Skip to main content
SpringerLink
Log in

Incorporating boundary constraints to predict mean velocities in turbulent channel flow

  • Article
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

We derive exact near-wall and centerline constraints and apply them to improve a recently proposed LPR model for finite Reynolds number (Re) turbulent channel flows. The analysis defines two constants which are invariant with Re and suggests two more layers for incorporating boundary effects in the prediction of the mean velocity profile in the turbulent channel. These results provide corrections for the LPR mixing length model and incorrect predictions near the wall and the centerline. Moreover, we show that the analysis, together with a set of well-defined sensitive indicators, is useful for assessment of numerical simulation data.

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. Pope S B. Turbulent Flows. Cambridge: Cambridge University Press, 2000

    Book  MATH  Google Scholar 

  2. Prandtl L. Bericht über die Entstehung der turbulence. Z Angew Math Mech, 1925, 5: 136–139

    MATH  Google Scholar 

  3. von Karman T. Mechanische Ahnlichkeit und Turbulenz. In: Proc Third Int Congr Applied Mechanics, Stockholm, 1930. 85–105

  4. Wilcox D C. Turbulence Modeling for CFD. California: DCW Industries, 2006

    Google Scholar 

  5. Zagarola M V, Perry A E, Smits A J. Log laws or power laws: The scaling in the overlap region. Phys Fluids, 1997, 9: 2094–2100

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. George W K. Is there a universal log-law for turbulent wall-bounded flow? Phil Trans R Soc London Ser A, 2007, 365: 789–806

    Article  ADS  MATH  Google Scholar 

  7. Barenblatt G I. Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J Fluid Mech, 1993, 248: 513–520

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Barenblatt G I, Prostokishin V M. Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data. J Fluid Mech, 1993, 248: 521–529

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Barenblatt G I, Chorin A J. A mathematical model for the scaling of turbulence. Proc Natl Acad Sci, 2004, 101: 15032–15026

    Article  MathSciNet  ADS  Google Scholar 

  10. Kim J, Moin P, Moser R D. Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech, 1987, 177: 133–166

    Article  ADS  MATH  Google Scholar 

  11. Moin P, Mahesh K. Direct numerical simulation: A tool in turbulence research. Annu Rev Fluid Mech, 1998, 30: 539–578

    Article  MathSciNet  ADS  Google Scholar 

  12. L’vov V S, Procaccia I, Rudenco O. Universal model of finite Reynolds number turbulent flow in channels and pipes. Phys Rev Lett, 2008, 100: 050504

    Google Scholar 

  13. Iwamoto K, Suzuki Y, Kasagi N. Database of fully developed channel flow. THTLAB Internal Report, No. ILR-0201, 2002. http://www.thtlab.t.u-tokyo.ac.jp

  14. Hoyas S, Jimenez J. Scaling of the velocity fluctuations in turbulent channels up to Re τ=2003. Phys Fluids, 2006, 18: 011702

    Article  ADS  Google Scholar 

  15. She Z S, Chen X, Wu Y, et al. New perspectives in statistical modeling of wall-bounded turbulence. Acta Mech Sin, 2010, 26: 847–861

    Article  MathSciNet  ADS  Google Scholar 

  16. Moser R D, Kim J, Mansour N N. Direct numerical simulation of turbulent channel flow up to Re τ=590. Phys Fluids, 1999, 11: 943–945

    Article  ADS  MATH  Google Scholar 

  17. Schlatter P, Qiang L, Brethouwer G, et al. Simulations of spatially evolving turbulent boundary layers up to Re θ=4300. Inter J Heat Fluid Flow, 2010, 31: 251–261

    Article  Google Scholar 

  18. She Z S, Hu N, Wu Y. Structural ensemble dynamics based closure model for wall-bounded turbulent flow. Acta Mech Sin, 2009, 25: 731–736

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics, College of Engineering, Peking University, Beijing, 100871, China

    You Wu, Xi Chen & ZhenSu She

  2. Department of Mechanical Engineering, University of Houston, Houston, TX, 77204-4006, USA

    Fazle Hussain

Authors
  1. You Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ZhenSu She
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fazle Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ZhenSu She.

Additional information

Contributed by SHE ZhenSu (Associate Editor)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Y., Chen, X., She, Z. et al. Incorporating boundary constraints to predict mean velocities in turbulent channel flow. Sci. China Phys. Mech. Astron. 55, 1691–1695 (2012). https://doi.org/10.1007/s11433-012-4828-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-012-4828-0

Keywords

Search

Navigation