TY - JOUR

T1 - One-point statistics for turbulent pipe flow up to Re휏≈6000

AU - Pirozzoli, Sergio

AU - Romero, Joshua

AU - Fatica, Massimiliano

AU - Verzicco, Roberto

AU - Orlandi, Paolo

N1 - Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.

PY - 2021/11/10

Y1 - 2021/11/10

N2 - We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number using direct numerical simulation (DNS) of the Navier-Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately, which would extrapolate to approximately at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant, which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at, as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

AB - We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number using direct numerical simulation (DNS) of the Navier-Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately, which would extrapolate to approximately at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant, which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at, as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

KW - Pipe flow

KW - Turbulence simulation

KW - Turbulence theory

KW - UT-Hybrid-D

UR - http://www.scopus.com/inward/record.url?scp=85115099538&partnerID=8YFLogxK

U2 - 10.1017/jfm.2021.727

DO - 10.1017/jfm.2021.727

M3 - Article

AN - SCOPUS:85115099538

SN - 0022-1120

VL - 926

SP - 355

EP - 377

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

M1 - A28

ER -