Distribution of non-uniform particles in an open channel flow from the concept of mixing length

Abstract

This study deals with unsteady transport of suspended sediment in a fluid flow through an open channel that carries non-uniform particles coming from erodible sediment beds in which the flow is considered to be uniform and time-independent. To that purpose, the advection-diffusion equation is modified for the i-th grain-size class. The hiding and hindering effects caused by the interactions between non-uniform sediment particles have been taken into account through the modified expression of settling velocity. Additionally, the study utilizes the concentration-dependent expression of mixing length, which has been used previously for the transport of uniform sediment particles. The reference level for each non-uniform grain-size class has been calculated by determining the average saltation height of that class of grain. The effects of incipient motion probability, non-ceasing possibility and particle pick-up probability are taken into account while computing the reference concentration for each grain-size class. The governing equation has been solved numerically by the fourth order Runge-Kutta method. The temporal evolution of the grain-size distribution over a sediment bed has been shown at different heights. The findings indicate that starting from a unimodal bed distribution, a bimodal distribution of grain-size with one strong peak and one weak peak evolves to a bimodal distribution with two strong peaks as the vertical height increases. The effects of mixing length and modified settling velocity on the concentration profiles of non-uniform sediment particles have been shown. Both the effects result in a decrease in the magnitude of the concentration profile. Due to lack of data for unsteady transport, the obtained solution has been compared with the experimental data for steady transport of non-uniform grain-size particles at a sufficiently large time. Because the model reaches steady state after a sufficiently long time, has been shown through the analysis of relative change in concentration over time. Close agreement has been observed in all the cases. Also, the efficacy of the considered effects has been shown through the error analysis. The main advantage of the study is that, unlike most of the previous studies, the present model is able to predict the grain-size distribution in suspension without having any fitting parameters.