论文标题
湍流管道的直接数值模拟最高为$re_τ= 5200 $
Direct numerical simulation of turbulent pipe flow up to $Re_τ=5200$
论文作者
论文摘要
已解决良好的直接数值模拟（DNSS）在光滑的半径$ r $和轴向长度的光滑圆管中进行了流动，摩擦雷诺数的$10πr$最高为$re_τ= 5200 $。记录了各种湍流统计数据，并将管道和通道中的其他DNS和实验数据进行比较。确定了各种数据集之间的小但明显差异。摩擦因子$λ$ $ 2 \％$和$ 0.6 \％$ $ $ $ $ $ $范围的$ 0.6 \％。此外，我们的结果中的$λ$略高于Pirozzoli等人的结果。 （J.Fluid。Mech。，926，A28，2021），但与Furuichi等人的实验非常匹配。 （Phys。Fluids，27，095108，2015）。日志法指示器功能在管道和通道之间几乎无法区分的函数流动到$ y^+= 250 $，尚未在距管道墙壁更远的地方发展出一个高原，即使对于$re_τ= 5200 $ cases。壁剪应力波动和轴向速度强度的内部峰（用$re_τ$单调生长）在管道中比通道中低，但差异随着$re_τ$的增加而降低。虽然通道中的壁值略低于相同$re_τ$的管道流量，但压力波动的内峰显示它们之间的差异可忽略不计。如果适当选择系数，所有这些数量的雷诺数缩放量表与对数和缺陷功率定律一致。轴向速度波动的一维光谱在距墙壁中间距离处表现出$ k^{ - 1} $依赖性 - 在通道流中也可以看到。总而言之，这种高保真数据使我们能够更好地了解管道中的流动物理学以及不同类型的壁湍流之间的相似性/差异。
Well-resolved direct numerical simulations (DNSs) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10πR$ at friction Reynolds numbers up to $Re_τ=5200$. 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 $λ$ overshoots by $2\%$ and undershoots by $0.6\%$ of the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $λ$ 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 $Re_τ=5200$ cases. The wall shear stress fluctuations and the inner peak of the axial velocity intensity -- which grow monotonically with $Re_τ$ -- are lower in the pipe than in the channel, but the difference decreases with increasing $Re_τ$. While the wall values are slightly lower in channel than pipe flows at the same $Re_τ$, 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.
