Connection between the mass flow rate and the base and bulk normal stresses in silo discharge

Abstract

The discharge of polydisperse grains in a two-dimensional silo, operating in a continuous-discharge mode, is studied with the help of soft-particle discrete element simulations. We find that the mass flow rate displays similar variation with vertical normal stress at the base and the transition-point in the bulk, signifying that the base normal stress can be considered as a representative of its bulk counterpart. The variation of the base and transition-point normal stresses with fill height follows the Janssen's model, with the former being larger than the latter. The transition-point ($y_t$) is defined as the vertical extent of Region of Orifice Influence (ROOI), which is situated directly above the orifice in its neighbourhood. The transition-point occurs largely at the same location irrespective of the fill height. It shifts, however, upon changing the orifice size, indicating its occurrence to be a localized phenomenon. Finally, the scaling of the vertical velocities at the transition-point and outlet uncovers $y_t$ to be a more relevant length scale than the orifice size $D$. This scaling provides a new insight into the dynamics of the silo discharge in the case where the flow rate varies but the normal stress stays largely invariant to change in the orifice size.