308
5 Numerical Models for Pebble-Bed Heat Transfer
with surface emissivity. The results of the SCM under different surface emissivities
are in good agreement with the existing correlations. With combined particle motion
and heat transfer model, including conduction and radiation, the discrete heat transfer model has been presented and validated by the transient experimental data. Coupled with the discrete particle simulation, the Sub-Cell radiation Model (SCM) was
extended to simulate the effective thermal conductivity of clumped and multi-sized
particles in packed nuclear beds. For the poly-dispersed beds of multi-component
pebbles, the effective particle diameter in SCM is calculated by the weighted harmonic mean of all components. From the simulations under different conditions, the
discrete heat transfer model in particle scale is in good agreement with the results of
effective particle diameter.
With regard to the effects of particle shape and emissivity distribution on heat
transfer behaviors, this work has demonstrated the application of the DEM-SCM
for simulating the radiative and conductive heat transfer within the bed filled with
non-overlapping clumped-sphere particles. By comparison of numerical results of
three kinds of clumped-shapes of particles, it indicates that the radiative heat transfer
is enhanced for particle shape C. For the pebble beds of different emissivity distributions, the SCM is applicable to predicting the effective thermal conductivity. Four
demonstrative cases of varied emissivities have been shown and 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 particle temperature distributions in the stagnant radial region
and along the flow direction have been well predicted by the DEM-SCM. 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.
5.4 CFD-DEM Coupled Simulation and Development
From the point of design and engineering applications, it is essential and significant to
simulate the flow and heat transfer in packed pebble beds. Before, a thorough understanding of the physical mechanisms involved in a packed bed was developed, and a
pseudo-porous medium model was established to provide an empirical approach to
analyze the steady-state behavior during normal conditions and the transient behaviors during nuclear accidents of HTGRs [39]. Theoretically, the flow through a packed
pebble bed is a complex gas–solid flow coupled with particle motion, fluid flow, and
the interactions between the particles. The CFD-DEM method is now fully developed
and widely applied to granular flows and fluidized beds [95–98]. It combines computational fluid dynamics for the continuous phase and the discrete element method
5 Numerical Models for Pebble-Bed Heat Transfer
with surface emissivity. The results of the SCM under different surface emissivities
are in good agreement with the existing correlations. With combined particle motion
and heat transfer model, including conduction and radiation, the discrete heat transfer model has been presented and validated by the transient experimental data. Coupled with the discrete particle simulation, the Sub-Cell radiation Model (SCM) was
extended to simulate the effective thermal conductivity of clumped and multi-sized
particles in packed nuclear beds. For the poly-dispersed beds of multi-component
pebbles, the effective particle diameter in SCM is calculated by the weighted harmonic mean of all components. From the simulations under different conditions, the
discrete heat transfer model in particle scale is in good agreement with the results of
effective particle diameter.
With regard to the effects of particle shape and emissivity distribution on heat
transfer behaviors, this work has demonstrated the application of the DEM-SCM
for simulating the radiative and conductive heat transfer within the bed filled with
non-overlapping clumped-sphere particles. By comparison of numerical results of
three kinds of clumped-shapes of particles, it indicates that the radiative heat transfer
is enhanced for particle shape C. For the pebble beds of different emissivity distributions, the SCM is applicable to predicting the effective thermal conductivity. Four
demonstrative cases of varied emissivities have been shown and 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 particle temperature distributions in the stagnant radial region
and along the flow direction have been well predicted by the DEM-SCM. 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.
5.4 CFD-DEM Coupled Simulation and Development
From the point of design and engineering applications, it is essential and significant to
simulate the flow and heat transfer in packed pebble beds. Before, a thorough understanding of the physical mechanisms involved in a packed bed was developed, and a
pseudo-porous medium model was established to provide an empirical approach to
analyze the steady-state behavior during normal conditions and the transient behaviors during nuclear accidents of HTGRs [39]. Theoretically, the flow through a packed
pebble bed is a complex gas–solid flow coupled with particle motion, fluid flow, and
the interactions between the particles. The CFD-DEM method is now fully developed
and widely applied to granular flows and fluidized beds [95–98]. It combines computational fluid dynamics for the continuous phase and the discrete element method