Computer simulation of rapid granular flow through an orifice

Rapid granular flow through an orifice (nozzle-shaped flow restrictor) located at the bottom of a vertical tube has been studied using three-dimensional direct computer simulation with the purpose of investigating (1) characteristics of rapid granular flows through the flow restrictor, (2) the choking condition of rapid flow at the orifice and thus conditions at which the maximum discharge rate takes place for the given orifice, and (3) a functional relationship between the discharge rate and flow quantities such as granular temperature and solid fraction. In the present simulation, where the frictional hard-sphere collision operator was employed, it was possible to obtain both rapid and slow (choked) flows through the orifice by controlling the number of particles in the system. The results show that the profile of granular temperature in the vicinity of the orifice plays an important role in determining the choking condition at the orifice. Flow appears to be choked when an adverse granular conduction occurs locally at the orifice in the direction opposite to the mean flow. On the other hand, flow is not choked when the fluctuation energy is conducted in the mean flow direction near the orifice. When flow is not choked, the discharge rate through the orifice increases with increasing solid fraction or normal stress. Once the flow becomes choked, however, the discharge rate decreases as the solid fraction or normal stress increases. Also for inelastic, rough particles, the discharge rate is found to be proportional to the granular temperature to the power of 1.5 and inversely proportional to the gravitational acceleration and the tube length.