26
1 Introduction
the simulation data, which revealed the expected results. Then, the repeatable results
and discussions of two vacuum tests and two atmospheric pressure helium tests up to
1200
◦ C were presented. The two tests were implemented with different heating
processes to verify the repeatability and validity of the experimental method. Both
of the results in vacuum and helium were repeatable and stable in this experiment,
and they were comparable with the results of SANA and HTTU. Moreover, in the
researches, as mentioned earlier [161, 287, 288], about this experiment, it has been
found that installation-position errors of thermocouples contributed to the primary
uncertainties of effective diffusivity and conductivity. Therefore, an extreme caution
was given to reduce this experimental error further by involving position-retrieve
iteration into the inverse method, which gave better results.
In the early stage of investigating the particle radiation in packed pebble beds, the
most efforts focused on the experimental measurements and developing the relevant
empirical correlations [237, 243, 284]. The particle radiation flux and the effective
thermal conductivity (ETC) increase significantly under high-temperatures in the
packed pebble beds [252, 289, 290]. Then the correlations of ETC are extended to
the polydisperse beds of multicomponent spheres [208, 272].
Moreover, for theoretical and numerical study, the macroscopic models based on
the porous-medium assumption of the packed pebble bed have been widely used in
the simulation [291] and analysis of transient thermal-hydraulics of HTGR [292].
There are three types of heat transfer modes in the packed pebble beds, i.e., the
convective, conduction, and thermal radiation heat transfers. For example, based on
dimensional analysis of the convective heat transfer, the Rayleigh–Darcy number for
natural convection will increase significantly at lower temperature and the contribution of natural convection to total heat transport will increase consequentially [293].
For other kinds of heat transfer modes, the concept of effective thermal conductivity of the packed pebble bed (k e f f ) is always incorporated to simplify the handling
of heat transfer. It is a critical parameter for HTGR and includes the fluid-particle
conduction, particle-particle heat conduction, and particle-particle thermal radiation.
k e f f is usually obtained from experimental data. It can affect the maximum temperature in nuclear fuel and vessel under, especially limiting events, which is closely
related to the nuclear safety margin of HTGR [196]. To date, theoretical models
of heat conduction in packed pebble beds of rough and mono-sized spheres have
been well-developed and verified by experiments [283, 294]. However, the particleparticle thermal radiation models are still poorly developed. The existing models and
empirical correlations usually deviate from each other, significantly [263].
In recent years, the experimental facilities targeted for HTGR, such as HTTU [30]
and TF-PBEC [248, 295], were tested and the operation conditions were similar to
that in the core of HTGR. When the solid conductivity of the particle material is
close to the ETC of the particle radiation, the effect of the solid conductivity on the
particle radiation is significant [295, 296].
However, in the particle-scale simulation, only the solid-solid conduction through
the contact area is considered in the heat transfer equation of particles. The contact
area is directly calculated from the contact force, and material properties [297], and
the effect of stagnant fluids is not taken into account. Thus, the area-based conduction
1 Introduction
the simulation data, which revealed the expected results. Then, the repeatable results
and discussions of two vacuum tests and two atmospheric pressure helium tests up to
1200
◦ C were presented. The two tests were implemented with different heating
processes to verify the repeatability and validity of the experimental method. Both
of the results in vacuum and helium were repeatable and stable in this experiment,
and they were comparable with the results of SANA and HTTU. Moreover, in the
researches, as mentioned earlier [161, 287, 288], about this experiment, it has been
found that installation-position errors of thermocouples contributed to the primary
uncertainties of effective diffusivity and conductivity. Therefore, an extreme caution
was given to reduce this experimental error further by involving position-retrieve
iteration into the inverse method, which gave better results.
In the early stage of investigating the particle radiation in packed pebble beds, the
most efforts focused on the experimental measurements and developing the relevant
empirical correlations [237, 243, 284]. The particle radiation flux and the effective
thermal conductivity (ETC) increase significantly under high-temperatures in the
packed pebble beds [252, 289, 290]. Then the correlations of ETC are extended to
the polydisperse beds of multicomponent spheres [208, 272].
Moreover, for theoretical and numerical study, the macroscopic models based on
the porous-medium assumption of the packed pebble bed have been widely used in
the simulation [291] and analysis of transient thermal-hydraulics of HTGR [292].
There are three types of heat transfer modes in the packed pebble beds, i.e., the
convective, conduction, and thermal radiation heat transfers. For example, based on
dimensional analysis of the convective heat transfer, the Rayleigh–Darcy number for
natural convection will increase significantly at lower temperature and the contribution of natural convection to total heat transport will increase consequentially [293].
For other kinds of heat transfer modes, the concept of effective thermal conductivity of the packed pebble bed (k e f f ) is always incorporated to simplify the handling
of heat transfer. It is a critical parameter for HTGR and includes the fluid-particle
conduction, particle-particle heat conduction, and particle-particle thermal radiation.
k e f f is usually obtained from experimental data. It can affect the maximum temperature in nuclear fuel and vessel under, especially limiting events, which is closely
related to the nuclear safety margin of HTGR [196]. To date, theoretical models
of heat conduction in packed pebble beds of rough and mono-sized spheres have
been well-developed and verified by experiments [283, 294]. However, the particleparticle thermal radiation models are still poorly developed. The existing models and
empirical correlations usually deviate from each other, significantly [263].
In recent years, the experimental facilities targeted for HTGR, such as HTTU [30]
and TF-PBEC [248, 295], were tested and the operation conditions were similar to
that in the core of HTGR. When the solid conductivity of the particle material is
close to the ETC of the particle radiation, the effect of the solid conductivity on the
particle radiation is significant [295, 296].
However, in the particle-scale simulation, only the solid-solid conduction through
the contact area is considered in the heat transfer equation of particles. The contact
area is directly calculated from the contact force, and material properties [297], and
the effect of stagnant fluids is not taken into account. Thus, the area-based conduction