Continuum simulation of non-local effects in a granular silo discharge flow using a regularized μ (I) rheology model
Journal
Physics of Fluids
Journal Volume
33
Journal Issue
9
Date Issued
2021
Author(s)
Lin C.-C
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 = C ρ g (L - k d) 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 Δ Q ¯, made dimensionless by ρ g d 3 / 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. ? 2021 Author(s).
Subjects
Aspect ratio
Elasticity
Fluidization
Missile silos
Momentum
Momentum transfer
Shear strain
Velocity
Continuum simulations
Discharge flow
High shear
Local flows
Momentum transports
Non-local effect
Nonlocal
Nonuniform field
Shear zone
Silo discharge
Orifices
Type
journal article