Sediment profiles in open channels are usually predicted by advection-diffusion models. Most basic forms consider the terminal settling velocity of a single particle in still clear water. Alternative forms account for hindered settling at higher concentrations. It is not known, however, how these modifications relate to mass and momentum conservation of each phase. For dilute flow, it is known that the original form can be derived from a two-phase analysis, assuming a dilute suspension, neglect of inertial effects in the momentum balance and using a linear drag force formulation. Here we study how and if it is possible to understand the hindered-settling modifications for the non-dilute case, and formulate a relation between advection-diffusion models and parameters involved in the turbulent drag force. This note verifies that the transient two-phase flow solutions converge to steady state, and compares the results to experimental data.

In recent years deep sea mining attracted a considerable amount of attention. The presence of valuable raw materials in the deep sea is interesting, securing the supply of these materials in the long term. These materials can be found, typically at depths of 2000-5000 meters, in the form of manganese nodules, massive sulfides and cobalt rich crusts. The deposits contain several metallic materials such as manganese, iron, copper, nickel and cobalt. Furthermore, massive deposits also contain elements such as germanium, selenium, tellurium and indium, which are in high demand in many industries. In order to process the manganese nodules the materials need to be transported from the deep sea to the surface. Typically this is done using a vertical hydraulic transport system or VTS in short. One of the challenges is to assure the flow, i.e. prevent possible clogging of the system. Particle sizes of manganese nodules range from 1/10 to 1/3 of the VTS pipe diameter. The objective of this paper is to numerically simulate the settling of one particle. Experimental data are used for validation. The equations of motion of a fluid flow are governed by the Navier-Stokes equations. These are discretized with the Finite Volume Method on a collocated grid and numerically solved using the fractional step method. Solids or particles are modeled using the Immersed Boundary Method (IBM). In this paper a free settling particle in a confined domain, in two dimensions, is simulated. The particle size with respect to the domain size is varied in the calculation. The settling velocity is lower in comparison with a free settling particle in an infinite domain. This is due to the so-called wall effect. The settling velocity from the numerical calculation is compared with the corrected settling velocity known from experimental data. The results from the calculation are in agreement with the experiments.