Scalar transport in random cylinder arrays at moderate Reynolds number
Scalar transport in random cylinder arrays at moderate Reynolds number
复制标题
DOI：
10.1017/s0022112003004579
复制
发表时间：
2003-06
影响因子：
3.7
通讯作者：
B. White;H. Nepf
中科院分区：
文献类型：
--
作者：
B. White;H. Nepf
本文从理论上描述和实验上验证了被动示踪剂在随机圆柱阵列中纵向弥散的两种机制。我们专注于中等雷诺数的顺序为10-1000，特别是范围内的特点是不稳定的缸尾流。在这种情况下，两种机制有助于分散，每一个都与不同的气缸尾流区域相关：（i）靠近每个气缸的非定常回流区，以及（ii）每个气缸后面的速度缺陷，其在气缸下游延伸超过气缸间距的数量级的距离。第一种机制称为涡捕分散，是由于示踪剂被夹带到非定常回流区，在那里它被暂时捕获，然后释放。根据回流区的停留时间和大小，推导出了这种分散机制的理论表达式。第二种机制是由于通过由尾流速度缺陷的随机分布产生的随机速度场的平流。我们推导出一个表达式的缺陷背后的平均圆柱体，并表明，它衰减由于阵列阻力的长度尺度称为衰减长度，这是圆柱体间距的顺序。每个圆柱后面的尾流缺陷的叠加产生了随机速度场。分散的理论预测同意非常好的实验室圆柱阵列中的示踪剂运输的观察，正确地捕捉阵列密度和雷诺数的依赖。实验室研究还记录了在圆柱雷诺数$\约200$的小尺度混合的过渡。低于这个极限，个别丝示踪剂保持不同，产生显着的波动，在当地的浓度场。在较高的雷诺数，圆柱尾迹提供足够的湍流擦除细丝签名和平滑的示踪剂分布。
This paper theoretically describes and experimentally verifies two mechanisms leading to longitudinal dispersion of a passive tracer in a random array of circular cylinders. We focus on moderate Reynolds numbers of order 10–1000, specifically the range characterized by unsteady cylinder wakes. In this regime, two mechanisms contribute to dispersion, each associated with a distinct region of the cylinder wakes: (i) the unsteady recirculation zone close to each cylinder, and (ii) the velocity defect behind each cylinder, which extends downstream of the cylinder over a distance of the order of the cylinder spacing. The first mechanism, termed vortex-trapping dispersion, is due to the entrainment of tracer into the unsteady recirculation zone, where it is momentarily trapped and then released. A theoretical expression for this dispersive mechanism is derived in terms of the residence time and size of the recirculation zone. The second mechanism is due to advection through the random velocity field created by the random distribution of the wake velocity defect. We derive an expression for the defect behind an average cylinder, and show that it decays owing to array drag over a length scale called the attenuation length, which is of the order of the cylinder spacing. The superposition of the wake defect behind each cylinder creates the random velocity field. Theoretical predictions for dispersion agree very well with observations of tracer transport in a laboratory cylinder array, correctly capturing the dependence on array density and Reynolds number. The laboratory studies also document a transition in small-scale mixing at cylinder Reynolds number $\approx 200$. Below this limit, individual filaments of tracer remain distinct, producing significant fluctuations in the local concentration field. At higher Reynolds number, cylinder wakes contribute sufficient turbulence to erase the filament signature and smooth the tracer distribution.