Technical Papers
May 27, 2023

Combined Impact of Density Stratification and Hindered Settling on Nonequilibrium Suspended Sediment Transport in Open Channel Flows

Publication: Journal of Hydrologic Engineering
Volume 28, Issue 8

Abstract

The present paper studies the two-dimensional unsteady suspended sediment transport problem through an open channel turbulent flow that carries large amounts of sediments. Presence of large amounts of sediments causes separate, distinct horizontal layers that result to differences in density, which is called density stratification. Also, due to interactions with neighboring particles, a particle settles at a reduced speed relative to that of a single particle in clear fluid, which is called hindered settling. The model includes both of these effects and the governing equation, which is a nonlinear partial differential equation (PDE), has been solved by the finite difference (FD) method. The model has been validated with existing models under certain specific conditions. It is found that stratification causes a decrement in sediment concentration values and the effect becomes prominent as time increases until it reaches a stable value. A reverse result is obtained for the case of hindered settling and both the effects are visible mainly in the main suspension region. Finally, the model has been validated with a few existing models together with some experimental data at steady-state and far-field conditions.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

References

Ali, S. Z., and S. Dey. 2016. “Mechanics of advection of suspended particles in turbulent flow.” Proc. R. Soc. London, Ser. A 472 (2195): 20160749. https://doi.org/10.1098/rspa.2016.0749.
Apmann, R. P., and R. R. Rumer Jr. 1970. “Diffusion of sediment in developing flow.” J. Hydraul. Div. 96 (1): 109–123. https://doi.org/10.1061/JYCEAJ.0002252.
Camp, T. R. 1943. The effect of turbulence in retarding settling. Cambridge, MA: MIT.
Carstens, M. 1952. “Accelerated motion of a spherical particle.” EOS Trans. Am. Geophys. Union 33 (5): 713–721. https://doi.org/10.1029/TR033i005p00713.
Cellino, M., and W. H. Graf. 1999. “Sediment-laden flow in open-channels under noncapacity and capacity conditions.” J. Hydraul. Eng. 125 (5): 455–462. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:5(455).
Cheng, K. J. 1984. “Bottom-boundary condition for nonequilibrium transport of sediment.” J. Geophys. Res. Oceans 89 (C5): 8209–8214. https://doi.org/10.1029/JC089iC05p08209.
Cheng, N.-S. 1997. “Simplified settling velocity formula for sediment particle.” J. Hydraul. Eng. 123 (2): 149–152. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(149).
Coleman, N. L. 1981. “Velocity profiles with suspended sediment.” J. Hydraul. Res. 19 (3): 211–229. https://doi.org/10.1080/00221688109499516.
Debnath, S., K. Ghoshal, and J. Kumar. 2021. “Unsteady two-dimensional suspended sediment transport in open channel flow subject to deposition and re-entrainment.” J. Eng. Math. 126 (1): 1–13. https://doi.org/10.1007/s10665-020-10070-7.
Dey, S. 2014. Fluvial hydrodynamics. Berlin: Springer.
Dobbins, W. E. 1944. “Effect of turbulence on sedimentation.” Trans. Am. Soc. Civ. Eng. 109 (1): 629–656. https://doi.org/10.1061/TACEAT.0005696.
Einstein, H., and N. Chien. 1955. Effect of heavy sediment concentration near the bed on velocity and sediment distribution. Berkeley, CA: Univ. of California.
Ghoshal, K., P. Jain, and R. Absi. 2022. “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. 148 (1): 04021123. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002045.
Ghoshal, K., and B. Mazumder. 2005. “Sediment-induced stratification in turbulent open-channel flow.” Environ.: Off. J. Int. Environ. Soc. 16 (7): 673–686. https://doi.org/10.1002/env.729.
Glenn, S. M., and W. D. Grant. 1987. “A suspended sediment stratification correction for combined wave and current flows.” J. Geophys. Res. Oceans 92 (C8): 8244–8264. https://doi.org/10.1029/JC092iC08p08244.
Graf, W., and M. Cellino. 2002. “Suspension flows in open channels; experimental study.” J. Hydraul. Res. 40 (4): 435–447. https://doi.org/10.1080/00221680209499886.
Herrmann, M. J., and O. S. Madsen. 2007. “Effect of stratification due to suspended sand on velocity and concentration distribution in unidirectional flows.” J. Geophys. Res. Oceans 112 (C2). https://doi.org/10.1029/2006JC003569.
Hjelmfelt, A. T., and C. W. Lenau. 1970. “Nonequilibrium transport of suspended sediment.” J. Hydraul. Div. 96 (7): 1567–1586. https://doi.org/10.1061/JYCEAJ.0002567.
Hossain, S., G. Singh, A. Dhar, and K. Ghoshal. 2022. “Generalized non-equilibrium suspended sediment transport model with hindered settling effect for open channel flows.” J. Hydrol. 612 (Sep): 128145. https://doi.org/10.1016/j.jhydrol.2022.128145.
Howard, L. N. 1961. “Note on a paper of john w. miles.” J. Fluid Mech. 10 (4): 509–512. https://doi.org/10.1017/S0022112061000317.
Hunt, J. 1954. “The turbulent transport of suspended sediment in open channels.” Proc. R. Soc. London, Ser. A 224 (1158): 322–335. https://doi.org/10.1098/rspa.1954.0161.
Jain, P., and K. Ghoshal. 2021. “Closed form solution of vertical concentration distribution equation: Revisited with homotopy perturbation method.” J. Theor. Appl. Mech. 52 (3): 277–300.
Jain, P., M. Kumbhakar, and K. Ghoshal. 2022. “Application of homotopy analysis method to the determination of vertical sediment concentration distribution with shear-induced diffusivity.” Supplement, Eng. Comput. 38 (S3): 2609–2628. https://doi.org/10.1007/s00366-021-01491-8.
Jing, H., G. Chen, W. Wang, and G. Li. 2018. “Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment.” Environ. Earth Sci. 77 (15): 1–10. https://doi.org/10.1007/s12665-018-7731-9.
Jobson, H. E., and W. W. Sayre. 1970. “Predicting concentration profiles in open channels.” J. Hydraul. Div. 96 (10): 1983–1996. https://doi.org/10.1061/JYCEAJ.0002723.
Kumbhakar, M., S. Mohan, K. Ghoshal, J. Kumar, and V. P. Singh. 2022. “Semianalytical solution for nonequilibrium suspended sediment transport in open channels with concentration-dependent settling velocity.” J. Hydrol. Eng. 27 (2): 04021048. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002160.
Kumbhakar, M., J. Saha, K. Ghoshal, J. Kumar, and V. P. Singh. 2018. “Vertical sediment concentration distribution in high-concentrated flows: An analytical solution using homotopy analysis method.” Commun. Theor. Phys. 70 (3): 367. https://doi.org/10.1088/0253-6102/70/3/367.
Kundu, S. 2020. “Study of unsteady nonequilibrium stratified suspended sediment distribution in open-channel turbulent flows using shifted chebyshev polynomials.” ISH J. Hydraul. Eng. 28 (1): 42–52. https://doi.org/10.1080/09715010.2020.1828195.
Kundu, S., and K. Ghoshal. 2014. “Effects of secondary current and stratification on suspension concentration in an open channel flow.” Environ. Fluid Mech. 14 (6): 1357–1380. https://doi.org/10.1007/s10652-014-9341-8.
Liu, X. 2016. “Analytical solutions for steady two-dimensional suspended sediment transport in channels with arbitrary advection velocity and eddy diffusivity distributions.” J. Hydraul. Res. 54 (4): 389–398. https://doi.org/10.1080/00221686.2016.1168880.
Liu, X., and M. Nayamatullah. 2014. “Semianalytical solutions for one-dimensional unsteady nonequilibrium suspended sediment transport in channels with arbitrary eddy viscosity distributions and realistic boundary conditions.” J. Hydraul. Eng. 140 (5): 04014011. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000874.
Mazumder, B., and K. Ghoshal. 2002. “Velocity and suspension concentration in sediment-mixed fluid.” Int. J. Sediment Res. 17 (3): 220–232.
Mazumder, B., and K. Ghoshal. 2006. “Velocity and concentration profiles in uniform sediment-laden flow.” Appl. Math. Modell. 30 (2): 164–176. https://doi.org/10.1016/j.apm.2005.03.015.
Mei, C. C. 1969. “Nonuniform diffusion of suspended sediment.” J. Hydraul. Div. 95 (1): 581–584. https://doi.org/10.1061/JYCEAJ.0002021.
Mendoza, C. 1991. “Transitional sediment concentration profiles.” Mech. Res. Commun. 18 (6): 429–434. https://doi.org/10.1016/0093-6413(91)90057-4.
Mohan, S., M. Kumbhakar, K. Ghoshal, and J. Kumar. 2019. “Semianalytical solution for simultaneous distribution of fluid velocity and sediment concentration in open-channel flow.” J. Eng. Mech. 145 (11): 04019090. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001671.
Mohan, S., M. Kumbhakar, K. Ghoshal, and J. Kumar. 2020. “Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity.” Phys. Scr. 95 (5): 055204. https://doi.org/10.1088/1402-4896/ab6f21.
Monin, A., and A. Yaglom. 1971. Statistical fluid mechanics. Cambridge, MA: MIT Press.
Muste, M., K. Yu, I. Fujita, and R. Ettema. 2005. “Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows.” Water Resour. Res. 41 (10). https://doi.org/10.1029/2004WR003595.
Muste, M., and V. C. Patel. 1997. “Velocity profiles for particles and liquid in open-channel flow with suspeneded sediment.” J. Hydraul. Eng. 123 (9): 742–751. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:9(742).
Pal, D., and K. Ghoshal. 2016. “Effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow.” Environ. Earth Sci. 75 (18): 1–11. https://doi.org/10.1007/s12665-016-6045-z.
Pal, D., and K. Ghoshal. 2017. “Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow.” Appl. Math. Modell. 49 (Sep): 630–646. https://doi.org/10.1016/j.apm.2017.02.045.
Richardson, J. F., and W. N. Zaki. 1954. “Sedimentation and fluidisation: Part 1.” Chem. Eng. Res. Des. 31: 35–53.
Rouse, H. 1937. “Modern conceptions of the mechanics of fluid turbulence.” Trans. Am. Soc. Civ. Eng. 102 (1): 463–505. https://doi.org/10.1061/TACEAT.0004872.
Sen, S., S. Hossain, and K. Ghoshal. 2022. “Distribution of non-uniform particles in an open channel flow from the concept of mixing length.” Sediment. Geol. 440 (Oct): 106242. https://doi.org/10.1016/j.sedgeo.2022.106242.
Sen, S., S. Kundu, R. Absi, and K. Ghoshal. 2023. “A model for coupled fluid velocity and suspended sediment concentration in an unsteady stratified turbulent flow through an open channel.” J. Eng. Mech. 149 (1): 04022088. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002158.
Smith, J. D., and S. McLean. 1977. “Spatially averaged flow over a wavy surface.” J. Geophys. Res. 82 (12): 1735–1746. https://doi.org/10.1029/JC082i012p01735.
Stull, R. B. 1988. Vol. 13 of An introduction to boundary layer meteorology. New York: Springer Science & Business Media.
Styles, R., and S. M. Glenn. 2000. “Modeling stratified wave and current bottom boundary layers on the continental shelf.” J. Geophys. Res. Oceans 105 (C10): 24119–24139. https://doi.org/10.1029/2000JC900115.
Sun, Z., H. Zheng, D. Xu, C. Hu, and C. Zhang. 2021. “Vertical concentration profile of nonuniform sediment.” Int. J. Sediment Res. 36 (1): 120–126. https://doi.org/10.1016/j.ijsrc.2020.06.008.
Tsujimoto, T. 2010. “Diffusion coefficient of suspended sediment and kinematic eddy viscosity of flow containing suspended load.” In River flow 2010, 801–806. Karlsruhe, Germany: Bundesanstalt für Wasserbau.
Umeyama, M. 1992. “Vertical distribution of suspended sediment in uniform open-channel flow.” J. Hydraul. Eng. 118 (6): 936–941. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:6(936).
Vanoni, V. A. 1946. “Transportation of suspended sediment by water.” Trans. Am. Soc. Civ. Eng. 111 (1): 67–102. https://doi.org/10.1061/TACEAT.0005975.
Vanoni, V. A. 1974. “Factors determining bed forms of alluvial streams.” J. Hydraul. Div. 100 (3): 363–377. https://doi.org/10.1061/JYCEAJ.0003906.
van Rijn, L. C. 1984. “Sediment transport, part II: Suspended load transport.” J. Hydraul. Eng. 110 (11): 1613–1641. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1613).
van Rijn, L. C. 1987. Mathematical modelling of morphological processes in the case of suspended sediment transport. Delft, Netherlands: Delft Hydraulics Laboratory.
Van Rijn, L., and K. Meijer. 1988. “Three-dimensional mathematical modelling of suspended sediment transport in currents and waves.” In Vol. 30 of Proc., IAHR Symp. on Mathematical Modelling of Sediment Transport in the Coastal Zone, Copenhagen, 89–99. Madrid, Spain: International Association for Hydro-Environment Engineering and Research.
Van Rijn, L. C. 1986. Mathematical modeling of suspended sediment in nonuniform flows. Delft, Netherlands: Waterloopkundig Laboratorium.
Wright, S., and G. Parker. 2004. “Flow resistance and suspended load in sand-bed rivers: Simplified stratification model.” J. Hydraul. Eng. 130 (8): 796–805. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:8(796).
Yoon, J.-Y., and S.-K. Kang. 2005. “A numerical model of sediment-laden turbulent flow in an open channel.” Can. J. Civ. Eng. 32 (1): 233–240. https://doi.org/10.1139/l04-089.

Information & Authors

Information

Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 28Issue 8August 2023

History

Received: Sep 10, 2022
Accepted: Mar 22, 2023
Published online: May 27, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 27, 2023

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Senior Research Scholar, Dept. of Mathematics, IIT Kharagpur, Kharagpur, West Bengal 721302, India (corresponding author). ORCID: https://orcid.org/0000-0002-9190-5897. Email: [email protected]
Senior Research Scholar, Dept. of Mathematics, IIT Kharagpur, Kharagpur, West Bengal 721302, India. Email: [email protected]
Koeli Ghoshal [email protected]
Associate Professor, Dept. of Mathematics, IIT Kharagpur, Kharagpur, West Bengal 721302, India. Email: [email protected]
Professor, Dept. of Civil Engineering, IIT Kharagpur, Kharagpur, West Bengal 721302, India. ORCID: https://orcid.org/0000-0002-0287-3791. Email: [email protected]

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.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share