Keynote Talk: Generating Macroscopic Quantities of Particle-Fluid Flows: Applications to Systems with Coarse or Cohesive Particles
There are continuum and discrete approaches for describing granular flows. A continuum approach relies on local quantities which can be derived through an averaging method based on a discrete approach. But the selection of an averaging domain and the validity of local quantities for constitutive relations are not well established, particularly for transient particle-fluid flows. Here, we demonstrate that invariant local quantities such as stress and solid volume fraction can be generated on a proper averaging domain in a fluidized and a moving bed with coarse or cohesive particles. Furthermore, the relation between solid pressure and solid volume fraction is established and compared to the ones in the literature. For coarse particle systems the relation agrees qualitatively well but is different to all the existing monotonic ones in the literature. It shows a bifurcation at a high solid volume fraction, essentially linked to the variation of short and enduring contacts among particles with flow state and solid volume fraction. For cohesive particle systems, it is found that the solid pressure is underestimated by the classical kinetic theory, even when the solid fraction is smaller than 0.49. Accordingly, a modified equation considering particle contacts and particle fluctuating velocity is proposed, which agrees well with the averaged relation. These findings should be well considered in continuum modelling of systems with coarse/cohesive particles.