5.4 CFD-DEM Coupled Simulation and Development
345
• Compared to the case without particle radiation, heat transfer is significantly
enhanced by particle radiation at high temperatures. A Particle Radiation Factor (PRF) is an independent non-dimensional parameter to quantify the effect of
particle-scale radiation in packed pebble beds. The PRF increases significantly
with temperature and decreases gradually as the heat storage capacity or the thermal conductivity of the fluid increases. A demonstrative utilization of the present
model is performed for a benchmark problem based on the HTR-10 nuclear reactor, and the results, in general, are in agreement with the results predicted by other
empirical codes. When the nuclear reactor is above full power, the power required
by the fan will increase significantly. In the decay heat removal process, particle
radiation is essential to retain the bed temperature below the allowable limit, which
is significant for nuclear reactor safety.
• For the three basic modes of heat transfer, namely conduction between particles at
contact, fluid–particle convection, and particle thermal radiation, particle thermal
radiation increases significantly at high temperatures. Radiation enhances the heat
transfer significantly, and the particle temperature field in a packed pebble bed
tends to be much more uniform. By using dimensional analysis, a particle radiation
factor ϕ can be defined. It is an independent parameter that can be used to quantify
the effect of particle radiation in a packed pebble bed. The particle radiation factor
increases significantly with the temperature from almost 0 at 400 K to 0.055 at
1,200 K, and about 0.13 (0.1) at 1,800 K, and is hardly affected by conduction and
convection heat transfer.
• Some fluid physical properties also make a contribution to the effect of particle
radiation. For example, the fluid density increases with the increase in pressure, and
the thermal conductivity varies for different gases. It was shown that the particle
radiation factor decreases gradually when the heat storage capacity or thermal
conductivity of the fluid increases. Additionally, although other fluid properties,
which are functions of varied temperatures, may also influence particle radiation in
HTGRs through the Reynolds number or Prandtl number, they are not as important
as the fluid density and thermal conductivity.
• The numerical results obtained with the SRM+ model for the HTR-10 benchmark
problem are, in general, in good agreement with the results obtained by the empirical codes. It was shown that when the reactor is operated above full power, the
power required by the fans to drive the convective flow will increase significantly,
and it may be a challenge to ensure the nuclear safety of the control systems. In
the removal of the decay heat of HTR-10, particle radiation plays an vital role in
maintaining the temperature below the maximum allowable level. This application
demonstrates the potential utilization of the present model for the prediction of
particle radiation and the analysis of many practical heat transfer devices.
• From the definition of the integral form for void fraction, the Spatial Distribution
Function (SDF) for the particle-Divided Finite Volume Method (DFVM) is a step
function. Using the step function is difficult to converge in CFD-DEM simulations
when cell size is close to particle diameter. The diffusion function is obtained
analytically from a mass diffusion case, and it converges to the step function
when the smoothing degree η goes to 0. Compared with the Gaussian function,
345
• Compared to the case without particle radiation, heat transfer is significantly
enhanced by particle radiation at high temperatures. A Particle Radiation Factor (PRF) is an independent non-dimensional parameter to quantify the effect of
particle-scale radiation in packed pebble beds. The PRF increases significantly
with temperature and decreases gradually as the heat storage capacity or the thermal conductivity of the fluid increases. A demonstrative utilization of the present
model is performed for a benchmark problem based on the HTR-10 nuclear reactor, and the results, in general, are in agreement with the results predicted by other
empirical codes. When the nuclear reactor is above full power, the power required
by the fan will increase significantly. In the decay heat removal process, particle
radiation is essential to retain the bed temperature below the allowable limit, which
is significant for nuclear reactor safety.
• For the three basic modes of heat transfer, namely conduction between particles at
contact, fluid–particle convection, and particle thermal radiation, particle thermal
radiation increases significantly at high temperatures. Radiation enhances the heat
transfer significantly, and the particle temperature field in a packed pebble bed
tends to be much more uniform. By using dimensional analysis, a particle radiation
factor ϕ can be defined. It is an independent parameter that can be used to quantify
the effect of particle radiation in a packed pebble bed. The particle radiation factor
increases significantly with the temperature from almost 0 at 400 K to 0.055 at
1,200 K, and about 0.13 (0.1) at 1,800 K, and is hardly affected by conduction and
convection heat transfer.
• Some fluid physical properties also make a contribution to the effect of particle
radiation. For example, the fluid density increases with the increase in pressure, and
the thermal conductivity varies for different gases. It was shown that the particle
radiation factor decreases gradually when the heat storage capacity or thermal
conductivity of the fluid increases. Additionally, although other fluid properties,
which are functions of varied temperatures, may also influence particle radiation in
HTGRs through the Reynolds number or Prandtl number, they are not as important
as the fluid density and thermal conductivity.
• The numerical results obtained with the SRM+ model for the HTR-10 benchmark
problem are, in general, in good agreement with the results obtained by the empirical codes. It was shown that when the reactor is operated above full power, the
power required by the fans to drive the convective flow will increase significantly,
and it may be a challenge to ensure the nuclear safety of the control systems. In
the removal of the decay heat of HTR-10, particle radiation plays an vital role in
maintaining the temperature below the maximum allowable level. This application
demonstrates the potential utilization of the present model for the prediction of
particle radiation and the analysis of many practical heat transfer devices.
• From the definition of the integral form for void fraction, the Spatial Distribution
Function (SDF) for the particle-Divided Finite Volume Method (DFVM) is a step
function. Using the step function is difficult to converge in CFD-DEM simulations
when cell size is close to particle diameter. The diffusion function is obtained
analytically from a mass diffusion case, and it converges to the step function
when the smoothing degree η goes to 0. Compared with the Gaussian function,