Skip to main content
SpringerLink
Log in

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Re τ  = 180, 360, 550 and \(1\text{,}000\). The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y  +  ≈ 100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.

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. Alfredsson, P.H., Segalini, A., Örlü, R.: A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the “outer” peak. Phys. Fluids 23, 041702 (2011)

    Article  Google Scholar 

  2. Boersma, B.J.: Direct numerical simulation of turbulent pipe flow up to a Reynolds number of 61,000. J. Phys. 318, 042045 (2011)

    Google Scholar 

  3. Chauhan, K.A., Monkewitz, P.A., Nagib, H.M.: Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41, 021404 (2009)

    Article  Google Scholar 

  4. Chevalier, M., Schlatter, P., Lundbladh, A., Henningson, D.S.: simson—A pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07, KTH Mechanics, Stockholm, Sweden (2007)

  5. Chin, C., Ooi, A.S.H., Marusic, I., Blackburn, H.M.: The influence of pipe length on turbulence statistics computed from direct numerical simulation data. Phys. Fluids 22, 115107 (2010)

    Article  Google Scholar 

  6. Coles, D.: The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  7. del Álamo, J.C., Jiménez, J.: Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41–L44 (2003)

    Article  Google Scholar 

  8. Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R., Nieuwstadt, F.T.M.: Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209 (1994)

    Article  Google Scholar 

  9. Fischer, P.F., Lottes, J.W., Kerkemeier, S.G.: nek5000 web page. http://nek5000.mcs.anl.gov (2008)

  10. Fukagata, K., Kasagi, N.: Highly energy-conservative finite difference method for the cylindrical coordinate system. J. Comput. Phys. 181, 478–498 (2002)

    Article  MATH  Google Scholar 

  11. Guala, M., Hommema, S.E., Adrian, R.J.: Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542 (2006)

    Article  MATH  Google Scholar 

  12. Hoyas, S., Jiménez, J.: Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511 (2008)

    Article  Google Scholar 

  13. Jiménez, J., Hoyas, S.: Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236 (2008)

    Article  MATH  Google Scholar 

  14. Jiménez, J., Hoyas, S., Simens, M.P., Mizuno, Y.: Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360 (2010)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  16. Kim, K.C., Adrian, R.J.: Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Klewicki, J., Chin, C., Blackburn, H.M., Ooi, A., Marusic, I.: Emergence of the four layer dynamical regime in turbulent pipe flow. Phys. Fluids 24, 045107 (2012)

    Article  Google Scholar 

  18. Lenaers, P., Li, Q., Brethouwer, Schlatter, P., Örlü, R.: Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. Phys. Fluids 24, 035110 (2012)

    Article  Google Scholar 

  19. Maday, Y., Patera, A.: Spectral element methods for the Navier–Stokes equations. In: Noor, A.K. (ed.) State of the Art Surveys in Computational Mechanics ASME, pp. 71–143 (1989)

  20. Marusic, I., McKeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J.: Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103 (2010)

    Article  Google Scholar 

  21. Monty, J.P., Stewart, J.A., Williams, R.C., Chong, M.S.: Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156 (2007)

    Article  MATH  Google Scholar 

  22. Moody, L.F.: Friction factors for pipe flow. Trans. ASME 66, 671–684 (1944)

    Google Scholar 

  23. Nagib, H.M., Chauhan, K.A.: Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518 (2008)

    Article  Google Scholar 

  24. Ohlsson, J., Schlatter, P., Mavriplis, C., Henningson, D.S.: The spectral-element method and the pseudo-spectral method—a comparative study. In: Rønquist, E. (ed.) Lecture Notes in Computational Science and Engineering, pp. 459–467. Springer, Berlin, Germany (2011)

    Google Scholar 

  25. Orlandi, P., Fatica, M.: Direct simulations of turbulent flow in a pipe rotating about its axis. J. Fluid Mech. 343, 43–72 (1997)

    Article  MATH  Google Scholar 

  26. Örlü, R., Schlatter, P.: On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows. Phys. Fluids 23, 021704 (2011)

    Article  Google Scholar 

  27. Schlatter, P., Örlü, R.: Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126 (2010)

    Article  MATH  Google Scholar 

  28. Schlatter, P., Örlü, R.: Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 5–34 (2012)

    Article  MATH  Google Scholar 

  29. Schlatter, P., Örlü, R., Li, Q., Brethouwer, G., Fransson, J.H.M., Johansson, A.V., Alfredsson, P.H., Henningson, D.S.: Turbulent boundary layers up to \({R}e_\theta=2\text{,}500\) studied through simulation and experiment. Phys. Fluids 21, 051702 (2009)

    Article  Google Scholar 

  30. Smits, A.J., McKeon, B.J., Marusic, I.: High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375 (2011)

    Article  Google Scholar 

  31. Spalart, P.R.: Direct simulation of a turbulent boundary layer up to R θ  = 1410. J. Fluid Mech. 187, 61–98 (1988)

    Article  MATH  Google Scholar 

  32. Talamelli, A., Persiani, F., Fransson, J.H.M., Alfredsson, P.H., Johansson, A., Nagib, H.M., Rüedi, J., Sreenivasan, K.R., Monkewitz, P.A.: CICLoPE—a response to the need for high Reynolds number experiments. Fluid Dyn. Res. 41, 1–22 (2009)

    Article  Google Scholar 

  33. Wagner, C., Hüttl, T.J., Friedrich, R.J.: Low-Reynolds-number effects derived from direct numerical simulations of turbulent pipe flow. Comp. Fluids 30, 581–590 (2001)

    Article  MATH  Google Scholar 

  34. Walpot, R.J.E., van der Geld, C.W.M., Kuerten, J.G.M.: Determination of the coefficients of langevin models for inhomogeneous turbulent flows by three-dimensional particle tracking velocimetry and direct numerical simulation. Phys. Fluids 19, 045102 (2007)

    Article  Google Scholar 

  35. Wu, X., Baltzer, J.R., Adrian, R.J.: Direct numerical simulation of a 30R long turbulent pipe flow at R  +  = 685: large- and very large-scale motions. J. Fluid Mech. 698, 235–281 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wu, X., Moin, P.: A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112 (2008)

    Article  MATH  Google Scholar 

  37. Zagarola, M.V., Smits, A.J.: Scaling of the mean velocity profile for turbulent pipe flow. Phys. Rev. Lett. 78, 239–242 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    George K. El Khoury, Philipp Schlatter, Azad Noorani, Geert Brethouwer & Arne V. Johansson

  2. MCS, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, 60439, USA

    Paul F. Fischer

Authors
  1. George K. El Khoury
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philipp Schlatter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Azad Noorani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paul F. Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Geert Brethouwer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Arne V. Johansson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George K. El Khoury.

Rights and permissions

Reprints and permissions

About this article

Cite this article

El Khoury, G.K., Schlatter, P., Noorani, A. et al. Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers. Flow Turbulence Combust 91, 475–495 (2013). https://doi.org/10.1007/s10494-013-9482-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-013-9482-8

Keywords

Search

Navigation