

Averaged wall shear stress

ϕi, i+1

(i = 1, 2, …, 15), phase shift between adjacent actuator

ωx

Streamwise vorticity

ωy

Wall-normal vorticity

Abbreviations

PIV

Particle image velocimetry

POD

Proper orthogonal decomposition

TBL

Turbulent boundary layer

TKE

Turbulent kinetic energy

Superscripts

+

Normalization by wall units

Ensemble average

Notes

Acknowledgements

YZ wishes to acknowledge support given to him from NSFC through grant 11632006, from RGC of HKSAR through grant PolyU 5329/11E. H.L.B. would like to acknowledge support given to him from NSFC through grant 11302062 and from State Key Laboratory of Aerodynamics through grant SKLA20130102.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

References

  1. 1.
    Kline, S.J., Reynolds, W.C., Schraub, F.A., Runstadler, P.W.: The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773 (1967)CrossRefGoogle Scholar
  2. 2.
    Robinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–39 (1991)CrossRefGoogle Scholar
  3. 3.
    Schoppa, W., Hussain, F.: Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108 (2002)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Jiménez, J.: Near-wall turbulence. Phys. Fluids 25, 101302 (2013)CrossRefGoogle Scholar
  5. 5.
    Panton, R. (ed.): Self-Sustaining Mechanisms of Wall Turbulence. Comp. Mech. Publ, Southampton, UK (1997)MATHGoogle Scholar
  6. 6.
    Wallace, J.M.: Highlights of from 50 years of turbulent boundary layer research. J. Turbul. 13(53), 1–70 (2013)Google Scholar
  7. 7.
    Kravchenko, A.G., Choi, H., Moin, P.: On the generation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5, 3307–9 (1993)CrossRefGoogle Scholar
  8. 8.
    Orlandi, P., Jiménez, J.: On the generation of turbulent wall friction. Phys. Fluids A 6, 634–41 (1994)CrossRefGoogle Scholar
  9. 9.
    Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)CrossRefMATHGoogle Scholar
  10. 10.
    Kim, J.: On the structure of wall-bounded turbulent flows. Phys. Fluids 26(8), 2088–97 (1983)CrossRefMATHGoogle Scholar
  11. 11.
    Kim, J.: Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. A 369, 1396–1411 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Jeong, J., Hussain, F., Schoppa, W., Kim, J.: Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214 (1997)CrossRefMATHGoogle Scholar
  13. 13.
    Lu, S.S., Willmarth, W.W.: Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481–511 (1973)CrossRefGoogle Scholar
  14. 14.
    Smith, C.R., Walker, J.D.A.: Turbulent Wall-Layer Vortices in Fluid Vortices. Springer, New York (1994)Google Scholar
  15. 15.
    Zhou, J., Adrian, R.J., Balachandar, S., Kendall, T.M.: Mechanisms of generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Hamilton, J.M., Kim, J., Waleffe, F.: Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348 (1995)CrossRefMATHGoogle Scholar
  17. 17.
    Gad-el-Hak, M.: Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press (2000)Google Scholar
  18. 18.
    Karniadakis, G.E., Choi, K.-S.: Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62 (2003)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Kim, J.: Control of turbulent boundary layers. Phys. Fluids A 15, 1093–1105 (2003)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Quadrio, M.: Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. A 369, 1428–1442 (2011)CrossRefGoogle Scholar
  21. 21.
    Bai, H.L., Zhou, Y., Zhang, W.G., Xu, S., Wang, Y., Antonia, R.A.: Active control of a turbulent boundary layer based on local surface perturbation. J. Fluid Mech. 750, 316–354 (2014)CrossRefGoogle Scholar
  22. 22.
    Berger, T.W., Kim, J., Lee, C., Lim, J.: Turbulent boundary layer control utilizing the Lorentz force. Phys. Fluids 12, 631–49 (2000)CrossRefMATHGoogle Scholar
  23. 23.
    Huang, L., Fan, B., Dong, G.: Turbulent drag reduction via a transverse wave travelling along streamwise direction induced by Lorentz force. Phys. Fluids 22, 015103 (2010)CrossRefMATHGoogle Scholar
  24. 24.
    Nakanishi, R., Mamori, H., Fukagata, K.: Relaminarization of turbulent channel flow using traveling wave-like wall deformation. Int. J. Heat Fluid Flow 35, 152–159 (2012)CrossRefGoogle Scholar
  25. 25.
    Tomiyama, N., Fukagata, K.: Direct numerical simulation of drag reduction in a turbulent channel flow using spanwise travelling wave-like wall deformation. Phys. Fluids 25, 105115 (2013)CrossRefGoogle Scholar
  26. 26.
    Koh, S.R., Meysonnat, P., Meinke, M., Schröder, W.: Drag reduction via spanwise transversal surface waves at high Reynolds numbers. Flow Turb. Combust. 95, 169–190 (2015)CrossRefGoogle Scholar
  27. 27.
    Koh, S.R., Meysonnat, P., Statnikov, V., Meinke, M., Schröder, W.: Dependence of turbulent wall-shear stress on the amplitude of spanwise transversal surface waves. Comp. Fluids 119, 261–275 (2015)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Meysonnat, P.S., Roggenkamp, D., Li, W., Roidl, B., Schröder, W.: Experimental and numerical investigation of transversal traveling surface waves for drag reduction. Euro. J. Mech. B/Fluids 55, 313–323 (2016)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Mamori, H., Fukagata, K.: Drag reduction effect by a wave-like wall-normal body force in a turbulent channel flow. Phys. Fluids 26, 115104 (2014)CrossRefGoogle Scholar
  30. 30.
    Kang, S., Choi, H.: Active wall motions for skin-friction drag reduction. Phys. Fluids 12(12), 3301–04 (2000)CrossRefMATHGoogle Scholar
  31. 31.
    Choi, K.-S., DeBisschop, J.-R., Clayton, B.R.: Turbulent boundary-layer control by means of spanwise-wall oscillation. AIAA J. 36(7), 1157–63 (1998)CrossRefGoogle Scholar
  32. 32.
    Dhanak, M.R., Si, C.: On reduction of turbulent wall friction through spanwise wall oscillations. J. Fluid Mech. 383, 175–195 (1999)CrossRefMATHGoogle Scholar
  33. 33.
    Iuso, G., Di Cicca, G.M., Onorato, M., Spazzini, P.G., Malvano, R.: Velocity streak structure modifications induced by flow manipulation. Phys. Fluids 15, 2602 (2003)CrossRefMATHGoogle Scholar
  34. 34.
    Du, Y., Karniadakis, G.E.: Suppressing wall turbulence by means of a transverse travelling wave. Science 288, 1230–34 (2000)CrossRefGoogle Scholar
  35. 35.
    Du, Y., Symeonidis, V., Karniadakis, G.E.: Drag reduction in wall-bounded turbulence via a transverse travelling wave. J. Fluid Mech. 457, 1–34 (2002)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Khoo, B.C., Chew, Y.T., Teo, C.J.: On near-wall hot-wire measurements. Exps. Fluids 29, 448–460 (2000)CrossRefGoogle Scholar
  37. 37.
    Huang, J.F., Zhou, Y., Zhou, T.M.: Three-dimensional wake structure measurement using a modified PIV technique. Exps. Fluids 40, 884–896 (2006)CrossRefGoogle Scholar
  38. 38.
    Sciacchitano, A., Wieneke, B.: PIV Uncertainty propagation. Meas. Sci. Technol. 27, 084006 (2016)CrossRefGoogle Scholar
  39. 39.
    Hu, J.C., Zhou, Y.: Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification. J. Fluid Mech. 607, 51–80 (2006)MATHGoogle Scholar
  40. 40.
    Sciacchitano, A., Neal, D.R., Smith, B.L., Warner, S.O., VIachos, P.P., Wieneke, B., Scarano, F.: Collaborative framework for PIV uncertainty quantification: comparative assessment of methods. Meas. Sci. Technol. 26, 074004 (2015)CrossRefGoogle Scholar
  41. 41.
    Chong, M., Perry, A. E., Cantwell, B.J.: A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765 (1990)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Gouder, K., Potter, M., Morrison, J.F.: Turbulent friction drag reduction using electroactive polymer and electromagnetically driven surfaces. Exp Fluids 54, 1441 (2013)CrossRefGoogle Scholar
  43. 43.
    Touber, E., Leschziner, A.: Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200 (2012)CrossRefMATHGoogle Scholar
  44. 44.
    Di Cicca, G.M., Iuso, G., Spazzini, P.G., Onorato, M.: Particle image velocimetry investigation of a turbulent boundary layer manipulated by spanwise wall oscillations. J. Fluid Mech. 467, 41–56 (2002)CrossRefMATHGoogle Scholar
  45. 45.
    Ricco, P.: Modification of near-wall turbulence due to spanwise wall oscillations. J. Turbul. 5, N24 (2004)CrossRefGoogle Scholar
  46. 46.
    Yang, L.: Turbulent Drag Reduction with Piezo-Ceramic Actuator Array. Master Degree Thesis, The Hong Kong Polytechnic University (2013)Google Scholar
  47. 47.
    Qiao, Z.X., Zhou, Y., Wu, Z.: Turbulent boundary layer under the control of different schemes. Proc. R. Soc. A 473, 20170038 (2017)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Ricco, P., Wu, S.: On the effects of lateral wall oscillations on a turbulent boundary layer. Exp. Therm. Fluid Sci. 29(1), 41–52 (2004)CrossRefGoogle Scholar
  49. 49.
    Lardeau, S., Leschziner, M.A.: The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion. Phys. Fluids 25, 075109 (2013)CrossRefGoogle Scholar
  50. 50.
    Choi, K.-S.: Near-wall structure of turbulent boundary layer with riblets. J. Fluid Mech. 208, 417–458 (1989)CrossRefGoogle Scholar
  51. 51.
    Antonia, R.A., Fulachier, L., Krishnamoorthy, L.V., Benabid, T., Anselmet, F.: Influence of wall suction on the organized motion in a turbulent boundary layer. J. Fluid Mech. 190, 217–240 (1988)CrossRefGoogle Scholar
  52. 52.
    Lumley, J.L.: Stochastic Tools in Turbulence. Academic Press, London (1970)MATHGoogle Scholar
  53. 53.
    Berkooz, G., Holmes, P., Lumley, J.L.: The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575 (1993)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Sirovich, L.: Turbulence and the dynamics of coherent structures, part I. Quart. Appl. Math. 45, 561–590 (1987)MathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    Fiedler, H.E., Gad-el-Hak, M., Pollard, A., Bonnet, J.-P.: Control of free turbulent shear flows. In: Flow Control: Fundamental and Practices, Lecture Notes. Phys. 53, pp 336–429. Springer, Berlin (1998)Google Scholar
  56. 56.
    Antonia, R.A., Zhu, Y., Sokolov, M.: Effect of concentrated wall suction on a turbulent boundary layer. Phys. Fluids 7, 2465–2474 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • H. L. Bai
    • 1
    • 2
    • 3
  • Y. Zhou
    • 1
  • W. G. Zhang
    • 2
  • R. A. Antonia
    • 4
  1. 1.Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate SchoolHarbin Institute of TechnologyShenzhenChina
  2. 2.State Key Laboratory of AerodynamicsMianyangChina
  3. 3.Department of Civil and Environmental EngineeringHong Kong University of Science and TechnologyKowloonChina
  4. 4.School of EngineeringUniversity of NewcastleCallaghanAustralia

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