Fig 1.
a: The simplified DGT; b: The sketch of ADS.
Fig 2.
a: The sketch of DGT; b: Experimental setup.
Table 1.
Parameters for the simulations and experiments.
Fig 3.
Relation of the flow rate with H.
In the simulations and experiments. H ranges from 20 to 200d as Table 1 shows, while D, D0 and D1 are fixed to 100d, 24d and 50d, respectively. Error bars of experimental results are given in blue color and the largest error bar is magnified.
Fig 4.
Relation of the flow rate with D1.
In the simulations (experiments), D1 ranges from 30 to 70d (80d), while D, D0 and H are fixed to 100d, 24d and 200d, respectively. Error bars of experimental results are given in blue color and the largest error bar is magnified.
Fig 5.
Relation of the flow rate with D.
In the simulations (experiments), D ranges from 50d (40d) to 100d, while D1, D0 and H are fixed to 30d, 24d and 200d, respectively. Error bars of experimental results are given in blue color and the largest error bar is magnified.
Fig 6.
Relation of the flow rate with D0.
In the simulations (experiments), D0 ranges from 8d to 40d, while D1, D and H are fixed to 50d, 100d and 200d, respectively. Error bars of experimental results are given in blue color and the largest error bar is magnified.
Fig 7.
Sketch map of the free surface.
A slice with the width 0.005 m in the flowing grain system.
Fig 8.
Free surface in simulation and experiment: a, top view of averaged free surface from simulation; b, front view of averaged free surface from simulation; the color in the map represent the height in Fig a & Fig b; c, top view of one snapshot free surface from experiment. For these figures, parameters are H = 200d, D = 100d; D1 = 70d; D0 = 24d, respectively.
Fig 9.
Front views of averaged free surface with different pipe diameter: a, D1 = 30d; b, D1 = 40d; c, D1 = 60d, d, D1 = 70d. The other parameters are H = 200d, D = 100d, D0 = 24d, respectively.
Fig 10.
δz of the fitted free surface and the grains with different pipe diameter: a, D1 = 30d; b, D1 = 40d; c, D1 = 60d, d, D1 = 70d. The other parameters are H = 200d, D = 100d, D0 = 24d, respectively.
Table 2.
Fitted parameters with formula 3.
Fig 11.
Standard deviation of the free surface with different pipe’s diameter: a, D1 = 30d; b, D1 = 40d; c, D1 = 60d, d, D1 = 70d. The other parameters are H = 200d, D = 100d, D0 = 24d, respectively.
Fig 12.
Velocity field of grains on the free surface: a, vertical velocity filed; b, radical velocity field. c, the distribution of the vertical velocity. d, resultant velocity calculated from vertical velocity and radical velocity. In this Fig, Both radical and vertical directions are the same as that in the cylindrical coordinate system. The parameters are H = 200d, D = 100d, D1 = 70d, D0 = 24d, respectively.