Direct numerical simulations of turbulent pipe flow up to Reτ≈5200

Jie Yao, Saleh Rezaeiravesh, Philipp Schlatter, Fazle Hussain

Research output: Contribution to journalArticlepeer-review


Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius R and axial length 10πR at friction Reynolds numbers up to Reτ = 5200 using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor λ overshoots by 2 % and undershoots by 0.6 % the Prandtl friction law at low and high Re ranges, respectively. In addition, λ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to y+ = 250, has not yet developed a plateau farther away from the wall in the pipes even for the Reτ = 5200 cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with Reτ – are lower in the pipe than in the channel, but the difference decreases with increasing Reτ . While the wall value is slightly lower in the channel than in the pipe at the same Reτ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a k−1 dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

Original languageEnglish
Article numberA18
JournalJournal of Fluid Mechanics
Publication statusPublished - 10 Feb 2023


  • pipe flow
  • turbulence simulation
  • turbulent boundary layers


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