232
4 Numerical Methods and Simulation for Pebble Flows
Also, the effects of recirculation flow rates on the Dense Pebble Flow (DPF) in
a drained pebble bed are investigated through DEM simulation. The effects can be
entirely described by two parameters C and RFKE. Thus, the suggested criterion for
categorizing the flow regimes of dense granular flow based on the values of C and
RFKE is proposed to describe the effects of the flow rates. For a better understanding
of the effects of flow rates, the specific categorization principles for dense granular
flow are suggested
• C ≥ 0.5: Intermittent pebble flow
• C <0.5, RFKE > 0.1: Transition Fluctuation pebble flow
• C <0.5, RFKE ≤ 0.1: Continuous pebble flow
With regards to three-dimensional pebble flow, the radial, and axial distributions
of the void fraction of HTGR are analyzed. In the cylindrical volume of the bed,
results clearly show the damping oscillation of void fraction in the radial direction,
and the oscillation is within about four diameters from the wall, as a result of the
regular lattice of pebble packing called the crystallization phenomenon. However,
the radial distribution of the void fraction in the core region of the pebble bed is
uniform. As for the conical base, the voids follow the normal Gaussian distribution
of variation.
In terms of axial void fraction, the increase of it in the cylindrical volume is almost
linearly proportional to the height, which is caused by the linearly increased effect
of weight and compression force of the pebbles. The averaged value of the radial
void fraction should be affected by the height of the cylindrical volume. It is also
observed that the axial variation of void fraction in the conical base is still linear.
Besides, the depth of penetration of the introduced void can be affected by the bed
configuration, especially the base shape and angle, and also by the ratio of pebble
drainage or discharging speed.
Finally, the pebble flow characteristics are further analyzed both in the Lagrangian
framework through the pebble spindles and in the Eulerian framework through the
pebble streamlines. Results show that the number of resident particles within the
corner of the bed is smaller within the bed with a larger base angle, and the pebble
flow within the main body of the pebble is rather uniform. It is reasonable to consider
the pebble flow within the main body as a perfect mass flow pattern and that within
the conical base as a funnel flow pattern.
References
1. Cundall, P.A., and O.D.L. Strack. 1980. Discussion: A discrete numerical model for granular
assemblies. Géotechnique 30 (3): 331–336.
2. Anand, Anshu, Jennifer S. Curtis, Carl R. Wassgren, Bruno C. Hancock, and William R.
Ketterhagen. 2015. Experimental study of wet cohesive particles discharging from a rectangular
hopper. Industrial & Engineering Chemistry Research 54 (16): 4545–4551.
4 Numerical Methods and Simulation for Pebble Flows
Also, the effects of recirculation flow rates on the Dense Pebble Flow (DPF) in
a drained pebble bed are investigated through DEM simulation. The effects can be
entirely described by two parameters C and RFKE. Thus, the suggested criterion for
categorizing the flow regimes of dense granular flow based on the values of C and
RFKE is proposed to describe the effects of the flow rates. For a better understanding
of the effects of flow rates, the specific categorization principles for dense granular
flow are suggested
• C ≥ 0.5: Intermittent pebble flow
• C <0.5, RFKE > 0.1: Transition Fluctuation pebble flow
• C <0.5, RFKE ≤ 0.1: Continuous pebble flow
With regards to three-dimensional pebble flow, the radial, and axial distributions
of the void fraction of HTGR are analyzed. In the cylindrical volume of the bed,
results clearly show the damping oscillation of void fraction in the radial direction,
and the oscillation is within about four diameters from the wall, as a result of the
regular lattice of pebble packing called the crystallization phenomenon. However,
the radial distribution of the void fraction in the core region of the pebble bed is
uniform. As for the conical base, the voids follow the normal Gaussian distribution
of variation.
In terms of axial void fraction, the increase of it in the cylindrical volume is almost
linearly proportional to the height, which is caused by the linearly increased effect
of weight and compression force of the pebbles. The averaged value of the radial
void fraction should be affected by the height of the cylindrical volume. It is also
observed that the axial variation of void fraction in the conical base is still linear.
Besides, the depth of penetration of the introduced void can be affected by the bed
configuration, especially the base shape and angle, and also by the ratio of pebble
drainage or discharging speed.
Finally, the pebble flow characteristics are further analyzed both in the Lagrangian
framework through the pebble spindles and in the Eulerian framework through the
pebble streamlines. Results show that the number of resident particles within the
corner of the bed is smaller within the bed with a larger base angle, and the pebble
flow within the main body of the pebble is rather uniform. It is reasonable to consider
the pebble flow within the main body as a perfect mass flow pattern and that within
the conical base as a funnel flow pattern.
References
1. Cundall, P.A., and O.D.L. Strack. 1980. Discussion: A discrete numerical model for granular
assemblies. Géotechnique 30 (3): 331–336.
2. Anand, Anshu, Jennifer S. Curtis, Carl R. Wassgren, Bruno C. Hancock, and William R.
Ketterhagen. 2015. Experimental study of wet cohesive particles discharging from a rectangular
hopper. Industrial & Engineering Chemistry Research 54 (16): 4545–4551.