Advertisement

Spectral Assessment of the Turbulent Convection Velocity in a Spatially Developing Flat Plate Turbulent Boundary Layer at Reynolds Number \(Re_\theta = 13\,000\)

  • Nicolas RenardEmail author
  • Sébastien Deck
  • Pierre Sagaut
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 23)

Abstract

A method inspired by del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, [7] is derived to assess the wavelength-dependent convection velocity in a zero pressure gradient spatially developing flat plate turbulent boundary layer at \(Re_\theta = 13\,000\) for all wavelengths and all wall distances, using only estimates of the time power spectral density of the streamwise velocity and of its local spatial derivative. The resulting global convection velocity has a least-squares interpretation and is easily related to the wavelength-dependent convection velocity. The method intrinsically provides an estimation of the validity of Taylor’s hypothesis by a correlation coefficient identical to the one from del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, [7]. The results reveal some similarities between the convection of the superstructures, the hairpin packets, and the near-wall structures. The convection velocity of the superstructures is isolated by restricting the global convection velocity to the largest wavelengths. The spatial spectrum is estimated from the temporal spectrum using the frequency-dependent convection velocity. The results are consistent with a classical correlation-based evaluation.

Keywords

High Reynolds Number Streamwise Velocity Convection Velocity Coherent Motion Dilatation Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was performed using HPC resources from GENCI-CINES (Project ZDESWALLTURB, Grant 2012-[c2012026817]). The authors wish to thank Pierre-Élie Weiss and Romain Laraufie for fruitful discussions. All the people involved in the evolution of the FLU3M code are warmly acknowledged. The thesis of Nicolas Renard is partly funded by the French defense procurement agency DGA.

References

  1. 1.
    C. Atkinson, N. Buchmann, O. Amili, J. Soria, High-resolution large field-of-view experimental investigation of turbulent convection velocities in a turbulent boundary layer. in International Symposium on Turbulence and Shear Flow Phenomena (TSFP-8) (2013)Google Scholar
  2. 2.
    D. Chung, B.J. McKeon, Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341–364 (2010)CrossRefzbMATHGoogle Scholar
  3. 3.
    S. Davoust, L. Jacquin, Taylor’s hypothesis convection velocities from mass conservation equation. Phys. Fluids 23, 051701 (2011)CrossRefGoogle Scholar
  4. 4.
    S. Deck, Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation. Theor. Comput. Fluid Dyn. 26, 523–550 (2012)CrossRefGoogle Scholar
  5. 5.
    S. Deck, N. Renard, R. Laraufie, P. Sagaut, Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range \(3\,150 \le Re_\theta \le 14\,000\). Phys. Fluids 26, 025116 (2014)CrossRefGoogle Scholar
  6. 6.
    S. Deck, N. Renard, R. Laraufie, P.E. Weiss, Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to \(Re_\theta \) =13650. J. Fluid Mech. 743, 202–248 (2014). doi: 10.1017/jfm.2013.629 CrossRefGoogle Scholar
  7. 7.
    J.C. del Álamo, J. Jiménez, Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D.J.C. Dennis, T.B. Nickels, On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    M.J. Fisher, P.A.L. Davies, Correlation measurements in a non-frozen pattern of turbulence. J. Fluid Mech. 18, 97–116 (1963)CrossRefGoogle Scholar
  10. 10.
    N. Hutchins, I. Marusic, Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28 (2007)CrossRefzbMATHGoogle Scholar
  11. 11.
    J. Jiménez, Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45 (2012)CrossRefGoogle Scholar
  12. 12.
    J. Jiménez, S. Hoyas, M.P. Simens, Y. Mizuno, Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360 (2010)CrossRefzbMATHGoogle Scholar
  13. 13.
    R. de Kat, L. Gan, J.R. Dawson, B. Ganapathisubramani, Limitations of estimating turbulent convection velocities from PIV, in 16th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal (2012)Google Scholar
  14. 14.
    P.A. Krogstad, J.H. Kaspersen, S. Rimestad, Convection velocities in a turbulent boundary layer. Phys. Fluids 10–4, 949–957 (1998)CrossRefGoogle Scholar
  15. 15.
    J.H. Lee, H.J. Sung, Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80–120 (2011)CrossRefzbMATHGoogle Scholar
  16. 16.
    J. LeHew, M. Guala, B.J. McKeon, A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer. Exp. Fluids 51, 997–1012 (2011)CrossRefGoogle Scholar
  17. 17.
    C.C. Lin, On Taylor’s hypothesis and the acceleration terms in the Navier-Stokes equations. Q. Appl. Math. X(4), 154–165 (1953)Google Scholar
  18. 18.
    I. Marusic, R. Mathis, N. Hutchins, High Reynolds number effects in wall turbulence. Int. J. Heat Fluid Flow 31, 418–428 (2010)CrossRefGoogle Scholar
  19. 19.
    I. Mary, P. Sagaut, Large eddy simulation of flow around an airfoil near stall. AIAA J. 40, 1139–1145 (2002)CrossRefGoogle Scholar
  20. 20.
    R. Mathis, N. Hutchins, I. Marusic, Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    P. Moin, Revisiting Taylor’s hypothesis. J. Fluid Mech. Focus Fluids 640, 1–4 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    A.J. Smits, B.J. McKeon, I. Marusic, High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375 (2011)CrossRefGoogle Scholar
  23. 23.
    J.A.B. Wills, On convection velocities in turbulent shear flows. J. Fluid Mech. 20(3), 417–432 (1964)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nicolas Renard
    • 1
    Email author
  • Sébastien Deck
    • 1
  • Pierre Sagaut
    • 2
  1. 1.Onera, The French Aerospace LabMeudonFrance
  2. 2.Institut Jean le Rond D’AlembertUniversité Pierre Et Marie CurieParisFrance

Personalised recommendations