Relationship between streamwise and azimuthal length scales in a turbulent pipe flow

• Published in: Physics of fluids (1994) Vol. 29; no. 10
• Main Authors: Ahn, Junsun, Sung, Hyung Jin
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.10.2017
• Subjects: Angles (geometry); Boundary layer; Computational fluid dynamics; Computer simulation; Direct numerical simulation; Energy spectra; Fluid dynamics; Offsets; Physics; Pipe flow; Proper Orthogonal Decomposition; Superposition (mathematics); Turbulence; Turbulent flow; Variation
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4997346

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.