Skip to main content
SpringerLink
Log in

Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Many recent laboratory experiments and numerical simulations support a non-equilibrium dissipation scaling in decaying turbulence before it reaches an equilibrium state. By analyzing a direct numerical simulation (DNS) database of a transitional boundary-layer flow, we show that the transition region and the non-equilibrium turbulence region, which are located in different streamwise zones, present different non-equilibrium scalings. Moreover, in the wall-normal direction, the viscous sublayer, log layer, and outer layer show different non-equilibrium phenomena which differ from those in grid-generated turbulence and transitional channel flows. These findings are expected to shed light on the modelling of various types of non-equilibrium turbulent flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. KOLMOGOROV, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Proceedings: Mathematical and Physical Sciences, 434, 9–13 (1991)

    MathSciNet  MATH  Google Scholar 

  2. RICHARDSON, L. F. Weather Prediction by Numerical Process, Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  3. FANG, L., ZHAO, H. K., LU, L. P., LIU, Y. W., and YAN, H. Quantitative description of non-equilibrium turbulent phenomena in compressors. Aerospace Science and Technology, 71, 78–89 (2017)

    Article  Google Scholar 

  4. YAN, H., LIU, Y. W., LI, Q. S., and LU, L. P. Turbulence characteristics in corner separation in a highly loaded linear compressor cascade. Aerospace Science and Technology, 75, 139–154 (2018)

    Article  Google Scholar 

  5. VASSILICOS, J. C. Dissipation in turbulent flows. Annual Review of Fluid Mechanics, 47, 95–114 (2015)

    Article  MathSciNet  Google Scholar 

  6. BOS, W. J. T. and RUBINSTEIN, R. Dissipation in unsteady turbulence. Physics Review Fluids, 2, 022601 (2017)

    Article  Google Scholar 

  7. LIU, F., LU, L. P., BOS, W. J. T., and FANG, L. Assessing the non-equilibrium of decaying turbulence with reversed initial fields. Physical Review Fluids, 4, 084603 (2019)

    Article  Google Scholar 

  8. HEARST, R. J. and LAVOIE, P. Velocity derivative skewness in fractal-generated, non-equilibrium grid turbulence. Physics of Fluids, 27, 071701 (2015)

    Article  Google Scholar 

  9. ISAZA, J. C., SALAZAR, R., and WARHAFT, Z. On grid-generated turbulence in the near and far field regions. Journal of Fluid Mechanics, 753, 402–426 (2014)

    Article  Google Scholar 

  10. FANG, L., ZHU, Y., LIU, Y.W., and LU, L. P. Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling. Physics Letters A, 379, 2331–2336 (2015)

    Article  MATH  Google Scholar 

  11. VALENTE, P. C., ONISHI, R., and SILVA, C. B. D. Origin of the imbalance between energy cascade and dissipation in turbulence. Physical Review E, 90, 023003 (2014)

    Article  Google Scholar 

  12. GOTO, S. and VASSILICOS, J. C. Energy dissipation and flux laws for unsteady turbulence. Physics Letters A, 379, 1144–1148 (2015)

    Article  Google Scholar 

  13. SEOUD, R. E. and VASSILICOS, J. C. Dissipation and decay of fractal-generated turbulence. Physics of Fluids, 19, 105108 (2007)

    Article  MATH  Google Scholar 

  14. VALENTE, P. C. and VASSILICOS, J. C. Universal dissipation scaling for nonequilibrium turbulence. Physical Review Letters, 108, 214503 (2012)

    Article  Google Scholar 

  15. GOMES-FERNANDES, R., GANAPATHISUBRAMANI, B., and VASSILICOS, J. C. Particle image velocimetry study of fractal-generated turbulence. Journal of Fluid Mechanics, 711, 306–336 (2012)

    Article  MATH  Google Scholar 

  16. NEDÍC, J., VASSILICOS, J. C., and GANAPATHISUBRAMANI, B. Axisymmetric turbulent wakes with new nonequilibrium similarity scalings. Physical Review Letters, 111, 144503 (2013)

    Article  Google Scholar 

  17. DAIRAY, T., OBLIGADO, M., and VASSILICOS, J. C. Non-equilibrium scaling laws in axisymmetric turbulent wakes. Journal of Fluid Mechanics, 781, 166–195 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. LAYEK, G. C. and SUNITA. Non-Kolmogorov scaling and dissipation laws in planar turbulent plume. Physics of Fluids, 30, 115105 (2018)

    Article  Google Scholar 

  19. LAYEK, G. C. and SUNITA. Non-Kolmogorov dissipation in a turbulent planar jet. Physical Review Fluids, 3, 124605 (2018)

    Article  Google Scholar 

  20. LESIEUR, M. Turbulence in Fluids, Kluwer Academic, Dordrecht (1997)

    Book  MATH  Google Scholar 

  21. LIU, F., LU, L. P., and FANG, L. Non-equilibrium turbulent phenomena in transitional channel flows. Journal of Turbulence, 19, 731–753 (2018)

    Article  MathSciNet  Google Scholar 

  22. KAMRUZZAMAN, M., DJENIDI, L., and ANTONIA, R. A. Behaviour of the energy dissipation coefficient in a rough wall turbulent boundary layer. Experiments in Fluids, 59, 9 (2018)

    Article  Google Scholar 

  23. NEDIC, J., TAVOULARIS, S., and MARUSIC, I. Dissipation scaling in constant-pressure turbulent boundary layers. Physical Review Fluids, 2, 032601 (2017)

    Article  Google Scholar 

  24. FANG, J., YAO, Y. F., LI, Z. R., and LU, L. P. Investigation of low-dissipation monotonicity-preserving scheme for direct numerical simulation of compressible turbulent flows. Computers and Fluids, 104, 55–72 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  25. FANG, J., YAO, Y. F., ZHELTOVODOV, A. A., LI, Z. R., and LU, L. P. Direct numerical simulation of supersonic turbulent flows around a tandem expansion compression corner. Physics of Fluids, 27, 125104 (2015)

    Article  Google Scholar 

  26. FANG, J., YAO, Y. F., ZHELTOVODOV, A. A., and LU, L. P. Investigation of three dimensional shock wave/turbulent boundary layer interaction initiated by a single-fin. AIAA Journal, 55, 509–523 (2016)

    Article  Google Scholar 

  27. KELE, S. K. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103, 16–42 (1992)

    Article  MathSciNet  Google Scholar 

  28. FANG, J., GAO, F., MOULINEC, C., and EMERSON, D. R. An improved parallel compact scheme for domain-decoupled simulation of turbulence. International Journal for Numerical Methods in Fluids, 90, 479–500 (2019)

    Article  MathSciNet  Google Scholar 

  29. GAITONDE, D. V. and VISBAL, M. R. Pade-type higher-order boundary filters for the Navier-Stokes equations. AIAA Journal, 38, 2103–2112 (2000)

    Article  Google Scholar 

  30. GOTTLIEB, S. and SHU, C. W. Total variation diminishing Runge-Kutta schemes. Mathematics of Computation, 67, 73–85 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  31. KIM, W. and LEE, D. J. Generalized characteristic boundary conditions for computational aeroacoustics. AIAA Journal, 38, 2040–2049 (2000)

    Article  Google Scholar 

  32. FASEL, H. and KONZELMANN, U. Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations. Journal of Fluid Mechanics, 221, 311–347 (1990)

    Article  MATH  Google Scholar 

  33. SAYADI, T., HAMMAN, C., and MOIN, P. Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. Journal of Fluid Mechanics, 724, 480–509 (2013)

    Article  MATH  Google Scholar 

  34. SMITS, A. J., MATHESON, N., and JOUBERT, P. N. Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. Journal of Ship Research, 27, 147–157 (1983)

    Article  Google Scholar 

  35. ZHANG, X. X., WATANABE, T., and NAGATA, K. Turbulent/nonturbulent interfaces in high-resolution direct numerical simulation of temporally evolving compressible turbulent boundary layers. Physical Review Fluids, 3, 094605 (2018)

    Article  Google Scholar 

  36. SPALART, P. R. Direct simulation of a turbulent boundary layer up to R θ = 1410. Journal of Fluid Mechanics, 187, 61–98 (1988)

    Article  MATH  Google Scholar 

  37. WU, X. H. and MOIN, P. Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. Journal of Fluid Mechanics, 630, 5–41 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. DUCROS, F., COMTE, P., and LESIEUR, M. Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. Journal of Fluid Mechanics, 326, 1–36 (1996)

    Article  MATH  Google Scholar 

  39. HINZE, J. O. Turbulence, 2nd ed., McGraw-Hill, New York (1975)

    Google Scholar 

  40. WEI, T., FIFE, P., KLEWICKI, J., and MCMURTRY, P. Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. Journal of Fluid Mechanics, 522, 303–327 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. PINTON, J. F., HOLDSWORTH, P. C. W., and LABBÉ, R. Power fluctuations in a closed turbulent shear flow. Physical Review E, 60, R2452–R2455 (1999)

    Article  Google Scholar 

  42. LAUNDER, B. E. and SPALDING, D. B. Lecture in Mathematical Models of Turbulence, Academic Press, London (1972)

    MATH  Google Scholar 

  43. POPE, S. Turbulent Flows, Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Energy and Power Engineering, North University of China, Taiyuan, 030051, China

    Feng Liu

  2. Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing, 100191, China

    Feng Liu & Le Fang

  3. Scientific Computing Department, STFC Daresbury Laboratory, Warrington, WA4 4AD, UK

    Jian Fang

Authors
  1. Feng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Le Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Liu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 12002318, 11572025, 11772032, and 51420105008) and the Science Foundation of North University of China (No. XJJ201929)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, F., Fang, L. & Fang, J. Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows. Appl. Math. Mech.-Engl. Ed. 42, 567–582 (2021). https://doi.org/10.1007/s10483-021-2728-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-021-2728-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation