Semianalytical Solution for Simultaneous Distribution of Fluid Velocity and Sediment Concentration in Open-Channel Flow

To understand the sediment-transport process in an open-channel turbulent flow, the time-averaged profiles of streamwise fluid velocity and volumetric particle concentration in suspension must be given simultaneous treatment because they are closely interrelated through particle-turbulence interaction. Presence of sediment particles increases the density of a fluid-sediment mixture, which makes the flow stratified and obstructs the settling of sediment particles. The greater the amount of sediment particles in fluid, the stronger the effects of stratification and hindered settling. Therefore, generalizing existing works, this study attempts to model the velocity and concentration simultaneously, incorporating the aforementioned effects. The coupled system of odes arising from the derivation is strongly nonlinear in nature, and the analytical solution needs a special mathematical tool. To that end, a novel analytical method called the homotopy analysis method (HAM) is employed to obtain the explicit series solution to the system. The methodology is a nonperturbation approach, and the convergence can be tackled easily through some convergence control parameters. The solutions obtained are found to be stable and are validated with numerical solution as well as with relevant experimental data available in the literature. Further, the models have been physically interpreted through the effects of the turbulent factors incorporated.