Rheology of high speed accelerating granular flows*

The inertial number-based rheology, popularly known as the JFP model, is well known for describing the rheology of granular materials in the dense flow regime. While most of the recent studies focus on the steady-state rheology of granular materials, the time-dependent rheology of such materials has received less attention. Owing to this fact, we perform three-dimensional DEM simulations of frictional inelastic spheres flowing down an inclined bumpy surface varying over a wide range of inclination angles and restitution coefficients. We show that steady, fully developed flows are possible at inclinations much higher than those predicted from the JFP model rheology. We show that, in addition to a modified effective friction law, the rheological description also needs to account for the stress anisotropy by means of a first and second normal stress difference law.

To investigate the transient rheological behaviour of granular materials, we perform three-dimensional continuum simulations of granular flows over an inclined plane considering the fact, the extensive computational cost of DEM simulations. The flow properties computed from continuum simulations are obtained by solving the momentum balance equations supplemented by different constitutive rheological models, i.e. JFP model and a modified rheology model accounting for the first and second normal stress difference law. The predicted flow properties obtained from continuum simulations are compared with the DEM simulations. The validity of the numerical method for low as well as moderate inertial numbers will be discussed in this work. The applicability of the different rheological models at the moderate and high inertial numbers and their detailed study will be the main focus of this work.