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TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

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  • Fluid Mechanics
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Abstract

The present experimental work is devoted to investigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Re θ = 2 460 is measured by tomographic time-resolved particle image velocimetry (Tomo-TRPIV). The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity represents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wall-bounded flow, the elliptic model remains valid.

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References

  1. Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR. 30, 299–303 (1941)

    Google Scholar 

  2. Saric, W.S., Reed, H.L. Kerschen, E.J.: Boundary-layer receptivity to free-stream disturbance. Ann. Rev. Fluid Mech. 34, 291 (2002)

    Article  MathSciNet  Google Scholar 

  3. Lumley, J., Blossy, P.: Control of turbulence. Ann. Rev. Fluid Mech. 30, 311 (1998)

    Article  Google Scholar 

  4. Taylor, G.I.: The spectrum of turbulence. Proc. R. Soc. Lond. 164, 476–490 (1938)

    Article  Google Scholar 

  5. Lin, C.C.: On Taylor’s hypothesis and the acceleration terms in Navier-Stokes equation. Q. Appl. Math. 10, 295 (1953)

    MATH  Google Scholar 

  6. He, G.W., Zhang, J.B.: Elliptic model for space-time correlations in turbulent shear flows. Phys. Rev. E. 73, 055303 (2006)

    Article  Google Scholar 

  7. Zhao, X., He, G.W.: Space-time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E. 79, 046316 (2009)

    Article  Google Scholar 

  8. Kraichnan, R.H.: Kolmogorov’s hypotheses and Eulerian turbulence theory. Phys. Fluids 7, 1723 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tennekes, H.: Eulerian and Lagrangian time micro-scales in isotropic turbulence. J. Fluid. Mech. 67, 561–567 (1975)

    Article  MATH  Google Scholar 

  10. Zhou, Q., Li, C.M., Lu, Z.M., et al.: Experimental investigation of longitudinal space-time correlations of the velocity field in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 683, 94–111 (2011)

    Article  MATH  Google Scholar 

  11. Elsinga, G.E., Wieneke, F., van Oudheusden, B.W.: Tomographic particle image velocimetry. Exp. Fluids. 41, 933–947 (2006)

    Article  Google Scholar 

  12. Wieneke, B.: Volume self-calibration for 3D particle image velocimetry. Exp. Fluids 45, 549–556 (2008)

    Article  Google Scholar 

  13. Schröder, A., Geisler, R., Staack, K., ét al.: Eulerian and Lagrangian views of a turbulent boundary layer flow using timeresolved tomographic PIV. Exp. Fluids 50, 1071–1091 (2010)

    Article  Google Scholar 

  14. Adrian, R.J., Meinhart, C.D., Tomkins, C.D.: Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Christensen, K.T., Adrian, R.J.: Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid. Mech. 431, 433–443 (2001)

    Article  MATH  Google Scholar 

  16. Kim J., Hussain F.: Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids 5, 695–705 (1992)

    Article  Google Scholar 

  17. Ganapathisubramani, B., Clemens, N.T., Dolling, D.S.: Largescale motions in a supersonic boundary layer. J. Fluid Mech. 556, 271–282 (2006)

    Article  MATH  Google Scholar 

  18. Ganapathisubramani, B.: Statistical properties of streamwise velocity in a supersonic turbulent boundary layer. Phys. Fluids 19, 098108 (2007)

    Article  Google Scholar 

  19. Zhou, J., Adrian, R.J., Balachandar, S., et al.: Mechanism for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech. 387, 353–396 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  20. He, X.Z., He, G.W., Tong, P.E.: Small-scale turbulent fluctuations beyond Taylor’s frozen-flow hypothesis. Phys. Rev. E. 81, 065303 (2010)

    Article  Google Scholar 

  21. Guo, L., Li D., Zhang, X., He, G.W.: LES prediction of spacetime correlations in turbulent shear flows. Acta Mechanica Sinica 28, 993–998 (2012)

    Article  MathSciNet  Google Scholar 

  22. Wills, J.A.B.: On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417–432 (1964)

    Article  MATH  Google Scholar 

  23. Hussain, A.K.M.F., Clark, A.R.: Measurements of wavenumber-celerity spectrum in plane and axisymmetric jets. AIAA J. 19, 51–55 (1981)

    Article  Google Scholar 

  24. Goldschmidt, V.W., Young, M.F., Ott, E.S.: Turbulent convective velocities(broadband and wavenumber dependent) in a plane jet. J. Fluid Mech. 105, 327–345 (1981)

    Article  Google Scholar 

  25. Krogstad, P., Kaspersen, J.H., Rimestad, S.: Convection velocities in a turbulent boundary layer. Phys. Fluids. 10, 949–957 (1997)

    Article  Google Scholar 

  26. Del Alamo, J.C., Jiménez, J.: Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. Tomkins, C.D., Adrian, R.J.: Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74 (2003)

    Article  MATH  Google Scholar 

  28. Dennis, D.J.C., Nickels, T.B.: On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  29. Rodinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mec. 23, 601–639 (1991)

    Article  Google Scholar 

  30. Hussain, F.: Coherent structures-Reality and myth. Phys. Fluids 26, 2816–2850 (1983)

    Article  MATH  Google Scholar 

  31. Schoppa, W., Hussain, F.: Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Panton, R.L.: Overview of the self-sustaining mechanisms of wall turbulence. Progress in Aerospace Sciences 37, 341–383 (2001)

    Article  Google Scholar 

  33. Brooke, J.W., Hanratty, T.J.: Origin of turbulence producing eddies in a channel flow. Phys. Fluids A 5, 1011–1022 (1993)

    Article  MATH  Google Scholar 

  34. Buckles, J., Hanratty, T.J., Adrian, R.J.: Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech. 140, 27–44 (1984)

    Article  Google Scholar 

  35. Hudson, J.D., Dykhno, L., Hanratty, T.J.: Turbulence production in flow over a wavy wall. Exp. Fluids. 20, 257–265 (1996)

    Article  Google Scholar 

  36. Kruse, N., Kuhn, S., von Rohr, P.R.: Wavy wall effects on turbulence production and large-scale modes. Journal of Turbulence 7, 1–24 (2006)

    Article  MathSciNet  Google Scholar 

  37. Fan, X., Jiang, N.: Skin friction measurement in turbulent boundary layer by mean velocity profile method. Mechanics in Engineering. 27, 28–30 (2005)

    Google Scholar 

  38. Zilker, D.P., Cook, G.W., Hanratty, T.J.: Influence of the amplitude of a solid wavy wall on a turbulent flow Part 1. Nonseparated flows. J. Fluid Mech. 82, 29–51 (1977)

    Article  Google Scholar 

  39. Zilker, D.P., Hanratty, T.J.: Influence of the amplitude of a solid wavy wall on a turbulent flow Part 2. Separated flows. J. Fluid Mech. 90, 257–271 (1979)

    Article  Google Scholar 

  40. Kuzan, J.D., Hanratty, T.J., Adrian, R.J.: Turbulent flows with incipient separation over solid waves. Exp. Fluids 7, 88–98 (1989)

    Article  Google Scholar 

  41. Cherukat, P., Na, Y., Hanratty, T.J., et al.: Direct numerical simulation of a fully developed turbulent flow over a wavy wall. Theoretical and Computational Fluid Dynamics 11, 109–134 (1998)

    Article  MATH  Google Scholar 

  42. De Angelis, V., Lombardi, P., Banerjee, S.: Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 2429–2442 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, 300072, Tianjin, China

    Wei Wang, Xin-Lei Guan & Nan Jiang

  2. Tianjin Key Laboratory of Modern Engineering Mechanics, 300072, Tianjin, China

    Nan Jiang

  3. The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, 100190, Beijing, China

    Nan Jiang

Authors
  1. Wei Wang
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  2. Xin-Lei Guan
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  3. Nan Jiang
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Corresponding author

Correspondence to Nan Jiang.

Additional information

The project was supported by the National Natural Science Foundation of China (11332006 and 11272233), the National Key Basic Research Program (2012CB720101), Tianjin University Research and Innovation Foundation and the opening subjects of The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences.

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Wang, W., Guan, XL. & Jiang, N. TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls. Acta Mech Sin 30, 468–479 (2014). https://doi.org/10.1007/s10409-014-0060-7

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  • DOI: https://doi.org/10.1007/s10409-014-0060-7

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