Continuum simulation of non-local effects in a granular silo discharge flow using a regularized μ(I) rheology model

Abstract

The effect of non-local momentum transport on a silo discharge process is numerically investigated using a continuum simulation with the μ(I) rheology model in which the gradient expansion model is adopted to account for the non-local effects due to the non-uniform field of inertial number I [Bouzid et al., Phys. Rev. Lett. 111, 238301 (2013)]. The singularity for I = 0 is handled with a regularization scheme [Lin and Yang, J. Comput. Phys. 420, 109708 (2020)]. Compared to the discharge dynamics predicted with the local μ(I) rheology model, the non-local effect enhances the velocity field to increase the volume discharge flow rate Q, especially when the silo orifice L is narrower. Both the local and non-local flow simulations conform to the Beverloo relation Q=Cρg(L−kd)3/2, where d is the intrinsic grain diameter but the non-local effects appear to lessen the orifice reduction effect coefficient k. The difference between the local and the non-local flow rates ΔQ¯, made dimensionless by ρgd3/2, grew monotonically with decreasing L/d with a slight enhancement if the silo height-to-width aspect ratio deviates from unity. Finally, we evaluated the ratio of the shear strain rate to the instantaneous maximum value to define a high-shear zone when the ratio is above a threshold and studied its evolution from the onset to the end of the discharge process. Interestingly, non-local momentum transport helped to reduce the size of the high-shear zone to give a more uniformly fluidized central zone above the orifice.