16
1 Introduction
Recently, the spot model has been extended and improved, and it is now used in
industry to model bulk material mixing (Rycroft et al., 2010). The classical kinetic
theory of gasses can be applied to dilute granular flows, but it clearly breaks down
in dense flows with long-lasting, and frictional contacts [43, 126]; as occurred in
pebble-bed reactors. Other models, e.g., cellular automata model, steepest decent
model, and self-organized criticality theory, etc. [168], also offer some new ideas.
Among these models, discrete element method [169, 170], might be more appropriate
and adaptable for dense granular flow. However, the model has still been doubted on
the quantitative accuracy, especially about the arbitrarily shaped particles, although
its qualitative accuracy has been widely accepted.
For Pebble Flow Uniformity and Stagnation
Simply speaking, what we expect in the reactor core is a kind of flow pattern that is
uniform, productive, and consistent flow called mass flow. Problems like flooding of
powders, channeling, and hang-ups do not occur, and stagnant regions are eliminated.
Caking or crystallization is also minimized. Pebbles circulated in the core should
follow the “First-In-First Out” sequence, so that each fuel pebble can reach nearly
the same burn-up level when it is drained out.
Mass flow index (MFI) is introduced as a quantitative measure to evaluate the
radial flow uniformity [41, 142, 171], considering a simple index to recognize the
mass and funnel flow regime [172], in the silo pebble flow. The pebbles move rapidly
in the mass flow regime locating in the central part of the pebble bed, whereas funnel
flow stays nearly stagnant near the walls and corners. That is to say, the pebbles
firstly loaded will be discharged firstly in the middle region, but lastly in the nearwall region. The occurrence of the two regimes is analogous with the field of boundary
layer theory [173], in fluid mechanics, although the physics of fluids is fundamentally
different from the granular media. Nevertheless, the rich body of work devoted to
the analysis of the boundary layer characteristics (such as displacement thickness,
momentum thickness) and the work relating to the analysis and design of contraction
pipes (for instance, the wind tunnel [174, 175], is similar with the base configuration
of the pebble bed).
In nuclear engineering, some strategies have been studied to make a very slow
pebble flow field uniform. The major strategy is to modify the geometry of the
pebble bed, especially the cone angle and shape of the bed’s contraction bottom [63,
145]. For the sake of relieving caking and crystallization in the near-wall region,
the internal wall with specific-designed structures has also been studied through
simulations [104]. Surface treatment like polishing contact surfaces between particle
and particle, or particle and wall to reduce friction, is also a possible way to facilitate a
relatively uniform flow field [144, 176]. At the same time, it is sometimes unrealistic
because of material restricts and economic consideration in practical engineering.
These works provide a suitable framework to be applied to characterize the pebble
flow regime and the near-wall flow behaviors.
For Two-Region Pebble Bed Design
1 Introduction
Recently, the spot model has been extended and improved, and it is now used in
industry to model bulk material mixing (Rycroft et al., 2010). The classical kinetic
theory of gasses can be applied to dilute granular flows, but it clearly breaks down
in dense flows with long-lasting, and frictional contacts [43, 126]; as occurred in
pebble-bed reactors. Other models, e.g., cellular automata model, steepest decent
model, and self-organized criticality theory, etc. [168], also offer some new ideas.
Among these models, discrete element method [169, 170], might be more appropriate
and adaptable for dense granular flow. However, the model has still been doubted on
the quantitative accuracy, especially about the arbitrarily shaped particles, although
its qualitative accuracy has been widely accepted.
For Pebble Flow Uniformity and Stagnation
Simply speaking, what we expect in the reactor core is a kind of flow pattern that is
uniform, productive, and consistent flow called mass flow. Problems like flooding of
powders, channeling, and hang-ups do not occur, and stagnant regions are eliminated.
Caking or crystallization is also minimized. Pebbles circulated in the core should
follow the “First-In-First Out” sequence, so that each fuel pebble can reach nearly
the same burn-up level when it is drained out.
Mass flow index (MFI) is introduced as a quantitative measure to evaluate the
radial flow uniformity [41, 142, 171], considering a simple index to recognize the
mass and funnel flow regime [172], in the silo pebble flow. The pebbles move rapidly
in the mass flow regime locating in the central part of the pebble bed, whereas funnel
flow stays nearly stagnant near the walls and corners. That is to say, the pebbles
firstly loaded will be discharged firstly in the middle region, but lastly in the nearwall region. The occurrence of the two regimes is analogous with the field of boundary
layer theory [173], in fluid mechanics, although the physics of fluids is fundamentally
different from the granular media. Nevertheless, the rich body of work devoted to
the analysis of the boundary layer characteristics (such as displacement thickness,
momentum thickness) and the work relating to the analysis and design of contraction
pipes (for instance, the wind tunnel [174, 175], is similar with the base configuration
of the pebble bed).
In nuclear engineering, some strategies have been studied to make a very slow
pebble flow field uniform. The major strategy is to modify the geometry of the
pebble bed, especially the cone angle and shape of the bed’s contraction bottom [63,
145]. For the sake of relieving caking and crystallization in the near-wall region,
the internal wall with specific-designed structures has also been studied through
simulations [104]. Surface treatment like polishing contact surfaces between particle
and particle, or particle and wall to reduce friction, is also a possible way to facilitate a
relatively uniform flow field [144, 176]. At the same time, it is sometimes unrealistic
because of material restricts and economic consideration in practical engineering.
These works provide a suitable framework to be applied to characterize the pebble
flow regime and the near-wall flow behaviors.
For Two-Region Pebble Bed Design