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Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

  • Yitong Fan
  • Cheng Cheng
  • Weipeng LiEmail author
Article
  • 11 Downloads

Abstract

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73–L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650. Journal of Fluid Mechanics, 743, 202–248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics, 774, 395–415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

Key words

drag decomposition mean skin friction turbulent channel flow Reynolds number effect 

Chinese Library Classification

O357.5 

2010 Mathematics Subject Classification

76F40 

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Notes

Acknowledgements

The large-scale computations were supported by the Center for High-Performance Computing, Shanghai Jiao Tong University.

References

  1. [1]
    GARIÉPY, M., TRÉPANIER, J. Y., and MALOUIN, B. Generalization of the far-field drag decomposition method to unsteady flows. AIAA Journal, 51(6), 1309–1319 (2013)CrossRefGoogle Scholar
  2. [2]
    GAD-EL-HAK, M. Interactive control of turbulent boundary layers: a futuristic overview. AIAA Journal, 32(9), 1753–1765 (1994)CrossRefGoogle Scholar
  3. [3]
    DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Re θ= 13 650. Journal of Fluid Mechanics, 743, 202–248 (2014)CrossRefGoogle Scholar
  4. [4]
    FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73–L76 (2002)CrossRefzbMATHGoogle Scholar
  5. [5]
    GOMEZ, T., FLUTET, V., and SAGAUT, P. Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Physical Review E, 79(3), 035301 (2009)CrossRefGoogle Scholar
  6. [6]
    BANNIER, A., GARNIER, É, and SAGAUT, P. Riblet flow model based on an extended FIK identity. Flow, Turbulence and Combustion, 95, 351–376 (2015)CrossRefGoogle Scholar
  7. [7]
    PEET, Y. and SAGAUT, P. Theoretical prediction of turbulent skin friction on geometrically complex surfaces. Physics of Fluids, 21(10), 105105 (2009)CrossRefzbMATHGoogle Scholar
  8. [8]
    MEHDI, F. and WHITE, C. M. Integral form of the skin friction coefficient suitable for experimental data. Experiments in Fluids, 50(1), 43–51 (2011)CrossRefGoogle Scholar
  9. [9]
    MEHDI, F., JOHANSSON, T. G., WHITE, C. M., and NAUGHTON, J. W. On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Experiments in Fluids, 55, 1656 (2014)CrossRefGoogle Scholar
  10. [10]
    LI, F. C., KAWAGUCHI, Y., SEGAWA, T., and HISHIDA, K. Reynolds-number dependence of turbulence structures in a drag-reducing surfactant solution channel flow investigated by particle image velocimetry. Physics of Fluids, 17(7), 075104 (2005)CrossRefzbMATHGoogle Scholar
  11. [11]
    DE GIOVANETTI, M., HWANG, Y., and CHOI, H. Skin-friction generation by attached eddies in turbulent channel flow. Journal of Fluid Mechanics, 808, 511–538 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    YOON, M., AHN, J., HWANG, J., and SUNG, H. J. Contribution of velocity-vorticity correlations to the frictional drag in wall-bounded turbulent flows. Physics of Fluids, 28(8), 081702 (2016)CrossRefGoogle Scholar
  13. [13]
    RENARD, N. and DECK, S. A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. Journal of Fluid Mechanics, 790, 339–367 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    KIM, J. Control of turbulent boundary layers. Physics of Fluids, 15(5), 1093–1105 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    WHITE, C. M. and MUNGAL, M. G. Mechanics and prediction of turbulent drag reduction with polymer additives. Annual Review Fluid Mechanics, 40, 235–256 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    TOUBER, E. and LESCHZINER, M. A. Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. Journal of Fluid Mechanics, 693, 150–200 (2012)CrossRefzbMATHGoogle Scholar
  17. [17]
    KAMETANI, Y. and FUKAGATA, K. Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. Journal of Fluid Mechanics, 681, 154–172 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    BHUSHAN, B. Shark-skin surface for fluid-drag reduction in turbulent flow. Biomimetics, Springer, Cham, 227–265 (2016)CrossRefGoogle Scholar
  19. [19]
    CHOI, H., MOIN, P., and KIM, J. Direct numerical simulation of turbulent flow over riblets. Journal of Fluid Mechanics, 255, 503–539 (1993)CrossRefzbMATHGoogle Scholar
  20. [20]
    GATTI, D., QUADRIO, M., and FROHNAPFEL, B. Reynolds number effect on turbulent drag reduction. 5th European Turbulence Conference, University of Delft, Delft (2015)Google Scholar
  21. [21]
    ROBINSON, S. K. The Kinematics of Turbulent Boundary Layer Structure, National Aeronautics and Space Administration, Washington, D.C. (1991)Google Scholar
  22. [22]
    ABBASSI, M. R., BAARS,W. J., HUTCHINS, N., and MARUSIC, I. Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures. International Journal of Heat and Fluid Flow, 67, 30–41 (2017)CrossRefGoogle Scholar
  23. [23]
    HWANG, Y. Near-wall turbulent fluctuations in the absence of wide outer motions. Journal of Fluid Mechanics, 723, 264–288 (2013)CrossRefzbMATHGoogle Scholar
  24. [24]
    LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Re t≈ 5 200. Journal of Fluid Mechanics, 774, 395–415 (2015)CrossRefGoogle Scholar
  25. [25]
    KIM, J., MOIN, P., and MOSER, R. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal of Fluid Mechanics, 177, 133–166 (1987)CrossRefzbMATHGoogle Scholar
  26. [26]
    LEE, M., MALAYA, N., and MOSER, R. D. Petascale direct numerical simulation of turbulent channel flow on up to 786K cores. Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Association for Computing Machinery, New York (2013)Google Scholar
  27. [27]
    LEE, M., ULERICH, R., MALAYA, N., and MOSER, R. D. Experiences from leadership computing in simulations of turbulent fluid flows. Computing in Science & Engineering, 16(5), 24–31 (2014)CrossRefGoogle Scholar
  28. [28]
    OLIVER, T. A., MALAYA, N., ULERICH, R., and MOSER, R. D. Estimating uncertainties in statistics computed from direct numerical simulation. Physics of Fluids, 26(3), 035101 (2014)CrossRefGoogle Scholar
  29. [29]
    DEAN, R. B. Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Journal of Fluids Engineering, 100(2), 215–223 (1978)CrossRefGoogle Scholar
  30. [30]
    ABE, H. and ANTONIA, R. A. Relationship between the energy dissipation function and the skin friction law in a turbulent channel flow. Journal of Fluid Mechanics, 798, 140–164 (2016)MathSciNetCrossRefGoogle Scholar
  31. [31]
    LAADHARI, F. Reynolds number effect on the dissipation function in wall-bounded flows. Physics of Fluids, 19(3), 038101 (2007)CrossRefzbMATHGoogle Scholar
  32. [32]
    HINZE, J. O. Turbulence, McGraw-Hill, New York (1975)Google Scholar
  33. [33]
    KIM, K. C. and ADRIAN, R. J. Very large-scale motion in the outer layer. Physics of Fluids, 11(2), 417–422 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    LIU, Z., ADRIAN, R. J., and HANRATTY, T. J. Large-scale modes of turbulent channel flow: transport and structure. Journal of Fluid Mechanics, 448, 53–80 (2001)CrossRefzbMATHGoogle Scholar
  35. [35]
    HWANG, J. and SUNG, H. J. Influence of large-scale motions on the frictional drag in a turbulent boundary layer. Journal of Fluid Mechanics, 829, 751–779 (2017)MathSciNetCrossRefGoogle Scholar
  36. [36]
    BALAKUMAR, B. J. and ADRIAN, R. J. Large- and very-large-scale motions in channel and boundary-layer flows. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 365(1852), 665–681 (2007)CrossRefzbMATHGoogle Scholar
  37. [37]
    IWAMOTO, K., FUKAGATA, K., KASAGI, N., and SUZUKI, Y. Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers. Physics of Fluids, 17(1), 011702 (2005)CrossRefzbMATHGoogle Scholar
  38. [38]
    DENG, B. Q. Research on Mechanism of Drag-Reduction Control Based on Coherent Structures in Wall-Turbulence (in Chinese), Ph. D. dissertation, Tsinghua University (2014)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Engineering Research Center of Gas Turbine and Civil Aero EngineShanghaiChina

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