5.6 Summary
391
fer is enhanced for particle shape C. For the pebble beds of different emissivity
distributions, the SCM applies to predict the effective thermal conductivity. Four
demonstrative cases of varied emissivities have been shown. The effective emissivities of the four cases have been obtained. Additionally, another demonstrative case
is on the application of the DEM-SCM coupled method to simulate the flow motion,
transient radiative, and conductive heat transfers for the pebble flow in the HTR-10
reactor. The DEM-SCM has well predicted the particle temperature distributions in
the stagnant radial region and along the flow direction. For a particular application,
effective heat transfer cells of SC and BCC and FCC packings were presented for
thermal radiation of nuclear-packed pebble beds. There was only a slight difference
between the present cell-particle area ratio η and the theoretical results.
Although the CFD-DEM method is now fully developed and widely applied to
granular flows and fluidized beds, the heat transfer model for packed pebble beds
needs to be improved substantially. Three basic modes of heat transfer need to be
considered in the simulations, i.e., conduction between particles in contact, fluid–
particle convection, and particle thermal radiation. Therefore, a complete CFD-DEM
method coupled with particle-scale radiation is discussed for packed pebble beds.
Simulations with different initial conditions or physical properties were performed. Results show that when the fluid heat storage capacity or the thermal conductivity is larger, the non-uniformity of the temperature in the packed pebble bed is
less. The effect of particle thermal radiation on packed pebble beds is discussed using
dimensional analysis. The CFD-DEM simulation of fluid–particle systems with particle thermal radiation is performed on sub-particle-scale mesh. For accomplishing
this purpose, a Smoothed Void Fraction Method (SVFM) is proposed to compute the
void fraction field based on the particle position and volume.
In the validation by a spout fluidized bed when the cell size is less than the particle
diameter, it is shown that SVFM is preferable to DFVM for the CFD-DEM simulation since it is in better agreement with the experimental measurements. Moreover,
the CFD-DEM simulation using the SVFM on sub-particle scale meshes is performed for the benchmark problem of the HTR-10 reactor. The numerical results
at the smoothing degree of η = 0.5 are in good agreement with the empirical code
of THERMIX—which is based on experimental measurements. In addition, the discussion indicates that the smoothing degree in SVFM is recommended to be 0.5–0.7
based on the void fraction distribution of Voronoï tessellation.
Moreover, the present SRM-based CFD-DEM model is assessed and proved to
be suitable for engineering applications, especially for HTGRs. Despite using the
Short-Range Model (SRM or SRM+) or the empirical model for radiation, it can be
used for the prediction and analysis of heat transfer in real reactors. This is essential
and significant for reactor design and improvement. Similarly, the present model
can also be potentially used for other engineering applications with radiation at high
temperatures.
Finally, multiscale modeling of particle radiation based on the gray-body assumption is performed in full integral scales for large-scale granular systems of random
packing. Besides, the black radiation model, the uniform radiation model, and the
local radiation model are also discussed for the particle–particle and particle–wall
391
fer is enhanced for particle shape C. For the pebble beds of different emissivity
distributions, the SCM applies to predict the effective thermal conductivity. Four
demonstrative cases of varied emissivities have been shown. The effective emissivities of the four cases have been obtained. Additionally, another demonstrative case
is on the application of the DEM-SCM coupled method to simulate the flow motion,
transient radiative, and conductive heat transfers for the pebble flow in the HTR-10
reactor. The DEM-SCM has well predicted the particle temperature distributions in
the stagnant radial region and along the flow direction. For a particular application,
effective heat transfer cells of SC and BCC and FCC packings were presented for
thermal radiation of nuclear-packed pebble beds. There was only a slight difference
between the present cell-particle area ratio η and the theoretical results.
Although the CFD-DEM method is now fully developed and widely applied to
granular flows and fluidized beds, the heat transfer model for packed pebble beds
needs to be improved substantially. Three basic modes of heat transfer need to be
considered in the simulations, i.e., conduction between particles in contact, fluid–
particle convection, and particle thermal radiation. Therefore, a complete CFD-DEM
method coupled with particle-scale radiation is discussed for packed pebble beds.
Simulations with different initial conditions or physical properties were performed. Results show that when the fluid heat storage capacity or the thermal conductivity is larger, the non-uniformity of the temperature in the packed pebble bed is
less. The effect of particle thermal radiation on packed pebble beds is discussed using
dimensional analysis. The CFD-DEM simulation of fluid–particle systems with particle thermal radiation is performed on sub-particle-scale mesh. For accomplishing
this purpose, a Smoothed Void Fraction Method (SVFM) is proposed to compute the
void fraction field based on the particle position and volume.
In the validation by a spout fluidized bed when the cell size is less than the particle
diameter, it is shown that SVFM is preferable to DFVM for the CFD-DEM simulation since it is in better agreement with the experimental measurements. Moreover,
the CFD-DEM simulation using the SVFM on sub-particle scale meshes is performed for the benchmark problem of the HTR-10 reactor. The numerical results
at the smoothing degree of η = 0.5 are in good agreement with the empirical code
of THERMIX—which is based on experimental measurements. In addition, the discussion indicates that the smoothing degree in SVFM is recommended to be 0.5–0.7
based on the void fraction distribution of Voronoï tessellation.
Moreover, the present SRM-based CFD-DEM model is assessed and proved to
be suitable for engineering applications, especially for HTGRs. Despite using the
Short-Range Model (SRM or SRM+) or the empirical model for radiation, it can be
used for the prediction and analysis of heat transfer in real reactors. This is essential
and significant for reactor design and improvement. Similarly, the present model
can also be potentially used for other engineering applications with radiation at high
temperatures.
Finally, multiscale modeling of particle radiation based on the gray-body assumption is performed in full integral scales for large-scale granular systems of random
packing. Besides, the black radiation model, the uniform radiation model, and the
local radiation model are also discussed for the particle–particle and particle–wall