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Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model

Publication ,  Journal Article
Li, S; Katul, G
Published in: Physics of Fluids
October 1, 2021

Drawing on an analogy to critical phenomena, it was shown that the Nikuradse turbulent friction factor (ft) measurements in pipes of radius R and wall roughness r can be collapsed onto a one-dimensional curve expressed as a conveyance law ft Re1/4 = go (χ), where Re is the bulk Reynolds number and χ = Re3/4 (r/R). The implicit function go (·) was conjectured based on matching two asymptotic limits of ft. However, the connection between go (·) and the phenomenon it proclaims to represent - turbulent eddies - remains lacking. Using models for the wall-normal velocity spectrum and return-to-isotropy for pressure-strain effects to close a co-spectral density budget, a derivation of go (·) is offered. The proposed method explicitly derives the solution for the conveyance law and provides a physical interpretation of χ as a dimensionless length scale reflecting the competition between the viscous sublayer thickness and characteristic height of roughness elements. Applications of the proposed method to other published measurements spanning roughness and Reynolds numbers beyond the original Nikuradse range are further discussed.

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Published In

Physics of Fluids

DOI

EISSN

1089-7666

ISSN

1070-6631

Publication Date

October 1, 2021

Volume

33

Issue

10

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Li, S., & Katul, G. (2021). Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model. Physics of Fluids, 33(10). https://doi.org/10.1063/5.0069705
Li, S., and G. Katul. “Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model.” Physics of Fluids 33, no. 10 (October 1, 2021). https://doi.org/10.1063/5.0069705.
Li, S., and G. Katul. “Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model.” Physics of Fluids, vol. 33, no. 10, Oct. 2021. Scopus, doi:10.1063/5.0069705.

Published In

Physics of Fluids

DOI

EISSN

1089-7666

ISSN

1070-6631

Publication Date

October 1, 2021

Volume

33

Issue

10

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences