Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow
Abstract
:1. Introduction
2. The Kinetic Model
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Yalin, M.S. Mechanics of Sediment Transport; Pergamon Press: Oxford, UK, 1972. [Google Scholar]
- Longo, S.G. Physical Models with Sediment Transport. In Principles and Applications of Dimensional Analysis and Similarity. Mathematical Engineering; Springer: Cham, Switzerland, 2021; pp. 351–382. [Google Scholar]
- Gorrick, S.; Rodríguez, J.F. Scaling of sediment dynamics in a laboratory model of a sand-bed stream. J. Hydro-Environ. Res. 2014, 8, 77–87. [Google Scholar] [CrossRef]
- Ancey, C.; Recking, A. Scaling behavior of bedload transport: What if Bagnold was right? Earth-Sci. Rev. 2023, 246, 104571. [Google Scholar] [CrossRef]
- Ali, S.Z.; Dey, S. Origin of the scaling laws of sediment transport. Proc. R. Soc. A Math. Phys. Eng. Sci. 2017, 473, 20160785. [Google Scholar] [CrossRef]
- Ali, S.Z.; Dey, S. Impact of phenomenological theory of turbulence on pragmatic approach to fluvial hydraulics. Phys. Fluids 2018, 30, 045105. [Google Scholar] [CrossRef]
- Zhong, D.; Wang, G.; Wu, B. Drift velocity of suspended sediment in turbulent open channel flows. J. Hydraul. Eng. 1937, 140, 35–47. [Google Scholar] [CrossRef]
- Rouse, H. Modern conceptions of the mechanics of fluid turbulence. Trans. ASCE 1937, 102, 463–543. [Google Scholar] [CrossRef]
- Hunt, J. The turbulent transport of suspended sediment in open channels. Proc. R. Soc. Lond. Ser. A 1954, 224, 322–335. [Google Scholar]
- Einstein, H.; Chien, N. Effects of Heavy Sediment Concentration Near the Bed on Velocity and Sediment Distribution; Missoury River Division, USACE: Washington, DC, USA, 1955.
- Elata, C.; Ippen, A.T. Dynamics of Open Channel Flow with Suspensions of Neutrally Buoyant Particles; Hydrodynamics Laboratory, Department of Civil and Sanitary Engineering, Massachusetts Institute of Technology: Cambridge, MA, USA, 1961. [Google Scholar]
- Coleman, N.L. Effects of suspended sediment on the open-channel velocity distribution. Water Resour. Res. 1986, 22, 1377–1384. [Google Scholar] [CrossRef]
- Parker, G.; Coleman, N.L. Simple-model of sediment-laden flows. J. Hydraul. Eng. 1986, 112, 356–375. [Google Scholar] [CrossRef]
- Umeyama, M. Vertical distribution of suspended sediment in uniform open-channel flow. J. Hydraul. Eng. 1992, 118, 936–941. [Google Scholar] [CrossRef]
- Cao, Z.X.; Wei, L.Y.; Xie, J.H. Sediment-laden flow in open-channels from two-phase flow viewpoint. J. Hydraul. Eng. 1995, 121, 725–735. [Google Scholar] [CrossRef]
- Chiu, C.-L.; Jin, W.; Chen, Y.-C. Mathematical models of distribution of sediment concentration. J. Hydraul. Eng. 2000, 126, 16–23. [Google Scholar] [CrossRef]
- Guo, J.K.; Julien, P.Y. Turbulent velocity profiles in sediment-laden flows. J. Hydraul. Res. 2001, 39, 11–23. [Google Scholar] [CrossRef]
- Graf, W.H.; Cellino, M. Suspension flows in open channels; experimental study. J. Hydraul. Res. 2002, 40, 435–447. [Google Scholar] [CrossRef]
- Cao, Z.X.; Egashira, S.J.; Carling, P.A. Role of suspended-sediment particle size in modifying velocity profiles in open channel flows. Water Resour. Res. 2003, 39, 1029. [Google Scholar] [CrossRef]
- Wright, S.; Parker, G. Density stratification effects in sand-bed rivers. J. Hydraul. Eng. 2004, 130, 783–795. [Google Scholar] [CrossRef]
- Herrmann, M.J.; Madsen, O.S. Effect of stratification due to suspended sand on velocity and concentration distribution in unidirectional flows. J. Geophys. Res. Oceans 2007, 112, C02006. [Google Scholar] [CrossRef]
- Toorman, E.A. Vertical mixing in the fully developed turbulent layer of sediment-laden open-channel flow. J. Hydraul. Eng. 2008, 134, 1225–1235. [Google Scholar] [CrossRef]
- Absi, R. Concentration profiles for fine and coarse sediments suspended by waves over ripples: An analytical study with the 1-DV gradient diffusion model. Adv. Water Resour. 2010, 33, 411–418. [Google Scholar] [CrossRef]
- Pittaluga, M.B. Stratification effects on flow and bed topography in straight and curved erodible streams. J. Geophys. Res. 2011, 116, F03026. [Google Scholar] [CrossRef]
- Dey, S.; Ali, S.Z.; Padhi, E. Advances in analytical modeling of suspended sediment transport. J. Hydro-Environ. Res. 2018, 20, 11066126. [Google Scholar] [CrossRef]
- Sun, H.; Nie, S.; Packman, A.I.; Zhang, Y.; Chen, D.; Lu, C.; Zheng, C. Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution. Int. J. Sediment Res. 2023, 38, 12–23. [Google Scholar] [CrossRef]
- Ghoshal, K.; Jain, P.; Absi, R. Nonlinear partial differential equation for unsteady vertical distribution of suspended sediments in open channel flows: Effects of hindered settling and concentration-dependent mixing length. J. Eng. Mech. 2022, 148, 04021123. [Google Scholar] [CrossRef]
- Kumbhakar, M.; Tsai, C.W.; Absi, R. Semi-Analytical Modelling of Sediment-Laden Open-Channel Flows with the Effects of Stratification, Hindered Settling, and Eddy Viscosities. Chaos Interdiscip. J. Nonlinear Sci. 2023, 33, 083113. [Google Scholar] [CrossRef]
- Greimann, B.P.; Muste, M.; Holly, F.M. Two-phase formulation of suspended sediment transport. J. Hydraul. Res. 1999, 37, 479–500. [Google Scholar] [CrossRef]
- Wu, W.M.; Wang, S.Y. Mathematical models for liquid–solid two-phase flow. Int. J. Sediment Res. 2000, 15, 288–298. [Google Scholar]
- Greimann, B.P.; Holly, F.M. Two-phase flow analysis of concentration profiles. J. Hydraul. Eng. 2001, 127, 753–762. [Google Scholar] [CrossRef]
- Hsu, T.J.; Jenkins, J.T.; Liu, P.L.F. On two-phase sediment transport: Sheet flow of massive particles. Proc. R. Soc. Lon. A 2004, 460, 2223–2250. [Google Scholar] [CrossRef]
- Jiang, J.S.; Law, A.W.K.; Cheng, N.S. Two-phase modeling of suspended sediment distribution in open channel flows. J. Hydraul. Res. 2004, 42, 273–281. [Google Scholar] [CrossRef]
- Nguyen, K.D.; Guillou, S.; Chauchat, J.; Barbry, N. A two-phase numerical model for suspended-sediment transport in estuaries. Adv. Water Resour. 2009, 32, 1187–1196. [Google Scholar] [CrossRef]
- Ishii, M.; Hibiki, T. Thermo-Fluid Dynamics of Two-Phase Flow; Springer: New York, NY, USA, 2006. [Google Scholar]
- Fu, X.; Wang, G.; Shao, X. Vertical dispersion of fine and coarse sediments in turbulent open-channel flows. J. Hydraul. Eng. 2005, 131, 877–888. [Google Scholar] [CrossRef]
- Wang, G.; Fu, X.; Huang, Y.; Huang, G. Analysis of suspended sediment transport in open-channel flows: Kinetic-model-based simulation. J. Hydraul. Eng. 2008, 134, 328–339. [Google Scholar] [CrossRef]
- Lei, Z.; Zhong, D.; Baosheng, W. Particle inertia effect on sediment dispersion in turbulent open-channel flows. Sci. China Technol. Sci. 2014, 57, 1977–1987. [Google Scholar]
- Ma, H.; Fu, X. Stochastic formulation of particle kinetics in wall-bounded two-phase flows. Sci. China Technol. Sci. 2014, 57, 2001–2011. [Google Scholar] [CrossRef]
- Nie, S.; Sun, H.; Zhang, Y.; Chen, D.; Chen, W.; Chen, L.; Schaefer, S. Vertical Distribution of Suspended Sediment under Steady Flow: Existing Theories and Fractional Derivative Model. Discret. Dyn. Nat. Soc. 2017, 16307, 5481531. [Google Scholar] [CrossRef]
- Huang, H.; Zhang, H.; Zhong, D.; Zhang, Y.J. Turbulent mechanisms in open channel sediment-laden flows. Int. J. Sediment Res. 2019, 34, 550–563. [Google Scholar] [CrossRef]
- Derevich, I.V.; Zaichik, L.I. Particle deposition from a turbulent flow. Fluid Dyn. 1988, 23, 722–729. [Google Scholar] [CrossRef]
- Absi, R. Suspended Sediments in Environmental Flows: Interpretation of Concentration Profiles Shapes. Hydrology 2023, 10, 5. [Google Scholar] [CrossRef]
- Absi, R.; Tanaka, H. Analytical Eddy Viscosity Model for Turbulent Wave Boundary Layers: Application to Suspended Sediment Concentrations over Wave Ripples. J. Mar. Sci. Eng. 2023, 11, 226. [Google Scholar] [CrossRef]
- Absi, R. Reinvestigating the parabolic-shaped eddy viscosity profile for free surface flows. Hydrology 2021, 8, 126. [Google Scholar] [CrossRef]
Run Number | h (cm) | (mm) | (cm/s) | |
---|---|---|---|---|
S2 | 12.0 | 1.3 | 12.85 | 2.65 |
S3 | 11.7 | 1.3 | 13.26 | 2.65 |
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Dalla Via, M.; Absi, R. Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow. Mathematics 2024, 12, 794. https://doi.org/10.3390/math12060794
Dalla Via M, Absi R. Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow. Mathematics. 2024; 12(6):794. https://doi.org/10.3390/math12060794
Chicago/Turabian StyleDalla Via, Marco, and Rafik Absi. 2024. "Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow" Mathematics 12, no. 6: 794. https://doi.org/10.3390/math12060794
APA StyleDalla Via, M., & Absi, R. (2024). Reinvestigating the Kinetic Model for the Suspended Sediment Concentration in an Open Channel Flow. Mathematics, 12(6), 794. https://doi.org/10.3390/math12060794