Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 9
Abstract
Numerical modeling of bed-load transport in shallow flows, particularly oriented toward environmental flows, is an active field of research. Nevertheless, other possible applications exist. In particular, bed-load transport phenomena are relevant in urban drainage systems, including sewers. However, few applications of coupled two-dimensional (2D) shallow-water and bed-load transport models can be found, and their transfer from environmental applications—usually river and floodplain—into sewer applications requires some adaptation. Unlike to river systems, where there is a thick layer of sediment that constitutes a movable riverbed, sewer systems have thin layers of sediment that need to be removed, thus exposing a rigid, nonerodible surface. This problem requires careful numerical treatment to avoid generating errors and instability in the simulation. This paper deals with a numerical approach to tackle this issue in an efficient way that allows large-scale studies to be performed and provides empirical evidence that the proposed approach is accurate and applicable for sewage and channel-flushing problems.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was partially funded by the Spanish Ministry of Economy and Competitiveness through Grant MINECO/FEDER CGL2015-66114-R and by the ITN-Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7-PEOPLE-2013-ITN under REA Grant Agreement n_607394-SEDITRANS. The authors would like to acknowledge the collaboration of the Consorcio de Aguas de Bilbao Bizkaia (CABB) for access to the design plans and data for the stormsewer tank tested in this work. The authors also thank the Nvidia Corporation for the hardware donation used in this work through the CUDA Research Center programme.
References
Ashida, K., and Michiue, M. (1972). “Study on the hydraulic resistance and bed-load transport rate in alluvial streams.” Proc. Jpn. Soc. Civil Eng., 1972(206), 59–69.
Ashley, R. M., and Verbanck, M. A. (1996). “Mechanics of sewer sediment erosion and transport.” J. Hydraul. Res., 34(6), 753–770.
Bakhtyar, R., Barry, D., Jeng, D., and Yeganeh-Bakhtiary, A. (2009). “Modeling sediment transport in the swash zone: A review.” Ocean Eng., 227(9–10), 227–240.
Begnudelli, L., and Sanders, F. (2006). “Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying.” J. Hydr. Eng., 371–384.
Bohorquez, P., and Ancey, C. (2015). “Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation.” Earth Surf. Process. Landforms, 83, 36–54.
Butt, T., and Russel, P. (2000). “Hydrodynamics and cross-shore sediment transport in the swash-zone of natural beaches: A review.” J. Coastal Res., 16(2), 255–268.
Campisano, A., Creaco, E., and Modica, C. (2004). “Experimental and numerical analysis of the scouring effects of flushing waves on sediment deposits.” J. Hydrol., 299(3–4), 324–334.
Campisano, A., Creaco, E., and Modica, C. (2013). “Numerical modelling of sediment bed aggradation in open rectangular drainage channels.” Urban Water J., 10(6), 365–376.
Cao, Z., Day, R., and Egashira, S. (2002). “Coupled and decoupled numerical modeling of flow and morphological evolution in alluvial rivers.” J. Hydr. Eng., 306–321.
Castro-Díaz, M., Fernández-Nieto, E., Ferreiro, A., and Parés, C. (2009). “Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes.” Comput. Methods Appl. Mech. Eng., 198(33–36), 2520–2538.
Creaco, E., and Bertrand-Krajewski, J.-L. (2009). “Numerical simulation of flushing effect on sewer sediments and comparison of four sediment transport formulas.” J. Hydraul. Res., 47(2), 195–202.
Dettmar, J. (2007). A new planning procedure for sewer flushing, NOVATECH, Lyon, France.
Engelund, F., and Fredsoe, J. (1976). “Sediment transport model for straight alluvial channels.” Nordic Hydrol., 7(5), 293–306.
Fernandez-Luque, R., and Beek, R. V. (2010). “Erosion and transport of bed-load sediment.” J. Hydraul. Res., 14(2), 127–144.
Fernández-Nieto, E., Lucas, C., de Luna, T. M., and Cordier, S. (2014). “On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems.” Comput. Fluids, 91, 87–106.
Furbish, D. J., Haff, P. K., Roseberry, J. C., and Schmeeckle, M. W. (2012). “A probabilistic description of the bed load sediment flux. I: Theory.” J. Geophys. Res., 117(F3), 2156–2202.
Grass, A. (1983). “Sediment transport by waves and currents.”, SERC, London Center for Marine Technology, London.
Heyman, J., Bohorquez, P., and Ancey, C. (2016). “Entrainment, motion and deposition of coarse particles transported by water over a sloping mobile bed.” J. Geophys. Res., 121(10), 1931–1952.
Heyman, J., Ma, H. B., Mettra, F., and Ancey, C. (2014). “Spatial correlations in bed load transport: Evidence, importance and modeling.” J. Geophys. Res., 119(8), 1751–1767.
Hou, J., Liang, Q., Zhang, H., and Hinkelmann, R. (2015). “An efficient unstructured MUSCL scheme for solving the 2D shallow water equations.” Environ. Modell. Software, 66, 131–152.
Hudson, J., and Sweby, P. (2003). “Formulations for numerically approximating hyperbolic systems governing sediment transport.” J. Sci. Comput., 19(1–3), 225–252.
Juez, C., Lacasta, A., Murillo, J., and García-Navarro, P. (2016). “An efficient GPU implementation for a faster simulation of unsteady bed-load transport.” J. Hydraul. Res., 54(3), 275–288.
Juez, C., Murillo, J., and Garcia-Navarro, P. (2013). “Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations.” J. Hydroinf., 15(4), 1234–1257.
Juez, C., Murillo, J., and García-Navarro, P. (2014). “A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed.” Adv. Water Resour., 71, 93–109.
Kalinske, A. A. (1947). “Movement of sediment as bed load in rivers.” Trans. AGU, 28(4), 615.
Lacasta, A., Morales-Hernández, M., Murillo, J., and García-Navarro, P. (2014). “An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes.” Adv. Eng. Software, 78, 1–15.
Leveque, R. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, New York.
Masselink, G., and Russel, P. (2006). “Flow velocities, sediment transport and morphological change in the swash zone of a dissipative and reflective beach.” Mar. Geol., 227(3), 227–240.
Meyer-Peter, E., and Müller, R. (1948). “Formulas for bed load transport.”, Stockholm, Sweden.
Morales de Luna, T., Castro-Díaz, M. J., and Parés Madroñal, M. (2010). “A duality method for sediment transport based on a modified Meyer-Peter & Müller model.” J. Sci. Comput., 48(1–3), 258–273.
Morales-Hernández, M., Murillo, J., and García-Navarro, P. (2013). “The formulation of internal boundary conditions in unsteady 2D shallow water flows: Application to flood regulation.” Water Resour. Res., 49(1), 471–487.
Murillo, J., and García-Navarro, P. (2010a). “An Exner-based coupled model for two-dimensional transient flow over erodible bed.” J. Comput. Phys., 229(23), 8704–8732.
Murillo, J., and García-Navarro, P. (2010b). “Weak solutions for partial differential equations with source terms: Application to the shallow water equations.” J. Comput. Phys., 229(11), 4327–4368.
Murillo, J., García-Navarro, P., and Burguete, J. (2009). “Time step restrictions for well-balanced shallow water solutions in non-zero velocity steady states.” Int. J. Numer. Methods Fluids, 60(12), 1351–1377.
Nielsen, P. (1992). Coastal bottom boundary layers and sediment transport, World Scientific, Singapore.
Ortiz, P., Anguita, J., and Riveiro, M. (2015). “Free surface flows over partially erodible beds by a continuous finite element method.” Environ. Earth Sci., 74(11), 7357–7370.
Parker, G. (1979). “Hydraulic geometry of active gravel rivers.” J. Hydraul. Div., 105(9), 1185–1201.
Rosatti, G., and Zugliani, D. (2015). “Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The composite Riemann problem and its numerical solution.” J. Comput. Phys., 285, 226–250.
Rulot, F., Dewals, B., Erpicum, S., Archambeau, P., and Pirotton, M. (2012). “Modelling sediment transport over partially non-erodible bottoms.” Int. J. Numer. Methods Fluids, 70(2), 186–199.
Schaffner, J. (2008). “Numerical investigations on the function of flush waves in a reservoir sewer.” Ph.D. thesis, Technischen Universität Darmstadt, Darmstadt, Germany.
Schlütter, F. (1999). “Numerical modelling of sediment transport in combined sewer systems.” Ph.D. thesis, Aalborg Univ., Aalborg, Denmark.
Shirazi, R. H. S. M., Campisano, A., Modica, C., and Willems, P. (2014). “Modelling the erosive effects of sewer flushing using different sediment transport formulae.” Water Sci. Technol, 69(6), 1198–1204.
Smart, G. (1984). “Sediment transport formula for steep channels.” J. Hydr. Eng., 267–276.
Soares-Frazao, S., and Zech, Y. (2011). “HLLC scheme with novel wave-speed estimators appropiate for two-dimensional shallow-water flow on erodible bed.” Int. J. Numer. Methods Fluids, 66(8), 1019–1036.
Staufer, P., Dettmar, J., and Pinnekamp, J. (2007). “Impact of the level of approximation on modeling flushing waves.” Water Pract. Technol., 2(2), 8.
Struiksma, N. (1999). “Mathematical modelling of bedload transport over non-erodible layers.” Proc., IAHR Symp. on River, Coastal and Estuarine Morphodynamics, IAHR, Genoa, Italy.
Wu, W. (2004). “Depth-averaged two-dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels.” J. Hydr. Eng., 1013–1024.
Xia, J., Lin, B., Falconer, R., and Wang, G. (2010). “Modelling dam-break flows over mobile beds using a 2D coupled approach.” Adv. Water Resour., 33(2), 171–183.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jun 16, 2016
Accepted: Feb 28, 2017
Published online: Jun 19, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 19, 2017
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.