Numerical Modeling of Sediment Transport and Bed Evolution in Nonuniform Open-Channel Flows

• Autorzy: Zerihun Yebegaeshet T.

Identyfikatory

DOI

10.2478/heem-2024-0001

• Języki publikacji: EN

Abstrakty

EN

The shallow-water and multilayer hydrostatic models have been commonly used to analyze the problems of a sediment-laden, plane open-channel flow. The models are adequate to solve a quasi-hydrostatic flow problem, but their accuracy deteriorates as the effects of the vertical acceleration gain in significance. Herein, a higher-order numerical model for treating the problems of unsteady, plane open-channel flow over a movable bed is proposed. In this model, the flow hydrodynamics is governed by the depth-averaged Boussinesq-type equations, and the bed morphodynamics is determined by an Exner-type equation and additional equations describing the non-equilibrium transports of suspended load and bed load. A hybrid finite-volume and finite-difference scheme was used to discretize and solve the governing equations, yielding solutions that are in satisfactory agreement with the experimental data. Overall, the results of the proposed model for the temporal free-surface profile and bed evolution were fairly adequate. For the two particular cases considered, however, the quality of its results was moderately affected by the effects of the three-dimensional characteristics of the dam-break flow and the sliding of the dike body due to sub-surface flow. The results of this investigation highlight the importance of including a higher-order Boussinesq-type correction for refining sediment transport computations.

Słowa kluczowe

EN

turbulent flow; sediment transport; dike breach; finite-volume method; non-equilibrium transport; morphodynamics

• Wydawca: Institute of Hydro-Engineering of Polish Academy of Sciences
• Czasopismo: Archives of Hydro-Engineering and Environmental Mechanics
• Rocznik: 2024
• Tom: Vol. 71, nr 1
• Strony: 1--26
• Opis fizyczny: Bibliogr. 74 poz., rys., wykr.

Twórcy

autor

Zerihun Yebegaeshet T.

• David & James – Engineering and Environmental Consultancy, 204 Albion Road, Vic 3350, Australia

Bibliografia

• Aureli F., Maranzoni A., Mignosa P., Ziveri C. (2008) A weighted surface-depth gradient method for the numerical integration of the 2D shallow-water equations with topography, Adv. Water Resour., 31(7), 962–974.
• Bashforth F., Adams J. C. (1883) An Attempt to Test the Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluid, with an Explanation of the Method of Integration Employed in Constructing the Tables which Give the Theoretical Forms of Such Drops, Cambridge University Press, Cambridge, UK, 18–19.
• Bechteler W., Schrimpf W. (1984) Improved numerical model for sedimentation, J. Hydraul. Eng., 110(3), 234–246.
• Bechteler W., Schrimpf W. (1988) Practical aspects for the application of the diffusion-convection theory for sediment transport in turbulent flows, [In:] Developments in Water Science, Celia et al (eds.), Elsevier, 35, 351–356, doi:10.1016/S0167-5648(08)70360-5.
• Bennett J. P. (1974) Concepts of mathematical modeling of sediment yield, Water Resour. Res., 10(3), 485–492.
• Berger R. C. (1992) Free-surface Flow over Curved Surfaces, Ph.D. Thesis, University of Texas, Austin, TX, USA.
• Bickley W. G. (1941) Formulae for numerical differentiation, Math. Gaz., 25(263), 19–27, doi:10.2307/3606475.
• Boussinesq J. (1877) Essai Sur la Th´eorie des Eaux Courantes [Essay on the Theory of Water Flow], M´emoires Pr´esent´es par Divers Savants `a l’Acad´emie des Sciences, Paris, 23(1), 1–680 [in French].
• Cantero-Chinchilla F. N., Castro-Orgaz O., Khan A. A. (2019) Vertically averaged and moment equations for flow and sediment transport, Adv. Water Resour., doi:10.1016/j.advwatres.2019.103387.
• Cao Z., Pender G., Wallis S., Carling P. (2004) Computational dam-break hydraulics over erodible sediment bed, J. Hydraul. Eng., 130(7), 689–703.
• Capart H., Young D. L. (1998) Formation of a jump by the dam-break wave over a granular bed, J. Fluid Mech., 372, 165–187.
• Cheng K. J. (1984) Bottom-boundary condition for non-equilibrium transport of sediment, J. Geophys. Res., 89(C5), 8209–8214.
• Cheng N. S. (1997) Simplified settling velocity formula for sediment particle, J. Hydraul. Eng., 123(2), 149–152.
• Daubert A., Lebreton J. C. (1967) Etude exp´erimentale sur mod`ele math´ematique de quelques aspects des processus d’´erosion des lits alluvionnaires, en r´egime permanent et nonpermanent [Experimental study on a mathematical model of some aspects of the erosion processes of alluvial beds, in steady and unsteady states], [In:] Proceedings of the 12th IAHR World Congress, Fort Collins, CO, USA, 11–14 Sept., 3, 26–37 [in French].
• Delft Hydraulics Laboratory (1980) Storm Surge Barrier Oosterschelde, Computation of Siltation In Dredged Trenches: Mathematical Model, Report 1267-V/M 1570, Delft, The Netherlands.
• Elgamal M. H., Steffler P. M. (2001) Stability analysis of dunes using 1D depth-averaged flow models, [In:] Proceedings of the 2nd IAHR Symposium on Rivers, Coastal and Estuarine Morphodynamics, Obihiro, Japan, 10–14 Sept., 197–206.
• El Kadi Abderrezzak K., Paquier A. (2009) One-dimensional numerical modeling of sediment transport and bed deformation in open channels, Water Resour. Res., 45, W05404, doi:10.1029/2008WR007134.
• Erduran K. S., Ilic S., Kutija V. (2005) Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations, Int. J. Numer. Meth. Fluids, 49, 1213–1232.
• Exner F. M. (1925) ¨Uber die Wechselwirkung Zwischen Wasser und Geschiebe in Fl¨ussen [On the Interaction between Water and Debris in Rivers], Sitzungsberichte der Akademie der Wissenschaften mathematisch-naturwissenschaftliche Klasse, 134(2a), 165–203 [in German].
• Ferziger J. H., Peric M. (2002) Computational Methods for Fluid Dynamics, 3rd rev. ed., Springer-Verlag Berlin Heidelberg: New York, NY, USA.
• Fischer B. H., List E. J., Koh R. C., Imberger J., Brooks N. H. (1979) Mixing in Inland and Coastal Waters, Academic Press: New York, NY, USA.
• Fraccarollo L., Capart H. (2002) Riemann wave description of erosional dam-break flows, J. Fluid Mech., 461, 183–228.
• Franzini F., Soares-Fraz˜ao S. (2018) Coupled finite-volume scheme with adapted Augmented Roe scheme for simulating morphological evolution in arbitrary cross-sections, J. Hydroinformatics, 20, 1111–1130.
• Ghamry H. K. (1999) Two-Dimensional Vertically Averaged and Moment Equations for Shallow Free-Surface Flows, Ph.D. Thesis, University of Alberta, Edmonton, AB, Canada.
• Guo Q. C., Jin Y. C. (1999) Modeling sediment transport using depth-averaged and moment equations, J. Hydraul. Eng., 125(12), 1262–1269.
• Guy H. P., Simons D. B., Richardson E. V. (1966) Summary of Alluvial Channel Data from Flume Experiments, 1956–61, Professional Paper 462-I, USGS, Washington, DC, USA.
• Harten A., Lax P. D., van Leer B. (1983) On upstream differencing and Godunov-type scheme for hyperbolic conservation laws, SIAM Rev. Soc. Ind. Appl. Math., 25(1), 35–61.
• Hirsch C. (2007) Numerical Computation of Internal and External Flows: Vol. 1 Fundamentals of Computational Fluid Dynamics, 2nd ed., Elsevier: Oxford, UK.
• Jin Y., Li B. (1996) The use of a one-dimensional depth-averaged moment of momentum equation for the non-hydrostatic pressure condition, Can. J. Civ. Eng., 23, 150–156.
• Karim F. (1995) Bed configuration and hydraulic resistance in alluvial-channel flows, J. Hydraul. Eng., 121(1), 15–25.
• Kim D. H., Lynett P. J., Socolofsky S. (2009) A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows, Ocean Model., 27(3–4), 198–214.
• Komura S. (1963) Discussion of “Sediment Transportation Mechanics: Introduction and Properties of Sediment, Progress Report by the Task Committee on Preparation of Sedimentation Manual of the Committee on Sedimentation of the Hydraulics Division”, J. Hydraul. Div., 89(HY1), 263–266. doi:10.1061/JYCEAJ.0000837.
• LeVeque R. J. (2004) Finite-Volume Methods for Hyperbolic Problems, Cambridge University Press: Cambridge, UK.
• Liang D., Zhao X., Soga K. (2020) Simulation of overtopping and seepage induced dike failure using two-point MPM, Soils Found., 60, 978–988.
• Lin B. N. (1984) Current study of unsteady transport of sediment in China, [In:] Proceedings of the Japan–China Bilateral Seminar on River Hydraulics and Engineering Experiences, Tokyo, Kyoto, and Sapporo, Japan, 23 July–6 Aug., 337–342.
• Marsooli R., Wu W. (2015) Three-dimensional numerical modeling of dam-break flows with sedyment transport over movable beds, J. Hydraul. Eng., 141, doi:10.1061/(ASCE)HY.1943-7900.0000947.
• Mizutani H., Nakagawa H., Yoden T., Kawaike K., Zhang H. (2013) Numerical modeling of river embankment failure due to overtopping flow considering infiltration effects, J. Hydraul. Res., 51(6), 681–695.
• Montes J. S. (1973) Interaction of Two-Dimensional Turbulent Flow with Suspended Particles, Ph.D. Thesis, Massachusetts Institute of Technology, Boston, MA, USA.
• Pickert G., Weitbrecht V., Bieberstein A. (2011) Breaching of overtopped river embankments controlled by apparent cohesion, J. Hydraul. Res., 49(2), 143–156.
• Pontillo M., Schmocker L., Greco M., Hager W. H. (2010) One-dimensional numerical evaluation of dike erosion due to overtopping, J. Hydraul. Res., 48(5), 573–582.
• Ramirez-León H., Cuevas C. R., D´ıaz E. H. (2005) Multilayer hydrodynamic models and their application to sediment transport in estuaries, [In:] Current Trends in High Performance Computing and Its Applications, Zhang et al (eds.), Springer, 59–70, doi:10.1007/3-540-27912-1−6.
• Reynolds O. (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Philos. Trans. Royal Soc. A, 186, 123–164, doi:10.1098/rsta.1895.0004.
• Richardson J. F., Zaki W. N. (1997) Sedimentation and fluidization: Part I, Chem. Eng. Res. Des., 75(1), S82–S100. doi:10.1016/S0263-8762(97)80006-8.
• Rowan T. (2019) Advances in Modeling and Numerical Simulation of Sediment Transport In Shallow-Water Flows, Ph.D. Thesis, Durham University, Durham, UK.
• Schlichting H., Gersten K. (2017) Boundary-Layer Theory, 9th ed., Springer-Verlag GmbH Berlin Heidelberg, Germany.
• Schmocker L. (2011) Hydraulics of Dike Breaching, Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Z¨urich, Switzerland.
• Soares-Fraz˜ao S., Guinot V. (2008) A second-order semi-implicit hybrid scheme for one-dimensional Boussinesq-type waves in rectangular channels, Int. J. Numer. Methods Fluids, 58(3), 237–261.
• Steffler P. M., Jin Y. (1993) Depth averaged and moment equations for moderately shallow free-surface flow, J. Hydraul. Res., 31(1), 5–17.
• Suwa H. (1988) Focusing Mechanisms of Large Boulders to a Debris-Flow Front, Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan.
• Tabrizi A. A. (2016) Modeling Embankment Breach due to Overtopping, Ph.D. Thesis, University of South Carolina, Columbia, SC, USA.
• Takahashi T. (2014) Debris Flow: Mechanics, Prediction and Counter Measures, 2nd ed. CRC Press, Taylor and Francis Group: Boca Raton, FL, USA.
• Tingsanchali T., Supharatid S. (1996) Experimental investigation and analysis of HEC-6 river morphological model, Hydrol. Process., 10, 747–761.
• Toro E. F. (2009) Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd ed., Springer-Verlag Berlin Heidelberg, Germany.
• van Rijn L. C. (1984a) Sediment transport, Part I: Bed-load transport, J. Hydraul. Eng., 110(10), 1431–1456.
• van Rijn L. C. (1984b) Sediment transport, Part II: Suspended-load transport, J. Hydraul. Eng., 110(11), 1613–1641.
• van Rijn L. C. (1986) Mathematical modeling of suspended sediment in non-uniform flows, J. Hydraul. Eng., 112(6), 433–455.
• Vasquez J. A., Millar R. G., Steffler P. M. (2011) Vertically averaged and moment model for meandering river morphology, Can. J. Civ. Eng., 38(8), 921–931.
• Vreugdenhil C. B. (1994) Numerical Methods for Shallow-Water Flow, Kluwer Academic Publishers: Dordrecht, The Netherlands.
• Wai O., Lu Q., Li Y. S. (1996) Multilayer modeling of three-dimensional hydrodynamic transport processes, J. Hydraul. Res., 34(5), 677–693.
• Wei G., Kirby J. T. (1995) Time-dependent numerical code for extended Boussinesq equations, J. Waterw. Port Coast. Ocean Eng., 121(5), 251–261.
• Wu W., Wang S. S. Y., Jia Y. (2000) Non-uniform sediment transport in alluvial rivers, J. Hydraul. Res., 38(6), 427–434.
• Wu W., Wang S. S. Y. (2006) Formulas for sediment porosity and settling velocity, J. Hydraul. Eng., 132(8), 858–862.
• Wu W., Wang S. S. Y. (2007) One-dimensional modeling of dam-break flow over movable beds, J. Hydraul. Eng., 133(1), 48–58.
• Wu W., Wang S. S. Y. (2008) One-dimensional explicit finite-volume model for sediment transport, J. Hydraul. Res., 46(1), 87–98.
• Xia J., Lin B., Falconer A. R., Wang G. (2010) Modeling dam-break flows over mobile beds using a 2D coupled approach, Adv. Water Resour., 33(2), 171–183.
• Yamamoto S., Daiguji H. (1993) Higher-order accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations, Comput. Fluids, 22(2–3), 259–270.
• Zerihun Y. T. (2004) A One-Dimensional Boussinesq-Type Momentum Model for Steady Rapidly-Varied Open-Channel Flows, Ph.D. Thesis, The University of Melbourne, Melbourne, Vic, Australia.
• Zerihun Y. T., Fenton J. D. (2006) One-dimensional simulation model for steady transcritical free-surface flows at short length transitions, Adv. Water Resour., 29(11), 1598–1607.
• Zerihun Y. T., Fenton J. D. (2007) A Boussinesq-type model for flow over trapezoidal profile weirs, J. Hydraul. Res., 45(4), 519–528.
• Zerihun Y. T. (2016) Modeling free-surface flow with curvilinear streamlines by a non-hydrostatic model, J. Hydrol. Hydromech., 64(3), 281–288.
• Zerihun Y. T. (2019) On steady two-dimensional free-surface flows with spatially-varied discharges, Slovak J. Civ. Eng., 27(3), 1–11.
• Zerihun Y. T. (2020) Free flow and discharge characteristics of trapezoidal-shaped weirs, Fluids, 5(4), doi:10.3390/fluids5040238.
• Zerihun Y. T. (2021) Non-hydrostatic transitional open-channel flows from a supercritical to a subcritical state, Slovak J. Civ. Eng., 29(2), 39–48.
• Zerihun Y. T. (2023) A study of the sedimentation and storage capacity depletion of a reservoir, Slovak J. Civ. Eng., 31(2), 37–47.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).