Lin C.-CFU-LING YANG2022-03-222022-03-22202110706631https://www.scopus.com/inward/record.uri?eid=2-s2.0-85115312239&doi=10.1063%2f5.0057598&partnerID=40&md5=2e66b4733c4d880ff204691da851e07bhttps://scholars.lib.ntu.edu.tw/handle/123456789/598829The 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).Aspect ratioElasticityFluidizationMissile silosMomentumMomentum transferShear strainVelocityContinuum simulationsDischarge flowHigh shearLocal flowsMomentum transportsNon-local effectNonlocalNonuniform fieldShear zoneSilo dischargeOrificesjournal article10.1063/5.00575982-s2.0-85115312239