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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1057–1072 | Cite as

Optimal transient growth in turbulent pipe flow

  • Yang Song
  • Chunxiao Xu
  • Weixi HuangEmail author
  • Guixiang Cui
Article
  • 86 Downloads

Abstract

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the subspace spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth amplification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δ v are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.

Keywords

turbulent pipe flow optimal transient growth coherent structure 

Chinese Library Classification

O357 

2010 Mathematics Subject Classification

76F02 76E05 76M22 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yang Song
    • 1
  • Chunxiao Xu
    • 1
  • Weixi Huang
    • 1
    Email author
  • Guixiang Cui
    • 1
  1. 1.Key Laboratory of Applied Mechanics, Department of Engineering MechanicsTsinghua UniversityBeijingChina

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