DISCRETE ELEMENT SIMULATION OF INTERNAL-STRESS AND FLOW-FIELDS IN FUNNEL FLOW HOPPERS

Newtonian dynamics simulations have been carried out for the filling a nd discharge of funnel flow hoppers under both plane-strain (2D) and a xially-symmetric (3D) conditions using assemblies of the order of 10(4 ) particles. The present work follows directly from our previous discr ete 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 c omponents of the bulk stresses, distributions of particle velocities a nd interstitial voidage in both static and flowing (dynamic) condition s. In order to illustrate the effects on the bulk phenomena of differe nt particle interaction laws, simulations have been carried out contra sting (i) Hertz-type (elastic) interaction which simulates well nearly rigid particles at high normal loads with (ii) a soft continuous inte raction which allows for significant frictional engagement between par ticles at very small normal loads similar to the conditions known to p revail near the hopper outlet during discharge. A non-intrusive local averaging technique was developed to compute bulk stresses from the va lues of local interparticle contact stresses which allowed us to monit or the changes in the orientation of the major principal normal stress as well as the magnitude of the shear stress in different hopper sect ions. Distributions of contact tangential displacement vectors have be en computed to compare the frequency of rupture zones (i.e. high shear regions) in both plane-strain and axial-symmetric flows. Correspondin g maps of particle velocity vectors have also been generated to provid e information about slow and fast moving regions of the flow fields an d the extent of bulk dilation accompanying flow. The internal flow pat terns and distributions of high shear regions are shown to be affected significantly by the nature of the particle interaction law chosen wi th softer interactions giving rise to more well-developed rupture zone s in both plane-strain and axial-symmetry. In some contrast, the inter nal distribution of the bulk normal stress is affected very little by the choice of the particle normal force interaction law.