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Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius$$R$$and axial length$$10{\rm \pi} R$$at friction Reynolds numbers up to$$Re_\tau =5200$$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$$\lambda$$overshoots by$$2\,\%$$and undershoots by$$0.6\,\%$$the Prandtl friction law at low and high$$Re$$ranges, respectively. In addition,$$\lambda$$in our results is slightly higher than in Pirozzoliet al.(J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichiet 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$$Re_\tau =5200$$cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with$$Re_\tau$$– are lower in the pipe than in the channel, but the difference decreases with increasing$$Re_\tau$$. While the wall value is slightly lower in the channel than in the pipe at the same$$Re_\tau$$, 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.
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This content will become publicly available on July 10, 2026
Turbulence-resolving integral simulations for wall-bounded flows
The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for turbulence-resolving integral simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three-component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier–Stokes with relatively simple closure approximations. Evidence from direct numerical simulations (DNS) suggests that TRIS can theoretically resolve$$35\,\%{-}40\,\%$$of the turbulent skin friction enhancement for friction Reynolds numbers between$$180$$and$$5200$$, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in$${\sim}1$$minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of$$395$$and$$590$$show that TRIS generates a relatively accurate representation of the flow, while highlighting discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modelling, motivating extension to more general flow configurations such as boundary layers on immersed objects.
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- Award ID(s):
- 2340121
- PAR ID:
- 10650824
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1014
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- A40
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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