Relationship between streamwise and azimuthal length scales in a turbulent pipe flow
The statistical relationships among the turbulence structures of the streamwise velocity fluctuations along the streamwise and azimuthal directions in a turbulent pipe flow were examined using direct numerical simulation data at Re τ = 3008. Two-point correlations of the streamwise velocity fluctuat...
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Published in | Physics of fluids (1994) Vol. 29; no. 10 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Melville
American Institute of Physics
01.10.2017
|
Subjects | |
Online Access | Get full text |
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Summary: | The statistical relationships among the turbulence structures of the streamwise velocity fluctuations along the streamwise and azimuthal directions in a turbulent pipe flow were examined using direct numerical simulation data at Re
τ
= 3008. Two-point correlations of the streamwise velocity fluctuations showed a linear relationship between the streamwise and azimuthal length scales (l
x
and l
θ
), where l
θ
/
l
x
= 0.07 along the wall-normal distance, indicating the long coherent structures called very-large-scale motions (VLSMs). The one-dimensional pre-multiplied energy spectra of the streamwise velocity fluctuations showed that the streamwise and the azimuthal wavelengths (λ
x
and λ
θ
) grew linearly along the wall-normal distance, λ
x
/
y = 20 and λ
θ
/
y = 7, respectively. The ratio between the two linear relationships was determined to be λ
θ
/
λ
x
= 0.35, indicative of large-scale motions (LSMs). The energetic modes obtained from a proper orthogonal decomposition (POD) analysis using the translational invariance method showed that the averaged helical angles of the wall mode (i
x
< i
θ
; β < 0.1 rad, where i
x
and i
θ
are the streamwise and azimuthal mode numbers and β is the helical angle) and lift mode (i
x
≥ i
θ
; β ≥ 0.1 rad) were related to l
θ
/
l
x
= 0.07 (VLSMs) and λ
θ
/
λ
x
≈ 0.35 (LSMs), respectively. The superposition of the energetic POD modes showed the superimposed X-shaped patterns. The helical angle of the wall mode in the near-wall region was similar to that in the outer region, implying the existence of the VLSMs in the entire wall-normal distance. The LSMs showed more inclined X-shaped patterns. The LSMs were concatenated with the azimuthal offsets to form meandering VLSMs. Most of the VLSMs and LSMs in the near-wall region inclined smaller and larger than 10° (0.17 rad), respectively. In the core region, VLSMs were distributed more helically along the azimuthal direction due to the space limitations of the pipe geometry. |
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ISSN: | 1070-6631 1089-7666 |
DOI: | 10.1063/1.4997346 |