Grain-size distribution in suspension under non-equilibrium conditions

This paper presents a model to characterize the distribution of non-uniform sediment in suspension above erodible sediment beds in turbulent flow under non-equilibrium conditions. The modeling process incorporates three crucial features of sediment-laden flow: mixing length, stratification, and settling velocity. The advection–diffusion equation for the $k$-th grain-size class is modified accordingly. The model's calculations encompass the determination of reference height and reference concentration, accounting for the presence of different-sized particles in the flow. The numerical solution of the model effectively captures concentration variations for distinct particle sizes in streamwise and vertical directions, as well as temporal changes. As experimental data under non-equilibrium conditions with different sediment sizes are unavailable, the study focuses on specific experiments involving various sediment beds with a mixture of different grain sizes under equilibrium conditions. The current findings reveal that the concentration magnitude decreases downstream with time for all grain sizes, eventually reaching an equilibrium state. This behavior is consistent with variations in downstream distance at a specific time. The mixing length which is concentration-dependent, first increases the suspension concentration for all grain sizes at smaller downstream distance and then the effect reverses for all grain sizes at larger downstream distance. A similar trend is observed when considering both stratification and mixing length. An error analysis evaluates the model's performance, indicating that the least error corresponds to datasets incorporating all considered effects.