自由面对明渠湍流的影响有多大?

IF 2.4 3区 工程技术 Q3 MECHANICS
Christian Bauer, Yoshiyuki Sakai, Markus Uhlmann
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引用次数: 0

摘要

众所周知,明渠湍流在自由表面附近具有多层结构。在目前的工作中,我们采用直接数值模拟,考虑到雷诺数高达\(\boldsymbol{R{e_\tau } = 900}\)和足够大的域尺寸(\(\boldsymbol{{L_x} = 12\pi h}\), \(\boldsymbol{{L_z} = 4\pi h}\)),以忠实地捕捉非常大规模运动的影响,以测试所提出的标度定律,并最终回答这个问题:自由表面的影响延伸到什么程度?在接近自由表面的区域,速度和涡度的波动强度变得高度各向异性,我们观察到先前记录的三层结构,包括一个与通道高度\(h\)成尺度的壁法向速度阻尼层,以及两个分别与近地表粘性长度尺度\(\boldsymbol{{\ell _{\boldsymbol{V}}} = {\boldsymbol{Re}}_{\boldsymbol{b}}^{ - 1/2}h}\)和Kolmogorov长度尺度\(\boldsymbol{{\ell _{\boldsymbol{K}}} = {\boldsymbol{Re}}_{\boldsymbol{b}}^{ - 3/4}h}\)成尺度的子层。Calmet和Magnaudet先前提出的标度律[J]。液体。械。474,355-378(2003)]被认为是成立的,但有以下例外。在薄层中,涡度的表面平行分量的强度迅速降至零,这里发现它与Kolmogorov长度尺度\(\boldsymbol{{\ell _{\boldsymbol{K}}}}\)成比例,而与近表面粘性尺度\(\boldsymbol{{\ell _{\boldsymbol{V}}}}\)成比例。此外,我们认为Kolmogorov长度尺度是自由表面附近平均速度梯度的相关尺度。在Kolmogorov亚层\(\boldsymbol{{\delta _{\boldsymbol{K}}} \approx 20{\ell _{\boldsymbol{K}}}}\)中,平均速度梯度和涡度面平行分量的波动强度均衰减为零。另一方面,在靠近自由表面的层中,壁法向湍流强度线性下降至零,用\(\boldsymbol{{\ell _{\boldsymbol{V}}}}\)而不是像Calmet和Magnaudet所建议的\(\boldsymbol{{\ell _{\boldsymbol{K}}}}\)来表示。对应的近地表粘性亚层测量值\(\boldsymbol{{\delta _{\boldsymbol{V}}} \approx {\ell _{\boldsymbol{V}}}}\)。重要的是,\(\boldsymbol{{\boldsymbol{R}}{{\boldsymbol{e}}_\tau } \geq 400}\)的顺流湍流强度分布表明,自由滑移边界的影响基本上通过增强的超大尺度运动的出现一直渗透到固体壁面(\(\boldsymbol{{\delta _{{\boldsymbol{SIL}}}} \approx h}\))。相反,表面法向湍流强度被阻尼到零的层被限制在自由表面(\(\boldsymbol{{\delta _{{\boldsymbol{NVD}}}} \approx 0.3h}\))。因此,受表面影响区域的划分必须扩展到跨越整个通道高度\(\boldsymbol{h}\)的四层结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
How Far Does the Influence of the Free Surface Extend in Turbulent Open Channel Flow?

Turbulent open channel flow is known to feature a multi-layer structure near the free surface. In the present work we employ direct numerical simulations considering Reynolds numbers up to \(\boldsymbol{R{e_\tau } = 900}\) and domain sizes large enough (\(\boldsymbol{{L_x} = 12\pi h}\), \(\boldsymbol{{L_z} = 4\pi h}\)) to faithfully capture the effect of very-large-scale motions in order to test the proposed scaling laws and ultimately answer the question: How far does the influence of the free surface extend? In the region near the free surface, where fluctuation intensities of velocity and vorticity become highly anisotropic, we observe the previously documented triple-layer structure, consisting of a wall-normal velocity damping layer that scales with the channel height \(h\), and two sublayers that scale with the near-surface viscous length scale \(\boldsymbol{{\ell _{\boldsymbol{V}}} = {\boldsymbol{Re}}_{\boldsymbol{b}}^{ - 1/2}h}\) and with the Kolmogorov length scale \(\boldsymbol{{\ell _{\boldsymbol{K}}} = {\boldsymbol{Re}}_{\boldsymbol{b}}^{ - 3/4}h}\), respectively. The scaling laws previously proposed by Calmet and Magnaudet [J. Fluid. Mech. 474, 355–378 (2003)] are found to hold with the following exceptions. The thin layer, where the intensity of surface-parallel components of the vorticity rapidly decreases to zero, is here found to scale with the Kolmogorov length scale \(\boldsymbol{{\ell _{\boldsymbol{K}}}}\) rather than with the near-surface viscous scale \(\boldsymbol{{\ell _{\boldsymbol{V}}}}\). In addition, we argue that the Kolmogorov length scale is the relevant scale for the mean velocity gradient near the free surface. Both the mean velocity gradient and the fluctuation intensity of the surface-parallel component of vorticity decay to zero in the Kolmogorov sublayer \(\boldsymbol{{\delta _{\boldsymbol{K}}} \approx 20{\ell _{\boldsymbol{K}}}}\). On the other hand, the layer, where the wall-normal turbulence intensity decreases linearly to zero near the free surface, scales with \(\boldsymbol{{\ell _{\boldsymbol{V}}}}\) rather than \(\boldsymbol{{\ell _{\boldsymbol{K}}}}\) as suggested by Calmet and Magnaudet. The corresponding near-surface viscous sublayer measures \(\boldsymbol{{\delta _{\boldsymbol{V}}} \approx {\ell _{\boldsymbol{V}}}}\). Importantly, the streamwise turbulence intensity profile for \(\boldsymbol{{\boldsymbol{R}}{{\boldsymbol{e}}_\tau } \geq 400}\) suggests that the influence of the free-slip boundary penetrates essentially all the way down to the solid wall through the appearance of enhanced very-large-scale motions (\(\boldsymbol{{\delta _{{\boldsymbol{SIL}}}} \approx h}\)). In contrast, the layer where the surface-normal turbulence intensity is damped to zero is restricted to the free surface (\(\boldsymbol{{\delta _{{\boldsymbol{NVD}}}} \approx 0.3h}\)). As a consequence, the partitioning of the surface-influenced region has to be expanded to a four-layer structure that spans the entire channel height \(\boldsymbol{h}\).

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来源期刊
Flow, Turbulence and Combustion
Flow, Turbulence and Combustion 工程技术-力学
CiteScore
5.70
自引率
8.30%
发文量
72
审稿时长
2 months
期刊介绍: Flow, Turbulence and Combustion provides a global forum for the publication of original and innovative research results that contribute to the solution of fundamental and applied problems encountered in single-phase, multi-phase and reacting flows, in both idealized and real systems. The scope of coverage encompasses topics in fluid dynamics, scalar transport, multi-physics interactions and flow control. From time to time the journal publishes Special or Theme Issues featuring invited articles. Contributions may report research that falls within the broad spectrum of analytical, computational and experimental methods. This includes research conducted in academia, industry and a variety of environmental and geophysical sectors. Turbulence, transition and associated phenomena are expected to play a significant role in the majority of studies reported, although non-turbulent flows, typical of those in micro-devices, would be regarded as falling within the scope covered. The emphasis is on originality, timeliness, quality and thematic fit, as exemplified by the title of the journal and the qualifications described above. Relevance to real-world problems and industrial applications are regarded as strengths.
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