Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-23T06:50:07.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Lateral dispersion in random cylinder arrays at high Reynolds number

Published online by Cambridge University Press:  26 March 2008

YUKIE TANINO  and
HEIDI M. NEPF
YUKIE TANINO
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USAytanino@alum.mit.edu; hmnepf@mit.edu
HEIDI M. NEPF
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USAytanino@alum.mit.edu; hmnepf@mit.edu
Get access Rights & Permissions [Opens in a new window]

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 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*.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 339 - 371
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baldyga, J. & Bourne, J. R. 1999 Turbulent Mixing and Chemical Reactions. John Wiley & Sons.Google Scholar
Bear, J. 1979 Hydraulics of Groundwater. McGraw-Hill.Google Scholar
Burke, R. W. & Stolzenbach, K. D. 1983 Free surface flow through salt marsh grass. MIT Sea Grant College Program Rep. MITSG 83-16. Massachusetts Institute of Technology, Cambridge.Google Scholar
Corrsin, S. 1974 Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18A, 25–60.Google Scholar
Davidson, M. J., Mylne, K. R., Jones, C. D., Phillips, J. C., Perkins, R. J., Fung, J. C. H. & Hunt, J. C. R. 1995 Plume dispersion through large groups of obstacles – a field investigation. Atmos. Environ. 29 (22), 3245–3256.CrossRefGoogle Scholar
Devore, J. L. 2000 Probabilty and Statistics For Engineering and the Sciences, 5th edn. Pacific Grove, California: Duxbury Thomson Learning.Google Scholar
Dullien, F. A. L. 1979 Porous Media. Fluid Transport and Pore Structure. Academic Press.Google Scholar
Finnigan, J. J. 1985 Turbulent transport in flexible plant canopies. In The Forest-Atmosphere Interaction (ed. Hutchison, B. A. & Hicks, B. B.), pp. 443–480. D. Reidel.CrossRefGoogle Scholar
Hackert, C. L., Ellzey, J. L., Ezekoye, O. A. & Hall, M. J. 1996 Transverse dispersion at high Peclet numbers in short porous media. Exps. Fluids 21, 286–290.CrossRefGoogle Scholar
Han, N.-W., Bhakta, J. & Carbonell, R. G. 1985 Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution. AIChE J. 31 (2), 277–288.Google Scholar
Jolls, K. R. & Hanratty, T. J. 1966 Transition to turbulence for flow through a dumped bed of spheres. Chem. Engng Sci. 21, 1185–1190.CrossRefGoogle Scholar
Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows. Their Structure and Measurement. Oxford University Press.CrossRefGoogle Scholar
Koch, D. L. & Brady, J. F. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399–427.CrossRefGoogle Scholar
Koch, D. L. & Brady, J. F. 1986 The effective diffusivity of fibrous media. AIChE J. 32 (4), 575–591.Google Scholar
Koch, D. L. & Ladd, A. J. C. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 31–66.CrossRefGoogle Scholar
Lam, K., Li, J. Y., Chan, K. T. & So, R. M. C. 2003 Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low {R}eynolds number. J. Fluids Struct. 17, 665–679.CrossRefGoogle Scholar
Leonard, L. A. & Luther, M. E. 1995 Flow hydrodynamics in tidal marsh canopies. Limnol. Oceanogr. 40 (8), 1474–1484.CrossRefGoogle Scholar
Lienhard, J. H. 1966 Synopsis of lift, drag, and vortex frequency data for rigid circular cylinders. Bulletin 300. Washington State University, College of Engineering Research Division, Technical Extension Service, Washington.Google Scholar
Masuoka, T. & Takatsu, Y. 1996 Turbulence model for flow through porous media. Intl J. Heat Mass Transfer 39 (13), 2803–2809.Google Scholar
Mazda, Y., Wolanski, E., King, B., Sase, A., Ohtsuka, D. & Magi, M. 1997 Drag force due to vegetation in mangrove swamps. Mangroves and Salt Marshes 1 (3), 193–199.Google Scholar
Meneghini, J. R., Saltara, F., Siqueira, C. L. R. & Ferrari, J. A. Jr. 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J. Fluids Struct. 15, 327–350.CrossRefGoogle Scholar
Mickley, H. S., Smith, K. A. & Korchak, E. I. 1965 Fluid flow in packed beds. Chem. Engng Sci. 20, 237–246.Google Scholar
Nepf, H. M. 1999 Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour. Res. 35 (2), 479–489.CrossRefGoogle Scholar
Nepf, H. M., Sullivan, J. A. & Zavistoski, R. A. 1997 A model for diffusion within emergent vegetation. Limnol. Oceanogr. 42 (8), 1735–1745.CrossRefGoogle Scholar
Neumeier, U. & Amos, C. L. 2006 The influence of vegetation on turbulence and flow velocities in European salt-marshes. Sedimentology 53, 259–277.Google Scholar
Nikora, V. I. 2000 Comment on “Drag, turbulence, and diffusion in flow through emergent vegetation” by H. M. Nepf. Water Resour. Res. 36 (7), 1985–1986.Google Scholar
Pearson, B. R., Krogstad, P.-Å. & van de Water, W. 2002 Measurements of the turbulent energy dissipation rate. Phys. Fluids 14 (3), 1288–1290.Google Scholar
Pereira, J. C. F., Malico, I., Hayashi, T. C. & Raposo, J. 2005 Experimental and numerical characterization of the transverse dispersion at the exit of a short ceramic foam inside a pipe. Intl J. Heat Mass Transfer 48, 1–14.Google Scholar
Petryk, S. 1969 Drag on cylinders in open channel flow. PhD thesis, Colorado State University, Fort Collins, Colorado.Google Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44 (1), 1–25.CrossRefGoogle Scholar
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary Layer Met. 22, 79–90.CrossRefGoogle Scholar
Serra, T., Fernando, H. J. S. & Rodriguez, R. V. 2004 Effects of emergent vegetation on lateral diffusion in wetlands. Water Res. 38 (1), 139–147.Google Scholar
Spielman, L. & Goren, S. L. 1968 Model for predicting pressure drop and filtration efficiency in fibrous media. Envir. Sci. Tech. 2 (4), 279–287.Google Scholar
Sullivan, J. A. 1996 Effects of Marsh Grass on Diffusivity. Master's thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Tanino, Y. & Nepf, H. M. 2007 Experimental investigation of lateral dispersion in aquatic canopies. In Proc. 32nd Congress of IAHR (ed. Di Silvio, G. & Lanzoni, S.).Google Scholar
Tanino, Y. & Nepf, H. M. 2008 Laboratory investigation of mean drag in a random array of rigid, emergent cylinders. J. Hydraul. Engng 134 (1), 34–41.Google Scholar
Taylor, J. R. 1997 An Introduction to Error Analysis. The Study of Uncertainties in Physical Mesurements, 2nd edn. Sausalito, California: University Science Books.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. The MIT Press.Google Scholar
Tummers, M. J. & Passchier, D. M. 2001 Spectral analysis of biased LDA data. Meas. Sci. Technol. 12, 1641–1650.CrossRefGoogle Scholar
Valiela, I., Teal, J. M. & Deuser, W. G. 1978 The nature of growth forms in the salt marsh grass Spartina alterniflora. Am. Nat. 112 (985), 461–470.Google Scholar
White, B. L. 2002 Transport in random cylinder arrays: A model for aquatic canopies. Master's thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
White, B. L. & Nepf, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43–79.Google Scholar
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 1–18.CrossRefGoogle Scholar
Yevseyev, A. R., Nakoryakov, V. E. & Romanov, N. N. 1991 Experimental investigation of a turbulent filtration flow. Intl J. Multiphase Flow 17 (1), 103–118.Google Scholar
Zavistoski, R. A. 1994 Hydrodynamic effects of surface piercing plants. Master's thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Zhang, H. J. & Zhou, Y. 2001 Effect of unequal cylinder spacing on vortex streets behind three side-by-side cylinders. Phys. Fluids 13 (12), 3675–3686.Google Scholar