Advertisement

Scaling of High-Order Statistics in Turbulent Pipe Flow

  • C. BauerEmail author
  • C. Wagner
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)

Abstract

Direct numerical simulations of turbulent pipe flow involving friction Reynolds numbers of \(Re_\tau \)=180,360,720,1500 were carried out and investigated in terms of high-order statistics. A logarithmic dependency on the Reynolds number was found for the streamwise Reynolds stress where \(Re_\tau \ge 360\), the streamwise skewness and the wall-normal flatness for \(Re_\tau \ge 360\). The scaling failure of the latter quantities is related to large-scale outer flow motions that become important at high Reynolds number flow and penetrate into the near-wall region. For the lowest Reynolds number \(Re_\tau =180\) the streamwise Reynolds stress peak and the wall-normal flatness at the wall exhibited discrepancies to values obtained from channel flow simulations, which can be explained by the different flow geometry interacting with the wall structures that are of large size compared with the geometry at such low Re.

References

  1. 1.
    Bauer, C., Feldmann, D., Wagner, C.: Revisiting the higher-order statistical moments in turbulent pipe flow using direct numerical simulations. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 136, pp. 75–84. Springer (2018)Google Scholar
  2. 2.
    Boersma, B.J.: Direct numerical simulation of turbulent pipe at high Reynolds numbers, velocity statistics and large scale motions. In: TSFP Digital Library Online. Begell House Inc (2013)Google Scholar
  3. 3.
    Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comput. 22, 745–762 (1968)MathSciNetCrossRefGoogle Scholar
  4. 4.
    El Khoury, G.K., Schlatter, P., Noorani, A., Fischer, P.F., Brethouwer, G., Johansson, A.V.: Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91(3), 475–495 (2013)CrossRefGoogle Scholar
  5. 5.
    Feldmann, D., Wager, C.: Direct numerical simulation of fully developed turbulent and oscillatory pipe flows at Re\(\tau =1440\). J. Turbul. 13(32), 1–28 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hoyas, S., Jiménez, J.: Scaling of the velocity fluctuations in turbulent channels up to Re\(\tau =2003\). Phys. Fluids 18(1), 11702 (2006)Google Scholar
  7. 7.
    Kim, J., Moin, P.: Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59(2), 308–323 (1985)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lee, M., Moser, R.D.: Direct numerical simulation of turbulent channel flow up to \(\mathit{Re} _ {{\tau }}\approx 5200\). J. Fluid Mech. 774, 395–415 (2015)CrossRefGoogle Scholar
  9. 9.
    Lenaers, P., Li, Q., Brethouwer, G., Schlatter, P., Örlü, R.: Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. Phys. Fluids 24(3), 035110 (2012)CrossRefGoogle Scholar
  10. 10.
    Mathis, R., Hutchins, N., Marusic, I.: Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337 (2009)CrossRefGoogle Scholar
  11. 11.
    Mathis, R., Marusic, I., Hutchins, N., Sreenivasan, K.R.: The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23(12), 121702 (2011)CrossRefGoogle Scholar
  12. 12.
    Vreman, A.W., Kuerten, J.G.M.: Comparison of direct numerical simulation databases of turbulent channel flow at Re\(\tau =180\). Phys. Fluids 26(1), 015102 (2014)Google Scholar
  13. 13.
    Xu, C., Zhang, Z., den Toonder, J.M.J., Nieuwstadt, F.T.M.: Origin of high kurtosis levels in the viscous sublayer. Direct numerical simulation and experiment. Phys. Fluids 8(7), 1938–1944 (1996)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.German Aerospace Center, Institute of Aerodynamics and Flow TechnologyGottingenGermany
  2. 2.Institute of Thermodynamics and Fluid Mechanics, Technische Universität IlmenauIlmenauGermany

Personalised recommendations