Unsteady numerical simulation of suspended load in relation to grain-size distribution

A theoretical model is presented here for the transient grain-size distribution of non-uniform sediments in suspension over erodible sediment beds based on the advection-diffusion equation in a turbulent open channel flow. The effect of particle-particle interaction near the channel bed is included in the reference level computation. In addition, pick-up probability, non-ceasing probability and incipient probability of sediment particles are incorporated in the calculation of reference concentration. Non-uniform sediments settle at a different velocity compared to uniform sediment and the difference in settling velocity in suspension influences their concentration in suspension. The present model accounts for the influence of non-uniform sediment on settling velocity through hindered and hiding effects. The governing equations in the proposed model are solved using OpenFOAM, an open source finite-volume method (FVM)-based framework. When settling velocity is calculated from uniform and non-uniform sediment expressions, the concentration difference is notable, especially in medium-size particles. In some particular heights, grain-size distributions have been analyzed over time for different sediment beds. Observations indicate that, as time passes, the stronger peak of the bimodal grain-size distribution in suspension weakens, while the weaker peak strengthens, until the distribution achieves a steady state at a specific height. In addition, grain-size distributions at various vertical heights over a long period of time have also been studied. It is found that the grain-size distribution becomes more skewed at the finer end with increasing vertical height. In the absence of unsteady transport data, the simulated numerical results were compared with existing steady transport data for non-uniform particle size over a suitably high time. After a considerable amount of time, the model attains a steady state and the numerical results under steady-state conditions depict good correspondence with the experimental data. In contrast to the majority of previous works, the present model can predict the transient grain-size distribution and reveal several latent phenomena of particle-particle and particle-turbulence interaction in the presence of suspended sediment particles of various sizes.