A micro-macro constitutive relationship for the pressure of solid phase in dense fluid-particle flows in hopper

Continuum modelling of fluid-particle multiphase flows is often challenging when the solid phase becomes dense. In this work, a micro-macro approach combining the microscale discrete element method and the averaging method is used to explore the normal stress (pressure) of the solid phase to better describe dense fluid-particle flows. Various effects of Young's modulus, Poisson ratio, sliding friction, and rolling friction are examined and an exponential relationship between pressure and solid volume fraction is proposed. With this relationship implemented, the Two-Fluid Model can reproduce the steady discharge of particles from hoppers, which is regarded as a critical test of dense particle flow for TFM. The generality of the model is tested in a variety of cases, such as different hopper angles, orifice widths and fill heights. Comparisons of the present model with previous models are also made to enhance the understandings of fluid-particle multiphase flows.