Calculation of Drag Coefficient for Arrays of Emergent Circular Cylinders with Pseudofluid Model
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 6
Abstract
The emergent vegetation in open-channel flows is usually simulated using arrays of circular cylinders in laboratory experiments. Analysis of recent experimental data reveals that for a given Reynolds number, the drag coefficient of a cylinder in a dense array is larger than that of an isolated cylinder. A new approach is applied to parameterize the drag coefficient and Reynolds number for flows through arrays of emergent cylinders. The approach is developed based on the concept of pseudofluid, for which an analogy is made between the cylinder-induced drag in an open-channel flow and that induced by the cylinder settling in a stationary fluid. With the proposed parameterization, the experimental database is successfully reorganized in such a way that a generalized drag coefficient is related to a generalized Reynolds number by one single curve, which is valid for a wide range of solid fractions and Reynolds numbers. However, it should be mentioned that only rigid circular stems are considered in this study and their induced drag is assumed to be dominant in comparison with the channel bed resistance.
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Acknowledgments
This study was partially supported by the Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, P. R. China. The author is grateful to the comments and suggestions, provided by the reviewers and editors, which yield significant improvements in the presentation of the results obtained.
References
Baptist, M. J., et al. (2007). “On inducing equations for vegetation resistance.” J. Hydraul. Res., 45(4), 435–450.
Cheng, N. S. (1997). “Effect of concentration on settling velocity of sediment particles.” J. Hydraul. Eng., 123(8), 728–731.
Cheng, N. S. (2011). “Representative roughness height of submerged vegetation.” Water Resour. Res., 47(W08517), 1–18.
Cheng, N. S., and Chiew, Y. M. (1999). “Incipient sediment motion with upward seepage.” J. Hydraul. Res., 37(5), 665–681.
Cheng, N. S., and Law, A. W. K. (2003). “Exponential formula for computing effective viscosity.” Powder Technol., 129(1–3), 156–160.
Cheng, N. S., and Nguyen, H. T. (2011). “Hydraulic radius for evaluating resistance induced by simulated emergent vegetation in open-channel flows.” J. Hydraul. Eng., 137(9), 995–1004.
Cheng, N. S., Nguyen, H. T., Tan, S. K., and Shao, S. D. (2012). “Scaling of velocity profiles for depth-limited open channel flows over simulated rigid vegetation.” J. Hydraul. Eng., 138(8), 673–683.
Clift, R., Grace, J. R., and Weber, M. E. (1978). Bubbles, drops, and particles, Academic Press, New York.
Einstein, A. (1906). “A new determination of the molecular dimensions.” Annalen Der Physik, 324(2), 289–306.
Ferreira, R. M. L., Ricardo, A. M., and Franca, M. J. (2009). “Discussion of ‘Laboratory investigation of mean drag in a random array of rigid, emergent cylinders’ by Yukie Tanino and Heidi M. Nepf.” J. Hydraul. Eng., 135(8), 690–693.
Finn, R. K. (1953). “Determination of the drag on a cylinder at low Reynolds numbers.” J. Appl. Phys., 24(6), 771–773.
Gibilaro, L. G. (2001). Fluidization-dynamics: The formulation and applications of a predictive theory for the fluidized state, Butterworth-Heinemann, Oxford, UK.
Gibilaro, L. G., Gallucci, K., Di Felice, R., and Pagliai, P. (2007). “On the apparent viscosity of a fluidized bed.” Chem. Eng. Sci., 62(1–2), 294–300.
Huthoff, F., Augustijn, D. C. M., and Hulscher, S. J. M. H. (2007). “Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation.” Water Resour. Res., 43(6), W06413, 1–10.
Ishikawa, Y., Mizuhara, K., and Ashida, S. (2000). “Effect of density of trees on drag exerted on trees in river channels.” J. For. Res., 5(4), 271–279.
James, C. S., Birkhead, A. L., Jordanova, A. A., and O’Sullivan, J. J. (2004). “Flow resistance of emergent vegetation.” J. Hydraul. Res., 42(4), 390–398.
Jayaweera, K. O. L. F., and Mason, B. J. (1965). “The behaviour of freely falling cylinders and cones in a viscous fluid.” J. Fluid Mech., 22(4), 709–720.
Jordanova, A. A., and James, C. S. (2003). “Experimental study of bed load transport through emergent vegetation.” J. Hydraul. Eng., 129(6), 474–478.
Kothyari, U. C., Hashimoto, H., and Hayashi, K. (2009a). “Effect of tall vegetation on sediment transport by channel flows.” J. Hydraul. Res., 47(6), 700–710.
Kothyari, U. C., Hayashi, K., and Hashimoto, H. (2009b). “Drag coefficient of unsubmerged rigid vegetation stems in open channel flows.” J. Hydraul. Res., 47(6), 691–699.
Kouwen, N., Unny, T. E., and Hill, H. M. (1969). “Flow retardance in vegetated channels.” J. Irrig. Drain. Div., 95(2), 329–342.
Kundu, P. K., Cohen, I. M., and Hu, H. H. (2004). Fluid mechanics, Elsevier Academic, Amsterdam, The Netherlands.
Lamb, H. S. (1945). Hydrodynamics, Dover Publications, New York.
Liu, D., Diplas, P., Fairbanks, J. D., and Hodges, C. C. (2008). “An experimental study of flow through rigid vegetation.” J. Geophys. Res. Earth Surf., 113, F04015, 1–16.
Luhar, M., Rominger, J., and Nepf, H. (2008). “Interaction between flow, transport and vegetation spatial structure.” Environ. Fluid Mech., 8(5–6), 423–439.
Nepf, H., Ghisalberti, M., White, B., and Murphy, E. (2007). “Retention time and dispersion associated with submerged aquatic canopies.” Water Resour. Res., 43(4), W04422, 1–10.
Nepf, H. M. (1999). “Drag, turbulence, and diffusion in flow through emergent vegetation.” Water Resour. Res., 35(2), 479–489.
Niemann, H. J., and Holscher, N. (1990). “A review of recent experiments on the flow past circular-cylinders.” J. Wind Eng. Ind. Aerodyn., 33(1–2), 197–209.
Poletto, M., and Joseph, D. D. (1995). “Effective density and viscosity of a suspension.” J. Rheol., 39(2), 323–343.
Stone, B. M., and Shen, H. T. (2002). “Hydraulic resistance of flow in channels with cylindrical roughness.” J. Hydraul. Eng., 128(5), 500–506.
Sumer, B. M., and Fredsøe, J. (1997). Hydrodynamics around cylindrical structures, World Scientific, Singapore.
Tanino, Y., and Nepf, H. M. (2008). “Laboratory investigation of mean drag in a random array of rigid, emergent cylinders.” J. Hydraul. Eng., 134(1), 34–41.
Tritton, D. J. (1959). “Experiments on the flow past a circular cylinder at low Reynolds numbers.” J. Fluid Mech., 6(4), 547–567.
Wan, Z., and Wang, Z. (1994). Hyperconcentrated flow, A.A. Balkema, Rotterdam, The Netherlands.
Wieselsberger, C. (1922). “New data on the laws of fluid resistance.”, National Advisory Committee for Aeronautics, Washington, DC.
Williamson, C. H. K. (1996). “Vortex dynamics in the cylinder wake.” Annu. Rev. Fluid Mech., 28(1), 477–539.
Zdravkovich, M. M. (1997). Flow around circular cylinders: A comprehensive guide through flow phenomena, experiments, applications, mathematical models, and computer simulations, Oxford University Press, Oxford, UK.
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Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 6 • June 2013
Pages: 602 - 611
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 5, 2012
Accepted: Dec 17, 2012
Published online: Dec 19, 2012
Published in print: Jun 1, 2013
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