1.3 Pebble Flows
15
kinematic model based on the Eulerian approach. This model is used to reconstruct
the granular flow velocity [129, 130]. The other category is the discrete element
method (DEM) based on the Lagrangian approach of modeling. DEM has already
been used extensively to simulate the packing structure of pebbles, pebble flows,
and effective thermal conductivity of pebbles [146, 147]. Besides, with the known
pebble structure known, the CFD tools, like large eddy simulation [148], were used
to simulate the interstitial flow configurations around nuclear fuels.
Many important issues have been arisen and extensively studied for pebble flows
in various applications. These works can be generally classified into four categories:
• The static packing structure of pebbles: For example, some investigations were
conducted on the effects of the pebble size distributions and friction coefficients on
the pebble packing [149], for the thermomechanical design of solid blanket, and
the effect of the pebble size and the side difference on the packing structures of the
ceramic breeder test blanket module [146, 150]. Moreover, some works focused
on the uncertainty and sensitivity analyses of the filling fraction of the pebble bed
HTR [151, 152] and the packing factor of pebbles in the molten salt reactor[153].
• Pebble flow dynamics and characteristics: for example, the measurement of the
pebble movements by the Radioactive Particle Tracking (RPT) in the PBMR [100]
and by the Particle Tracking Velocimetry (PTV) in the HTR-10 [154, 155]. The
analysis of the friction effect on the flow patterns in high-temperature gas-cooled
reactor was also performed [156].
• Interstitial helium flow characteristics: for example, the helium flow in fusion
engineering test reactors [157], and sometimes with the conjugate heat transfer
[158];
• effective thermal conductivity of the pebble beds: for example, the effects of bed
strain and pebble deformation on the effective thermal conductivity [147], and the
individual pebble temperature peaking factor in AVR and PBMR-400 MW were
explored [159]. The convective heat transfer of pebbles in fluoride-salt-cooled
high-temperature reactors [160], and the effective radiative thermal conductivity
measurement and modeling were intensively discussed [161]. In addition, some
models, e.g., the short-range and long-range radiation models [211], the sub-cell
radiation model [162], as well as the new uniform continuum medium-based models, have also been established [163].
For Pebble Flow Patterns and Regimes
Over the past 50 years, a number of theoretical approaches have been proposed for
granular flow. Continuum approach [129, 164], can calculate the mean velocity field,
but fails to predict the dispersion of the pebble flow. The void model [165, 166] and
spot model [43, 167], provide a different idea for dense pebble flow, in which the
pebble motion is modeled by the inverse motion of voids and spots. The models
achieve a certain agreement with the processed image of the pebble motion but lead
to some unexpected problems, such as excessive diffusion, anti-physical space, and
overlapped particles.
15
kinematic model based on the Eulerian approach. This model is used to reconstruct
the granular flow velocity [129, 130]. The other category is the discrete element
method (DEM) based on the Lagrangian approach of modeling. DEM has already
been used extensively to simulate the packing structure of pebbles, pebble flows,
and effective thermal conductivity of pebbles [146, 147]. Besides, with the known
pebble structure known, the CFD tools, like large eddy simulation [148], were used
to simulate the interstitial flow configurations around nuclear fuels.
Many important issues have been arisen and extensively studied for pebble flows
in various applications. These works can be generally classified into four categories:
• The static packing structure of pebbles: For example, some investigations were
conducted on the effects of the pebble size distributions and friction coefficients on
the pebble packing [149], for the thermomechanical design of solid blanket, and
the effect of the pebble size and the side difference on the packing structures of the
ceramic breeder test blanket module [146, 150]. Moreover, some works focused
on the uncertainty and sensitivity analyses of the filling fraction of the pebble bed
HTR [151, 152] and the packing factor of pebbles in the molten salt reactor[153].
• Pebble flow dynamics and characteristics: for example, the measurement of the
pebble movements by the Radioactive Particle Tracking (RPT) in the PBMR [100]
and by the Particle Tracking Velocimetry (PTV) in the HTR-10 [154, 155]. The
analysis of the friction effect on the flow patterns in high-temperature gas-cooled
reactor was also performed [156].
• Interstitial helium flow characteristics: for example, the helium flow in fusion
engineering test reactors [157], and sometimes with the conjugate heat transfer
[158];
• effective thermal conductivity of the pebble beds: for example, the effects of bed
strain and pebble deformation on the effective thermal conductivity [147], and the
individual pebble temperature peaking factor in AVR and PBMR-400 MW were
explored [159]. The convective heat transfer of pebbles in fluoride-salt-cooled
high-temperature reactors [160], and the effective radiative thermal conductivity
measurement and modeling were intensively discussed [161]. In addition, some
models, e.g., the short-range and long-range radiation models [211], the sub-cell
radiation model [162], as well as the new uniform continuum medium-based models, have also been established [163].
For Pebble Flow Patterns and Regimes
Over the past 50 years, a number of theoretical approaches have been proposed for
granular flow. Continuum approach [129, 164], can calculate the mean velocity field,
but fails to predict the dispersion of the pebble flow. The void model [165, 166] and
spot model [43, 167], provide a different idea for dense pebble flow, in which the
pebble motion is modeled by the inverse motion of voids and spots. The models
achieve a certain agreement with the processed image of the pebble motion but lead
to some unexpected problems, such as excessive diffusion, anti-physical space, and
overlapped particles.