โ Scribed by H.P. Zhu; A.B. Yu; Y.H. Wu
No coin nor oath required. For personal study only.
This paper presents a numerical study of the steady and unsteady state granular flows in a cylindrical hopper with flat bottom by means of the discrete element method (DEM). For both flows, the simulations were conducted under comparable conditions so that the similarity and difference between them can be examined. The distributions of the physical properties including velocity, force structure, stress and couple stress for the two hopper flows are investigated. The results suggest that the trends of these distributions for the two hopper flows are similar. In particular, for both cases, the distributions of the normal stresses are related to the normal force structures. Thus, corresponding to the large interaction forces between particles near the bottom corner and in the transitional zone, all the normal stresses are large near the bottom corner, and the radial and circumferential normal stresses are relatively large in the transitional zone. However, there are differences in the magnitudes of some physical properties for the unsteady and steady state flows. Compared with the steady state flow, the unsteady state flow has a narrower velocity distribution, and more particles experience large contact forces. Its radial and circumferential normal stresses in the plug flow and transitional zones are larger. With the decrease of the number of particles or with discharging time, the plug flow and transitional zones reduce, and the differences in the considered properties except wall shear stress and couple stress between the two flows decrease.
๐ SIMILAR VOLUMES
Systematic tests have been performed to study the behaviour of a numerical method developed to calculate 2D, steady free surface ยฏows. The Reynolds equations are solved in the physical space by employing a nonorthogonal staggered grid, while the kยฑe model is adopted to approximate the Reynolds stres
The limit cycle #utter of a two-dimensional wing with non-linear pitching sti!ness is investigated. For modelling the aerodynamic forces of the wing steady linear and non-linear models as well as an unsteady model were used. The #utter speed was calculated using the harmonic balance method and by pr