Effects of dimensional wall temperature on velocity-temperature correlations in supersonic turbulent channel flow of thermally perfect gas

  • XiaoPing Chen
  • XinLiang LiEmail author
  • ZuChao Zhu


Direct numerical simulations of temporally evolving supersonic turbulent channel flows of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 for various values of the dimensional wall temperature to study the influence of the latter on the velocity-temperature correlations. The results show that in a fully developed turbulent channel flow, as the dimensional wall temperature increases, there is little change in the mean velocity, but the mean temperature decreases. The mean temperature is found to be a quadratic function of the mean velocity, the curvature of which increases with increasing dimensional wall temperature. The concept of “recovery enthalpy” provides a connection between the mean velocity and the mean temperature, and is independent of dimensional wall temperature. The right tails of probability density function of the streamwise velocity fluctuation grows with increasing dimensional wall temperature. The dimensional wall temperature does not have a significant influence on the Reynolds analogy factor or strong Reynolds analogy (SRA). The modifications of SRA by Huang et al. and Zhang et al. provide reasonably good results, which are better than those of the modifications by Cebeci and Smith and by Rubesin.


direct numerical simulation velocity-temperature correlation supersonic flow channel flow thermally perfect gas strong Reynolds analogy 


  1. 1.
    L. Fulachier, F. Anselmet, R. Borghi, and P. Paranthoen, J. Fluid Mech. 203, 577 (1989).ADSCrossRefGoogle Scholar
  2. 2.
    C. Brun, M. Petrovan Boiarciuc, M. Haberkorn, and P. Comte, Theor. Comput. Fluid Dyn. 22, 189 (2008).CrossRefGoogle Scholar
  3. 3.
    P. Bradshaw, Annu. Rev. Fluid Mech. 9, 33 (1977).ADSCrossRefGoogle Scholar
  4. 4.
    S. K. Lele, Annu. Rev. Fluid Mech. 26, 211 (1994).ADSCrossRefGoogle Scholar
  5. 5.
    H. Schlichting, Boundary-layer theory 3rd (McGraw-Hill, New York, 1968).Google Scholar
  6. 6.
    E. F. Spina, A. J. Smits, and S. K. Robinson, Annu. Rev. Fluid Mech. 26, 287 (1994).ADSCrossRefGoogle Scholar
  7. 7.
    A. Busemann, In: Leipzig Geest, Portig (Handbuch der physik, 1931).Google Scholar
  8. 8.
    L. Crocco, L’Aerotecnica 12, 181 (1932).Google Scholar
  9. 9.
    M. V. Morkovin, Mécanique de la Turbulence (CNRS, Metz, 1961), p. 367.Google Scholar
  10. 10.
    A. J. Smits, and J. P. Dussauge, Turbulent Shear Layers in Supersonic Flow (Springer, Berlin, 2006).Google Scholar
  11. 11.
    O. Reynolds, Int. J. Heat Mass Transfer 3, 163 (1961).CrossRefGoogle Scholar
  12. 12.
    E. R. van Driest, J. Spacecraft Rockets 40, 1012 (2003).ADSCrossRefGoogle Scholar
  13. 13.
    A. Walz, Boundary Layers of Flow and Temperature (MIT Press, Cambridge, 1969).Google Scholar
  14. 14.
    D. L. Whitfield, and M. D. High, AIAA J. 15, 431 (1977).ADSGoogle Scholar
  15. 15.
    A. J. Laderman, and A. Demetriades, J. Fluid Mech. 63, 121 (1974).ADSCrossRefGoogle Scholar
  16. 16.
    A. J. Laderman, AIAA J. 16, 723 (1978).ADSGoogle Scholar
  17. 17.
    F. K. Owen, C. C. Horstman, and M. I. Kussoy, J. Fluid Mech. 70, 393 (1975).ADSCrossRefGoogle Scholar
  18. 18.
    M. J. Tummers, E. H. van Veen, N. George, R. Rodink, and K. Hanjalić, Exp. Fluid 37, 364 (2004).CrossRefGoogle Scholar
  19. 19.
    L. Pietri, M. Amielh, and F. Anselmet, Int. J. Heat Fluid Flow 21, 22 (2000).CrossRefGoogle Scholar
  20. 20.
    Y. Q. Wang, and C. Q. Liu, Sci. China-Phys. Mech. Astron. 60, 114712 (2017).ADSCrossRefGoogle Scholar
  21. 21.
    T. B. Gatski, and J. P. Bonnet, Compressibility, Turbulence and High Speed Flow (Elsevier, Amsterdam, 2009).Google Scholar
  22. 22.
    S. Pirozzoli, F. Grasso, and T. B. Gatski, Phys. Fluid 16, 530 (2004).ADSCrossRefGoogle Scholar
  23. 23.
    T. Maeder, N. A. Adams, and L. Kleiser, J. Fluid Mech. 429, 187 (2001).ADSCrossRefGoogle Scholar
  24. 24.
    L. Duan, I. Beekman, and M. P. Martín, J. Fluid Mech. 655, 419 (2010).ADSCrossRefGoogle Scholar
  25. 25.
    L. Duan, I. Beekman, and M. P. Martín, J. Fluid Mech. 672, 245 (2011).ADSCrossRefGoogle Scholar
  26. 26.
    Y. S. Zhang, W. T. Bi, F. Hussain, and Z. S. She, J. Fluid Mech. 739, 392 (2014).ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    L. Duan, and M. P. Martín, J. Fluid Mech. 684, 25 (2011).ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    S. E. Guarini, R. D. Moser, K. Shariff, and A. Wray, J. Fluid Mech. 414, 1 (2000).ADSCrossRefGoogle Scholar
  29. 29.
    J. Gaviglio, Int. J. Heat Mass Transfer 30, 911 (1987).CrossRefGoogle Scholar
  30. 30.
    P. G. Huang, G. N. Coleman, and P. Bradshaw, J. Fluid Mech. 305, 185 (1995).ADSCrossRefGoogle Scholar
  31. 31.
    R. Lechner, J. Sesterhenn, and R. Friedrich, J. Turbul. 2, N1 (2001).Google Scholar
  32. 32.
    T. Cebeci, and A. M. O. Smith, Analysis of Turbulent Boundary Layers (Academic Press, New York, 1974).zbMATHGoogle Scholar
  33. 33.
    M. W. Rubesin, Extra Compressibility Terms for Favre-Averaged Two- Equation Models of Inhomogeneous Turbulent Flows, Technical Report (NASA, 1990).Google Scholar
  34. 34.
    X. Liang, and X. L. Li, Sci. China-Phys. Mech. Astron. 56, 1408 (2013).ADSCrossRefGoogle Scholar
  35. 35.
    G. N. Coleman, J. Kim, and R. D. Moser, J. Fluid Mech. 305, 159 (1995).ADSCrossRefGoogle Scholar
  36. 36.
    S. Tamano, and Y. Morinishi, J. Fluid Mech. 548, 361 (2006).ADSCrossRefGoogle Scholar
  37. 37.
    Y. Morinishi, S. Tamano, and K. Nakabayashi, J. Fluid Mech. 502, 273 (2004).ADSCrossRefGoogle Scholar
  38. 38.
    J. D. Anderson, Hypersonic and High Temperature Gas Dynamics (AIAA, New York, 2000).Google Scholar
  39. 39.
    O. Marxen, T. Magin, G. Iaccarino, and E. S. G. Shaqfeh, Hypersonic boundary-layer instability with chemical reactions, AIAA Paper 2010–0707, 2010.CrossRefzbMATHGoogle Scholar
  40. 40.
    W. Jia, and W. Cao, Appl. Math. Mech.-Engl. Ed. 31, 979 (2010).CrossRefGoogle Scholar
  41. 41.
    X. P. Chen, X. P. Li, H.-S. Dou, and Z. C. Zhu, Sci. Sin.-Phys. Mech. Astron. 41, 969 (2011).CrossRefGoogle Scholar
  42. 42.
    X. Chen, X. Li, H. S. Dou, and Z. Zhu, J. Turbul. 19, 365 (2018).ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Z. Chen, C. P. Yu, L. Li, and X. L. Li, Sci. China-Phys. Mech. Astron. 59, 664702 (2016).CrossRefGoogle Scholar
  44. 44.
    Y. C. Hu, W. T. Bi, S. Y. Li, and Z. S. She, Sci. China-Phys. Mech. Astron. 60, 124711 (2017).ADSCrossRefGoogle Scholar
  45. 45.
    X. L. Li, D. X. Fu, Y. W. Ma, and X. Liang, Sci. China-Phys. Mech. Astron. 53, 1651 (2010).ADSCrossRefGoogle Scholar
  46. 46.
    X. Li, D. Fu, and Y. Ma, AIAA J. 46, 2899 (2008).ADSGoogle Scholar
  47. 47.
    X. Li, D. Fu, and Y. Ma, Phys. Fluids 22, 025105 (2010).ADSCrossRefGoogle Scholar
  48. 48.
    G. S. Jiang, and C. W. Shu, J. Comput. Phys. 126, 202 (1996).ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    J. Fan, Chin. J. Theor. Appl. Mech. 42, 591 (2010) (in Chinese).Google Scholar
  50. 50.
    S. B. Pope, Turbulence Flow (Cambridge University Press, Cambridge, 2001).Google Scholar
  51. 51.
    J. Wang, T. Gotoh, and T. Watanabe, Phys. Rev. Fluids 2, 053401 (2017).ADSCrossRefGoogle Scholar
  52. 52.
    C. J. Roy, and F. G. Blottner, Prog. Aerospace Sci. 42, 469 (2006).ADSCrossRefGoogle Scholar
  53. 53.
    D. Modesti, and S. Pirozzoli, Int. J. Heat Fluid Flow 59, 33 (2016).CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Fluid Transmission Technology of Zhejiang ProvinceZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.Key Laboratory of High Temperature Gas Dynamics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  3. 3.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations