Drag forces in statistically stationary and homogeneous submerged granular flows

: The paper deals with the interaction forces between the two phases of a granular flow immersed in water, analyzing in detail the effects on the drag of the concentration of the solid phase and of the interactions between velocities of the two phases and particle concentration. According to the system of equations, the relations between these variables are strongly nonlinear. In particular, this article addresses two issues: how the drag force varies as a function of the concentration only, and whether it is proper to determine the averaged drag force only as a function of the time-averaged values of velocities and concentration. We demonstrate, in fact, that by separating the average and the fluctuating part of each quantity, new terms arise representing a residual drag. To better understand the role of the interphases forces, we performed a series of tests on a two-phase flow (spherical particles in water) through a vertical column in a statistically stationary and homogeneous condition.