A Model for Coupled Fluid Velocity and Suspended Sediment Concentration in an Unsteady Stratified Turbulent Flow through an Open Channel

This study investigates the simultaneous distribution of suspended sediment concentration and streamwise velocity in an unsteady, uniform, one-dimensional sediment-laden open-channel flow. Theoretical models for concentration and velocity have been developed, incorporating the stratification effect through the coefficients of stratified sediment diffusivity and the hindered settling effect through the exponent coefficient of settling velocity reduction. The resulting coupled partial differential equations (PDEs) are highly nonlinear in nature and are solved numerically. The results indicate that the effects of stratification and hindered settling on concentration profiles exhibited less change over a period of time for the sediment-free initial conditions than for the uniform initial conditions. For the case of uniform initial concentration, it has been found that the effect of hindered settling on the concentration profiles is present only in the main flow region for the parabolic profile of eddy diffusivity, whereas for constant and linear profiles of eddy diffusivity, the effects can also be observed near the free surface initially. At a large time, this effect could only be noticed in the main flow region of concentration profiles for all three models of eddy diffusivity. A sensitivity analysis is presented showing the strong influence of the reference concentration on the concentration profiles. The numerical solution has been compared with previously obtained solutions as well as with experimental data for both unsteady and steady flow conditions under some restrictions. Good agreement has been observed in all the cases, which shows that the proposed model is capable of predicting the simultaneous distributions of velocity and sediment concentration efficiently.