Discrete element simulation of internal stress and flow fields in funnel flow hoppers

摘要

Newtonian dynamics simulations have been carried out for the filling and discharge of funnel flow hoppers under both plane-strain (2D) and axially-symmetric (3D) conditions using assemblies of the order of 10~4 particles. The present work follows directly from our previous discrete element simulations which were used to predict discharge rates and hopper wall stresses. In this paper, we concentrate on the prediction of the internal and wall distributions of the normal and tangential components of the bulk stresses, distributions of particle velocities and interstitial voidage in both static and flowing (dynamic) conditions. In order to illustrate the effects on the bulk phenomena of different particle interaction laws, simulations have been carried out contrasting (ⅰ) Hertz-type (elastic) interaction which simulates well nearly rigid particles at high normal loads with (ⅱ) a soft continuous interaction which allows for significant frictional engagement between particles at very small normal loads similar to the conditions known to prevail near the hopper outlet during discharge. A non-intrusive local averaging technique was developed to compute bulk stresses from the values of local interparticle contact stresses which allowed us to monitor the changes in the orientation of the major principal normal stress as well as the magnitude of the shear stress in different hopper sections. Distributions of contact tangential displacement vectors have been computed to compare the frequency of rupture zones (i.e. high shear regions) in both plane-strain and axial-symmetric flows. Corresponding maps of particle velocity vectors have also been generated to provide information about slow and fast moving regions of the flow fields and the extent of bulk dilation accompanying flow. The internal flow patterns and distributions of high shear regions are shown to be affected significantly by the nature of the particle interaction law chosen with softer interactions giving rise to more well-developed rupture zones in both plane-strain and axial-symmetry. In some contrast, the internal distribution of the bulk normal stress is affected very little by the choice of the particle normal force interaction law.