Resistance in Steep Open Channels due to Randomly Distributed Macroroughness Elements at Large Froude Numbers
Publication: Journal of Hydrologic Engineering
Volume 22, Issue 12
Abstract
Energy loss in a steep open channel due to randomly spaced spherically shaped macroroughness elements such as boulders was investigated using a three-dimensional fluid dynamics solver. First, a relationship for energy loss at large Froude numbers due to a single boulder was derived as a function of flow rate, flow depth, and boulder diameter. Nondimensional energy loss increases with Froude number and decreases with the relative submergence. However, the exponents in the power law relationship are different for three different ranges of submergence ratio: , 0.5–1.0, and . The energy loss attributable to a cluster of boulders depends on cluster density, Froude number, and submergence ratio. For the same number of boulders, energy loss decreases as cluster density increases. However, variation in the pattern of boulder arrangement has only a marginal effect () when the submergence ratio is more than 0.5. The simple procedure proposed for estimating energy loss due to a cluster of randomly distributed boulders of equal size predicts energy loss within 10% accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge financial support from the Indo-German Centre for Sustainability (IGCS) funded by the Department of Science and Technology, India, through the Indian Institute of Technology Madras and German Academic Exchange Service (DAAD) on behalf of the German Federal Ministry of Education and Research (BMBF).
References
Abdulla, A. A. (2013). “Three-dimensional flow model for different cross-section high-velocity channels.” Ph.D. thesis, School of Marine Sciences and Engineering, Univ. of Plymouth, Plymouth, U.K.
Agostino, V. D., and Michelini, T. (2015). “On kinematics and flow velocity prediction in step-pool channels.” Water Resour. Res., 51(6), 4650–4667.
Aguirre-Pe, J., and Fuentes, R. (1990). “Resistance to flow in steep rough streams.” J. Hydraul. Eng., 1374–1387.
Alonso, R. L., Fernández, J. B., and Cugat, M. C. (2009). “Flow resistance equations for mountain rivers.” Forest Syst., 18(1), 81–91.
ANSYS-CFX version 14.0 [Computer software]. ANSYS, Canonsburg, PA.
Baki, A. B. M., Zhu, D. Z., and Rajaratnam, N. (2014). “Mean flow characteristics in a rock-ramp type fish pass.” J. Hydraul. Eng., 156–168.
Baki, A. B. M., Zhu, D. Z., and Rajaratnam, N. (2016). “Flow simulation in a rock-ramp fish pass.” J. Hydraul. Eng., 4016031.
Bathurst, J. C. (1985). “Flow resistance estimation in mountain rivers.” J. Hydraul. Eng., 625–643.
Bathurst, J. C. (2002). “At-a-site variation and minimum flow resistance for mountain rivers.” J. Hydrol., 269(1–2), 11–26.
Bathurst, J. C., Li, R. M., and Simons, D. B. (1979). “Hydraulics of mountain rivers.”, Civil Engineering Dept., Colorado State Univ., Fort Collins, CO.
Bathurst, J. C., Li, R. M., and Simons, R. M. (1981). “Resistance equation for large-scale roughness.” J. Hydraul. Div., 107(12), 1593–1613.
Cassan, L., and Laurens, P. (2016). “Design of emergent and submerged rock-ramp fish passes.” Knowl. Manage. Aquat. Ecosyst., 417(10), 45.
Cassan, L., Tien, T., Courret, D., Laurens, P., and Dartus, D. (2014). “Hydraulic resistance of emergent macroroughness at large Froude numbers: Design of nature-like fishpasses.” J. Hydraul. Eng., 4014043.
Castillo, L. G., Carrillo, J. M., García, J. T., and Vigueras-Rodríguez, A. (2014). “Numerical simulations and laboratory measurements in hydraulic jumps.” Proc., 11th Int. Conf. on Hydroinformatics, CUNY Academic Works, New York.
Chin, A. (2003). “The geomorphic significance of step-pools in mountain streams.” Geomorphology, 55(1–4), 125–137.
Comiti, F., Mao, L., Wilcox, A., Wohl, E. E., and Lenzi, M. A. (2007). “Field-derived relationships for flow velocity and resistance in high-gradient streams.” J. Hydrol., 340(1–2), 48–62.
Evans, M. W., Harlow, F. H., and Bromberg, E. (1957). “The particle-in-cell method for hydrodynamic calculations.”, Lol Alamos Scientific Laboratory, Los Alamos.
Ferguson, R. (2007). “Flow resistance equations for gravel- and boulder-bed streams.” Water Resour. Res., 43(5), 1–12.
Ferguson, R. (2010). “Time to abandon the Manning equation?” Earth Surf. Processes Landforms, 35(15), 1873–1876.
Ferro, V. (2003). “Flow resistance in gravel-bed channels with large-scale roughness.” Earth Surf. Processes Landforms, 28(12), 1325–1339.
Haltigin, T. W., Biron, P. M., and Lapointe, M. F. (2007). “Three-dimensional numerical simulation of flow around stream deflectors: The effect of obstruction angle and length.” J. Hydraul. Res., 45(2), 227–238.
Hey, R. D. (1979). “Flow resistance in gravel-bed rivers.” J. Hydraul. Div., 105(4), 365–379.
Hirt, C. W., and Nichols, B. D. (1981). “Volume of fluid (VOF) method for the dynamics of free boundaries.” J. Comput. Phys., 39(1), 201–225.
Jones, W. P., and Launder, B. E. (1972). “The prediction of laminarization with a two-equation model of turbulence.” Int. J. Heat Mass Transfer, 15(2), 301–314.
Jordanova, A. A. (2008). “Low flow hydraulics in rivers for environmental applications in South Africa.” Ph.D. dissertation, Univ. of Witwatersrand, Johannesburg, South Africa.
Ma, L., Ashorth, P. I., Best, J. L., Elliott, L., Ingham, D. B., and Whitcombe, L. J. (2002). “Computational fluid dynamics and the physical modelling of an upland urban river.” Geomorphology, 44(3), 375–391.
Maloney, K. O., Munguia, P., and Mitchell, R. M. (2011). “Anthropogenic disturbance and landscape patterns affect diversity patterns of aquatic benthic macroinvertebrates.” J. North Am. Benthol. Soc., 30(1), 284–295.
Marriner, B. A., Baki, A. B. M., Zhu, D. Z., Thiem, J. D., Cooke, S. J., and Katopodis, C. (2014). “Field and numerical assessment of turning pool hydraulics in a vertical slot fishway.” Ecol. Eng., 63, 88–101.
Marriott, M. J., and Jayaratne, R. (2010). “Hydraulic roughness—Links between Manning’s coefficient, Nikuradse’s equivalent sand roughness and bed grain size.” Advances in computing and technology, Univ. of East London, London, 27–32.
Meier, W. K., and Reichert, P. (2005). “Mountain streams—Modeling hydraulics and substance transport.” J. Environ. Eng., 252–261.
Modrick, T. M., and Georgakakos, K. P. (2014). “Regional bankfull geometry relationships for southern California mountain streams and hydrologic applications.” Geomorphology, 221, 242–260.
Oertel, M., Peterseim, S., and Schlenkhoff, A. (2011). “Drag coefficients of boulders on a block ramp due to interaction processes.” J. Hydraul. Eng., 49(3), 372–377.
Pagliara, S., and Chiavaccini, P. (2006). “Flow resistance of rock chutes with protruding boulders.” J. Hydraul. Eng., 545–552.
Pagliara, S., and Dazzini, D. (2002). “Hydraulics of block ramp for riverrestoration.” Proc., New Trends in Water and Environmental Engineering for Safety and Life: Eco-Compatible Solution for Aquatic Environments, Capri, CSDU, Milano, Italy.
Pagliara, S., and Peruginelli, A. (2000). “Energy dissipation comparison among stepped channel, drop and ramp structures.” Proc., Workshop on Hydraulics of Stepped Spillways, A.A. Balkema, Rotterdam, Netherlands, 111–118.
Romero, M., Revollo, N., and Molina, J. (2010). “Flow resistance in steep mountain rivers in Bolivia.” J. Hydrodyn., 22(5), 702–707.
Salaheldin, T. M., Imran, J., and Chaudhry, M. H. (2004). “Numerical modeling of three-dimensional flow field around circular piers.” J. Hydraul. Eng., 91–100.
Shen, Y., and Diplas, P. (2008). “Application of two- and three-dimensional computational fluid dynamics models to complex ecological stream flows.” J. Hydrol., 348(1–2), 195–214.
Soto, A. U., and Madrid-Aris, M. (1994). Roughness coefficient in mountain rivers, ASCE, New York, 1–8.
Thompson, S. M., and Campbell, P. L. (1979). “Hydraulics of a large channel paved with boulders.” J. Hydraul. Res., 17(4), 341–354.
Thorne, C. R., and Zevenbergen, L. W. (1985). “Estimating mean velocity in mountain rivers.” J. Hydraul. Eng., 612–624.
Xiang, M., Cheung, S. C. P., Tu, J. Y., and Zhang, W. H. (2014). “A multi-fluid modelling approach for the air entrainment and internal bubbly flow region in hydraulic jumps.” Ocean Eng., 91, 51–63.
Yochum, S. E., Bledsoe, P. B., David, G. C. L., and Wohl, E. (2012). “Velocity prediction in high gradient channels.” J. Hydrol., 424, 84–98.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 12 • December 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 8, 2017
Accepted: Jun 1, 2017
Published online: Oct 13, 2017
Published in print: Dec 1, 2017
Discussion open until: Mar 13, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.