283341 Residence Time Distribution As Predicted by a Kinematic Model for Mass Flow Powder Discharge From a Conical Hopper
The mixing and residence time distribution of the elements comprising a powder inflow to a silo with a conical hopper is relevant and important in some industrial powder handling and storage systems, and could also provide a platform for testing the validity of different approaches to the determination of the velocity distribution in the hopper.
In this paper, we have followed a kinematic model for the velocity profile, [see Nedderman, R M. And Tüzün, U., A Kinematic Model for the flow of granular materials, Powder Technology, 1979 22 243; Choi, J. Kudrolli, A. Bazant, M. Z., Velocity profile of Granular flows inside silos and Hoppers, J. Phys.: Condens. Matter 17 (2005) S2533-S2548], and used this to estimate mixing parameters and the residence time distribution for the hopper. We have specifically considered a case where, initially, powder is deposited in the hopper and cylindrical bunker above it, in horizontal layers. When flow is initiated, any given layer is unable to keep its radius constant as it travels into the hopper, and hence, the volume of powder would decrease unless the horizontal structure is broken. The kinematic model allows us to specify how this displaced powder is repositioned in the layer. Residence time information is extracted from the reconfigured layers as they emerge from the hopper exit. We note that the parameters in the kinematic model must be fitted for a particular system.
Plans for further work in this area are briefly discussed, including a possible tracer experiment, and a model in which the velocity profile of the hopper is established using stress field theory (as in Nedderman, R M., Statics And Kinematics of Granular Materials, Cambridge University Press).