Direct numerical simulation of turbulent pipe flow up to $Re_\tau=5200$

TL;DR

This study presents high-fidelity direct numerical simulations of turbulent pipe flow at Reynolds numbers up to 5200, providing detailed turbulence statistics and insights into flow physics and comparisons with channel flows and experimental data.

Contribution

The paper offers the first DNS of turbulent pipe flow at Re_τ=5200, systematically comparing turbulence statistics with other datasets and analyzing flow physics and scaling laws.

Findings

Friction factor matches experimental data at high Re.

Log-law indicator function lacks a plateau in pipes at Re_τ=5200.

Wall shear stress fluctuations grow with Re_τ and differ from channel flow.

Abstract

Well-resolved direct numerical simulations (DNSs) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10\pi R$ at friction Reynolds numbers up to $Re_\tau=5200$. 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 $0.6\%$ of the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than that in Pirozzoli et al. (J. Fluid. Mech., 926, A28, 2021), but matches well with the experiments in Furuichi et al. (Phys. Fluids, 27, 095108, 2015). The log-law indicator function, which is nearly indistinguishable between the pipe and channel flows up to $y^+=250$, has not yet developed a plateau further 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 velocity 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 values are slightly lower in channel than pipe flows at the same $Re_\tau$, the inner peaks of the pressure fluctuations show 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 -- as also seen in the channel flow. In summary, this high-fidelity data enable us to provide better insights into the flow physics in the pipes and the similarity/difference among different types of wall turbulence.