Semianalytical Solution for Nonequilibrium Suspended Sediment Transport in Open Channels with Concentration-Dependent Settling Velocity
Publication: Journal of Hydrologic Engineering
Volume 27, Issue 2
Abstract
The present study aims to develop a steady two-dimensional suspended sediment transport model in an open channel for turbulent flow-carrying sediments. In such a flow, if sediment concentration is high, hindered settling occurs, meaning that the settling velocity of a particle reduces than that in clear water flow and should be considered in the mathematical modeling. Inclusion of hindered settling into the governing equation of transport leads to a highly nonlinear parabolic-type partial differential equation (PDE) with variable coefficients. Physically realistic and generalized boundary conditions are considered at the free surface and at the bed. A semianalytical solution of the nonlinear PDE together with these boundary conditions is proposed using two different approaches, namely, the Laplace transform-based homotopy analysis method (Laplace-HAM) and the method of lines-based HAM (MOL-HAM). Unlike existing analytical/semianalytical methods, the convergence behavior of the proposed solution can be handled efficiently through a convergence-control parameter. The proposed solutions have been validated with the numerical solution and the solution of an existing model under limited conditions. Further, the derived solution is also validated with experimental data for the far-field solution. The two derived solutions are compared with each other, and both are found to provide an approximate series solution. The concentration profiles of suspended sediment particles with different physical parameters and conditions are interpreted physically. This study can be extended to address other suspended sediment transport problems.
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Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors are thankful to Prof. Shijun Liao (State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, School of Physics and Astronomy, Shanghai Jiaotong University, Shanghai 200240, China), Prof. Robert A. Van Gorder (Senior Lecturer, Department of Mathematics and Statistics, University of Otago, New Zealand) and Dr. Xiaoxu Zhong (Mechanical Engineering, Purdue University) for helpful discussion regarding the methodology.
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Published In
Journal of Hydrologic Engineering
Volume 27 • Issue 2 • February 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: May 24, 2021
Accepted: Nov 2, 2021
Published online: Dec 11, 2021
Published in print: Feb 1, 2022
Discussion open until: May 11, 2022
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Cited by
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- Sumit Sen, Snehasis Kundu, Rafik Absi, Koeli Ghoshal, A Model for Coupled Fluid Velocity and Suspended Sediment Concentration in an Unsteady Stratified Turbulent Flow through an Open Channel, Journal of Engineering Mechanics, 10.1061/(ASCE)EM.1943-7889.0002158, 149, 1, (2023).
- Xiufeng Quan, Ruijie Li, Yuting Li, Feng Luo, Xiaoyan Fu, He Gou, The Influence of Vertical Velocity Distribution on the Calculation of Suspended Sediment Concentration, Discrete Dynamics in Nature and Society, 10.1155/2022/6455999, 2022, (1-15), (2022).
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