Semi-analytical solution for one-dimensional unsteady sediment transport model in open channel with concentration-dependent settling velocity

Abstract

This paper aims to solve the one-dimensional unsteady suspended sediment transport equation in open channels through a semi-analytical approach. The presence of a large amount of particles in flow change the settling velocity of a particle, and this phenomenon, commonly known as hindered settling effect, must be taken into account to deal with high concentrated flows. Inclusion of this mechanism makes the governing equation non-linear, and together with this non-linear governing equation, a generalized bottom boundary condition is taken in terms of deposition velocity and equilibrium bottom concentration. An explicit series solution is presented using the Method of Lines based Homotopy Analysis Method, and the convergence of the series solution is gained through a convergence control parameter. The solution is validated by comparing it with the existing solution as well as a numerical one. Apart from that, the solution has also been validated under a steady-state condition with available experimental data. Results are interpreted both graphically and physically. It is found that the hindered settling effect is dominant in the main flow region only, for sediment free inlet for all types of turbulent diffusion coefficients. On the other hand, in the case of uniform sediment concentration at the inlet, hindered settling affects the concentration in the top portion of the channel too for linear and parabolic profiles of turbulent diffusion coefficients.