Lateral dispersion in random cylinder arrays at high Reynolds number
Lateral dispersion in random cylinder arrays at high Reynolds number
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DOI：
10.1017/s0022112008000505
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发表时间：
2008-03
影响因子：
3.7
通讯作者：
Y. Tanino;H. Nepf
中科院分区：
文献类型：
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作者：
Y. Tanino;H. Nepf
利用激光诱导荧光技术，测量了固体体积分数φ=0.010-0.35时，随机排列的刚性突起圆柱体中被动溶质的横向弥散。这样的密度与在水生植物树冠中观察到的密度一致，并补充了球体填充床中的密度，其中φ≥为0.5。本文主要针对大于Res=0.031的孔雷诺数，我们的实验室实验表明，空间平均湍流强度和Kyy/(Upd)，即用流体体积中的平均速度归一化的横向弥散系数Up和圆柱体直径d，与Re无关。首先，Kyy/(Upd)随φ从φ=0.031增加到φ=25%而迅速增加。然后，Kyy/(Upd)从φ=0.031降至φ=0.2。最后，Kyy/(Upd)再次以更缓慢的方式增加，从φ=0.20到φ=0.35。由于圆柱体的存在产生了空间不均匀的速度场，所提出的湍流扩散模型和现有的弥散模型的线性叠加可以准确地描述这些观测结果。湍流扩散的贡献与平均湍流强度、湍流混合的特征长度尺度和有效孔隙率成比例关系。从圆柱尾迹产生的湍动能与其粘性耗散之间的平衡出发，预测了给定圆柱直径和圆柱密度时的平均湍流强度是形状阻力系数和积分长度尺度lt的函数。我们提出并实验验证了lt=min{d，<sn>A}，其中<sn>A是阵列中的圆柱体与其最近邻体之间的平均面间距离。我们进一步提出，只有混合长度尺度大于d的湍流涡才对净横向弥散有显著贡献，并且相邻圆柱体中心之间的距离必须大于r*，才能使它们之间的孔隙空间包含这样的涡流。如果积分长度标度和用于混合的长度标度相等，则r*=2d。我们的实验室数据与基于r*这一定义的预测很好地吻合。
Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction φ=0.010–0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where φ≥0.5. This paper focuses on pore Reynolds numbers greater than Res=250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and Kyy/(Upd), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, Up, and the cylinder diameter, d, are independent of Res. First, Kyy/(Upd) increases rapidly with φ from φ =0 to φ=0.031. Then, Kyy/(Upd) decreases from φ=0.031 to φ=0.20. Finally, Kyy/(Upd) increases again, more gradually, from φ=0.20 to φ=0.35. These observations are accurately described by the linear superposition of the proposed model of turbulent diffusion and existing models of dispersion due to the spatially heterogeneous velocity field that arises from the presence of the cylinders. The contribution from turbulent diffusion scales with the mean turbulence intensity, the characteristic length scale of turbulent mixing and the effective porosity. From a balance between the production of turbulent kinetic energy by the cylinder wakes and its viscous dissipation, the mean turbulence intensity for a given cylinder diameter and cylinder density is predicted to be a function of the form drag coefficient and the integral length scale lt. We propose and experimentally verify that lt=min{d, 〈sn〉A}, where 〈sn〉A is the average surface-to-surface distance between a cylinder in the array and its nearest neighbour. We farther propose that only turbulent eddies with mixing length scale greater than d contribute significantly to net lateral dispersion, and that neighbouring cylinder centres must be farther than r* from each other for the pore space between them to contain such eddies. If the integral length scale and the length scale for mixing are equal, then r*=2d. Our laboratory data agree well with predictions based on this definition of r*.