In this note, basic turbulent statistics in a pipe flow are computed accurately by large-eddy simulation using a mesh resolution coarser than the viscous sublayer. These results are obtained when a regular Cartesian mesh is used for the spatial discretization of the circular pipe thanks to an immersed boundary method combined with high-order schemes. In this particular computational configuration, the near-wall features of mean velocity and Reynolds stress profiles are found to be correctly captured at a scale significantly smaller than the mesh size. Comparisons between channel and pipe flow configurations suggest that an irregular mesh distribution in terms of wall distance may be a favourable condition to explicitly compute by large-eddy simulation reliable wall turbulence without any extra-modelling in the near-wall region.
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The collection of data for the turbulent statistics is made over a time T s t a t = 160D/U b ≈ 9.27D/u τ for R e D = 19000 and T s t a t = 160D/U b ≈ 10.9D/u τ for R e D = 5300 (in  the value T s t a t = 4D/U b is used).
The alternative approximation of u τ directly from the mean velocity profile <u z > (r) leads to a similar level of discrepancy.
Note that z is the streamwise direction for both the pipe and channel whereas x and y are respectively the wall-normal and spanwise direction for the channel
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This work was granted access to the HPC resources of IDRIS under the allocation 2017-2016-2a0912 made by GENCI. The authors would like to acknowlege EDF R&D for its scientific and financial support through the project P117Z and the collaboration contract EDF-CNRS-ENSMA-UP 8610-59200015175.
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Dairay, T., Lamballais, E. & Benhamadouche, S. Mesh Node Distribution in Terms of Wall Distance for Large-eddy Simulation of Wall-bounded Flows. Flow Turbulence Combust 100, 617–626 (2018). https://doi.org/10.1007/s10494-017-9863-5
- Large-eddy simulation
- Turbulent pipe flow
- Immersed boundary method
- High-order schemes
- Computational mesh resolution