Based on the time-driven discrete element method, granular flow within a hopper is investigated. The main focus is thereby set on hopper vessel design variables such as discharge rates and applied wall pressures. Within the used model contacts are assumed as linear viscoelastic in normal and frictional-elastic in tangential direction. The hopper geometry is chosen according to Yang and Hsiau (2001, “The Simulation and Experimental Study of Granular Materials Discharged From a Silo With the Placement of Inserts,” Powder Technol., 120(3), pp. 244–255), who performed both experimental and numerical investigations. The considered setup is attractive because it involves only a small number of particles enabling fast modeling. However, the results on the experimental flow rates reported are contradictory and are afflicted with errors. By an analysis of the hopper fill levels at different points of time, the correct average discharge times and flow rates are obtained. Own simulation results are in good agreement with the experimental flow rates and discharge times determined. Based on the thereby defined set of simulation parameters, a sensitivity analysis of parameters such as friction coefficients, stiffnesses, and time steps is performed. As flow properties, besides the overall discharge times, the discharge time averaged axial and radial velocity distributions within the hopper and the normal stresses on the side walls during the first seconds of discharge are considered. The results show a strong connection of the friction coefficients with the discharge times, the velocity distributions, and the stresses on the side walls. Other parameters only reveal a weak often indifferent influence on the studied flow properties.

1.
Yang
,
S. C.
, and
Hsiau
,
S. S.
, 2001, “
The Simulation and Experimental Study of Granular Materials Discharged From a Silo With the Placement of Inserts
,”
Powder Technol.
0032-5910,
120
(
3
), pp.
244
255
.
2.
Duran
,
J.
, 2000,
Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials
,
Springer
,
New York
.
3.
Drake
,
T. G.
, 1990, “
Structural Features in Granular Flows
,”
J. Geophys. Res., [Solid Earth Planets]
0148-0227,
95
(
B6
), pp.
8681
8696
.
4.
Savage
,
S. B.
, 1989,
Theoretical and Applied Mechanics
,
P.
Germane
,
M.
Piau
, and
D.
Caillerie
, eds.,
Elsevier
,
New York
, pp.
241
266
.
5.
Jenkins
,
J. T.
, and
Savage
,
S. B.
, 1983, “
A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical-Particles
,”
J. Fluid Mech.
0022-1120,
130
, pp.
187
202
.
6.
Haff
,
P. K.
, 1983, “
Grain Flow as a Fluid-Mechanical Phenomenon
,”
J. Fluid Mech.
0022-1120,
134
, pp.
401
430
.
7.
Jackson
,
R.
, 1983,
The Theory of Dispersed Multiphase Flow
,
R.
Meyer
, ed.,
Academic
,
New York
.
8.
Schaeffer
,
D. G.
, 1987, “
Instability in the Evolution-Equations Describing Incompressible Antigranulocytes Flow
,”
J. Differ. Equations
0022-0396,
66
(
1
), pp.
19
50
.
9.
Niemunis
,
A.
,
Wichtmann
,
T.
, and
Triantafyllidis
,
T.
, 2005, “
A High-Cycle Accumulation Model for Sand
,”
Comput. Geotech.
0266-3524,
32
(
4
), pp.
245
263
.
10.
Sanad
,
A. M.
,
Ooi
,
J. Y.
,
Holst
,
J. M. F. G.
, and
Rotter
,
J. M.
, 2001, “
Computations of Granular Flow and Pressures in a Flat-Bottomed Silo
,”
J. Eng. Mech.
0733-9399,
127
(
10
), pp.
1033
1043
.
11.
Cundall
,
P. A.
, and
Strack
,
O. D. L.
, 1979, “
A Discrete Numerical Model for Granular Assemblies
,”
Geotechnique
0016-8505,
29
, pp.
47
65
.
12.
Miller
,
S.
, and
Luding
,
S.
, 2004, “
Cluster Growth in Two- and Three-Dimensional Granular Gases
,”
Phys. Rev. E
1063-651X,
69
(
3
), p.
031305
.
13.
Aspelmeier
,
T.
,
Giese
,
G.
, and
Zippelius
,
A.
, 1998, “
Cooling Dynamics of a Dilute Gas of Inelastic Rods: A Many Particle Simulation
,”
Phys. Rev. E
1063-651X,
57
(
1
), pp.
857
865
.
14.
Luding
,
S.
, 1995, “
Granular-Materials Under Vibration—Simulations of Rotating Spheres
,”
Phys. Rev. E
1063-651X,
52
(
4
), pp.
4442
4457
.
15.
Bird
,
G. A.
, 1994,
Molecular Gas Dynamics and the Direct Simulation of Gas Flows
,
Clarendon
,
Oxford
.
16.
Tanaka
,
T.
,
Yonemura
,
S.
,
Kiribayashi
,
K.
, and
Tsuji
,
Y.
, 1996, “
Cluster Formation and Particle-Induced Instability in Gas-Solid Flows Predicted by the DSMC Method
,”
JSME Int. J., Ser. B
1340-8054,
39
(
2
), pp.
239
245
.
17.
Huilin
,
L.
,
Zhiheng
,
S.
Ding
,
J.
,
Xiang
,
L.
, and
Huanpeng
,
L.
, 2006, “
Numerical Simulation of Bubble and Particles Motions in a Bubbling Fluidized Bed Using Direct Simulation Monte-Carlo Method
,”
Powder Technol.
0032-5910,
169
(
3
), pp.
159
171
.
18.
Muntz
,
E. P.
, 1989, “
Rarefied-Gas Dynamics
,”
Annu. Rev. Fluid Mech.
0066-4189,
21
, pp.
387
417
.
19.
Brilliantov
,
N. V.
, and
Pöschel
,
T.
, 2004,
Kinetic Theory of Granular Gases
,
Oxford University Press
,
Berlin
.
20.
Alder
,
B. J.
, and
Wainwright
,
T. E.
, 1957, “
Phase Transition for a Hard Sphere System
,”
J. Chem. Phys.
0021-9606,
27
(
5
), pp.
1208
1209
.
21.
Alder
,
B. J.
, and
Wainwright
,
T. E.
, 1959, “
Studies in Molecular Dynamics. 1. General Method
,”
J. Chem. Phys.
0021-9606,
31
(
2
), pp.
459
466
.
22.
Alder
,
B. J.
, and
Wainwright
,
T. E.
, 1960, “
Studies in Molecular Dynamics. 2. Behavior of a Small Number of Elastic Spheres
,”
J. Chem. Phys.
0021-9606,
33
(
5
), pp.
1439
1451
.
23.
Allen
,
M. P.
, and
Tildesley
,
D. J.
, 1987,
Computer Simulation of Liquids
,
Oxford University Press
,
Oxford
.
24.
Rapaport
,
D. C.
, 2001,
The Art of Molecular Dynamics Simulation
,
Cambridge University Press
,
Cambridge
.
25.
Haff
,
P. K.
, and
Werner
,
B. T.
, 1986, “
Computer-Simulation of the Mechanical Sorting of Grains
,”
Powder Technol.
0032-5910,
48
(
3
), pp.
239
245
.
26.
Walton
,
O. R.
, and
Braun
,
R. L.
, 1986, “
Viscosity, Granular Temperature and Stress Calculations for Shearing Assemblies of Inelastic, Frictional Disks
,”
J. Rheol.
0148-6055,
30
, pp.
949
980
.
27.
Luding
,
S.
, 2004, “
Molecular Dynamics Simulations of Granular Materials
,”
The Physics of Granular Media
,
H.
Hinrichsen
and
D.
Wolf
, eds.,
Wiley-VCH
,
Weinheim
.
28.
Parker
,
D. J.
,
Dijkstra
,
A. E.
,
Martin
,
T. W.
, and
Seville
,
J. P. K.
, 1997, “
Positron Emission Particle Tracking Studies of Spherical Particle Motion in Rotating Drums
,”
Chem. Eng. Sci.
0009-2509,
52
(
13
), pp.
2011
2022
.
29.
Faderani
,
S.
,
Tuzun
,
U.
,
Smith
,
D. L. O.
,
Smith
,
D. L. O.
, and
Thorpe
,
R. B.
, 1998, “
Discharge and Transport of Nearly Buoyant Granular Solids in Liquids—Part I: Tomographic Study of the Interstitial Voidage Effects Governing Flow Regimes
,”
Chem. Eng. Sci.
0009-2509,
53
(
3
), pp.
553
574
.
30.
Ristow
,
G. H.
, 1992, “
Simulating Granular Flow With Molecular-Dynamics
,”
J. Phys. I
1155-4304,
2
(
5
), pp.
649
662
.
31.
Langston
,
P. A.
,
Tüzün
,
U.
, and
Heyes
,
D. M.
, 1994, “
Continuous Potential Discrete Particle Simulations of Stress and Velocity Fields in Hoppers: Transition From Fluid to Granular Flow
,”
Chem. Eng. Sci.
0009-2509,
49
(
8
), pp.
1259
1275
.
32.
Langston
,
P. A.
,
Nikitidis
,
M. S.
,
Tuzun
,
U.
,
Heyes
,
D. M.
, and
Spyrou
,
N. M.
, 1997, “
Microstructural Simulation and Imaging of Granular Flows in Two- and Three-Dimensional Hoppers
,”
Powder Technol.
0032-5910,
94
(
1
), pp.
59
72
.
33.
Rotter
,
J. M.
,
Holst
,
J. M. F. G.
,
Ooi
,
J. Y.
, and
Sanad
,
A. M.
, 1998, “
Silo Pressure Predictions Using Discrete-Element and Finite-Element Analyses
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
356
(
1747
), pp.
2685
2712
.
34.
Sanad
,
A. M.
,
Ooi
,
J. Y.
,
Holst
,
J. M. F. G.
, and
Rotter
,
J. M.
, 2001, “
Computations of Granular Flow and Pressures in a Flat-Bottomed Silo
,”
J. Eng. Mech.
0733-9399,
127
(
10
), pp.
1033
1043
.
35.
Landry
,
J. W.
,
Grest
,
G. S.
, and
Plimpton
,
S. J.
, 2004, “
Discrete Element Simulations of Stress Distributions in Silos: Crossover From Two to Three Dimensions
,”
Powder Technol.
0032-5910,
139
(
3
), pp.
233
239
.
36.
Goda
,
T. J.
, and
Ebert
,
F.
, 2005, “
Three-Dimensional Discrete Element Simulations in Hoppers And Silos
,”
Powder Technol.
0032-5910,
158
(
1–3
), pp.
58
68
.
37.
Balevicius
,
R.
,
Kacianauskas
,
R.
,
Mroz
,
Z.
, and
Sielamowicz
,
I.
, 2006, “
Discrete Element Method Applied to Multiobjective Optimization of Discharge Flow Parameters in Hoppers
,”
Struct. Multidiscip. Optim.
1615-147X,
31
(
3
), pp.
163
175
.
38.
Kruggel-Emden
,
H.
,
Simsek
,
E.
,
Wirtz
,
S.
, and
Scherer
,
V.
, 2006, “
Modeling of Granular Flow and Combined Heat Transfer in Hoppers by the Discrete Element Method (DEM)
,”
ASME J. Pressure Vessel Technol.
0094-9930,
128
(
3
), pp.
439
444
.
39.
Zhu
,
H. P.
, and
Yu
,
A. B.
, 2004, “
Steady-State Granular Flow in a Three-Dimensional Cylindrical Hopper With Flat Bottom: Microscopic Analysis
,”
J. Phys. D
0022-3727,
37
(
10
), pp.
1497
1508
.
40.
Zhu
,
H. P.
, and
Yu
,
A. B.
, 2005, “
Steady-State Granular Flow in a 3D Cylindrical Hopper With Flat Bottom: Macroscopic Analysis
,”
Granule Matter
,
7
(
2–3
), pp.
97
107
. 1434-5021
41.
Zhu
,
H. P.
,
Yu
,
A. B.
, and
Wu
,
Y. H.
, 2006, “
Numerical Investigation of Steady and Unsteady State Hopper Flows
,”
Powder Technol.
0032-5910,
170
(
3
), pp.
125
134
.
42.
Ketterhagen
,
W. R.
,
Curtis
,
J. S.
,
Wassgren
,
C. R.
,
Kong
,
A.
,
Narayan
,
P. J.
, and
Hancock
,
B. C.
, 2007, “
Granular Segregation in Discharging Cylindrical Hoppers: A Discrete Element and Experimental Study
,”
Chem. Eng. Sci.
0009-2509,
62
(
22
), pp.
6423
6439
.
43.
Ketterhagen
,
W. R.
,
Curtis
,
J. S.
,
Wassgren
,
C. R.
, and
Hancock
,
B. C.
, 2008, “
Modeling Granular Segregation in Flow From Quasi-Three-Dimensional, Wedge-Shaped Hoppers
,”
Powder Technol.
0032-5910,
179
(
3
), pp.
126
143
.
44.
Kruggel-Emden
,
H.
,
Strum
,
M.
,
Wirtz
,
S.
, and
Scherer
,
V.
, 2008, “
Selection of an Appropriate Time Integration Scheme for the Discrete Element Method (DEM)
,”
Comput. Chem. Eng.
0098-1354,
32
(
10
), pp.
2263
2279
.
45.
Johnson
,
K. L.
, 1989,
Contact Mechanics
,
Cambridge University Press
,
Cambridge
.
46.
Munjiza
A.
, 2004,
The Combined Finite-Discrete Element Method
,
Wiley
,
New York
.
47.
Kruggel-Emden
,
H.
,
Simsek
,
E.
,
Rickelt
,
S.
,
Wirtz
,
S.
, and
Scherer
,
V.
, 2007, “
Review and Extension of Normal Force Models for the Discrete Element Method
,”
Powder Technol.
0032-5910,
171
(
3
), pp.
157
173
.
48.
Kruggel-Emden
,
H.
,
Wirtz
,
S.
, and
Scherer
,
V.
, 2008, “
A Study on Tangential Force Laws Applicable to the Discrete Element Method (DEM) for Materials With Viscoelastic or Plastic Behavior
,”
Chem. Eng. Sci.
0009-2509,
63
(
6
), pp.
1523
1541
.
49.
Kruggel-Emden
,
H.
,
Wirtz
,
S.
, and
Scherer
,
V.
, 2007, “
An Analytical Solution of Different Configurations of the Linear Viscoelastic Normal and Frictional-Elastic Tangential Contact Model
,”
Chem. Eng. Sci.
0009-2509,
62
(
23
), pp.
6914
6926
.
50.
Schäfer
,
J.
,
Dippel
,
S.
, and
Wolf
,
D. E.
, 1996, “
Force Schemes in Simulations of Granular Materials
,”
J. Phys. I
1155-4304,
6
(
1
), pp.
5
20
.
51.
Drake
,
T. G.
, 1991, “
Antigranulocytes Flow-Physical Experiments and Their Implications for Microstructural Theories
,”
J. Fluid Mech.
0022-1120,
225
, pp.
121
152
.
You do not currently have access to this content.