Semianalytical Solution for Nonequilibrium Suspended Sediment Transport in Open Channels with Concentration-Dependent Settling Velocity

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.