Lateral dispersion in random cylinder arrays at high Reynolds number

Yukie Tanino, Heidi M. Nepf

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Abstract

Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction phi=0.010-0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where phi >= 0.5. This paper focuses on pore Reynolds numbers greater than Re-s = 250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and K-yy/(U(p)d), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, U-P,U- and the cylinder diameter, d, are independent of Re-s. First, K-yy/(U(p)d) increases rapidly with phi from phi = 0 to phi = 0.031. Then, K-yy/(U(p)d) decreases from phi = 0.031 to phi = 0.20. Finally, K-yy/(U(p)d) increases again, more gradually, from phi = 0.20 to phi = 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 l(t). We propose and experimentally verify that l(t) = min{d, < S-n > A}, where < S-n > 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*.

Original languageEnglish
Pages (from-to)339-371
Number of pages33
JournalJournal of Fluid Mechanics
Volume600
Early online date26 Mar 2008
DOIs
Publication statusPublished - Apr 2008

Cite this

Lateral dispersion in random cylinder arrays at high Reynolds number. / Tanino, Yukie; Nepf, Heidi M.

In: Journal of Fluid Mechanics, Vol. 600, 04.2008, p. 339-371.

Research output: Contribution to journalArticle

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abstract = "Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction phi=0.010-0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where phi >= 0.5. This paper focuses on pore Reynolds numbers greater than Re-s = 250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and K-yy/(U(p)d), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, U-P,U- and the cylinder diameter, d, are independent of Re-s. First, K-yy/(U(p)d) increases rapidly with phi from phi = 0 to phi = 0.031. Then, K-yy/(U(p)d) decreases from phi = 0.031 to phi = 0.20. Finally, K-yy/(U(p)d) increases again, more gradually, from phi = 0.20 to phi = 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 l(t). We propose and experimentally verify that l(t) = min{d, < S-n > A}, where < S-n > 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*.",
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T1 - Lateral dispersion in random cylinder arrays at high Reynolds number

AU - Tanino, Yukie

AU - Nepf, Heidi M.

PY - 2008/4

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N2 - Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction phi=0.010-0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where phi >= 0.5. This paper focuses on pore Reynolds numbers greater than Re-s = 250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and K-yy/(U(p)d), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, U-P,U- and the cylinder diameter, d, are independent of Re-s. First, K-yy/(U(p)d) increases rapidly with phi from phi = 0 to phi = 0.031. Then, K-yy/(U(p)d) decreases from phi = 0.031 to phi = 0.20. Finally, K-yy/(U(p)d) increases again, more gradually, from phi = 0.20 to phi = 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 l(t). We propose and experimentally verify that l(t) = min{d, < S-n > A}, where < S-n > 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*.

AB - Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction phi=0.010-0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where phi >= 0.5. This paper focuses on pore Reynolds numbers greater than Re-s = 250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and K-yy/(U(p)d), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, U-P,U- and the cylinder diameter, d, are independent of Re-s. First, K-yy/(U(p)d) increases rapidly with phi from phi = 0 to phi = 0.031. Then, K-yy/(U(p)d) decreases from phi = 0.031 to phi = 0.20. Finally, K-yy/(U(p)d) increases again, more gradually, from phi = 0.20 to phi = 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 l(t). We propose and experimentally verify that l(t) = min{d, < S-n > A}, where < S-n > 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*.

U2 - 10.1017/S0022112008000505

DO - 10.1017/S0022112008000505

M3 - Article

VL - 600

SP - 339

EP - 371

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -