1.4 Pebble Bed Heat Transfer
23
bed composed of large quantities of randomly packed mono-sized TRI-structural
ISOtropic (TRISO) spherical particles,such as 420,000 spheres in one reactor of
HTR-PM [20, 246]. Each fuel sphere uses 6-cm-diameter pebbles made of pyrolytic
graphite. The packed pebble bed operates at about 800
◦ C under normal conditions
[247]. The highest temperature in expected accidents of HTGR is about 1600
◦ C
[248].
As temperature rises, the amount of heat conduction almost remains constant,
while the amount of thermal radiation heat exchange between particles will increase
rapidly. It is estimated that particle radiation contributes to the dominant part (more
than 80%) of the total effective Thermal Conductivity (ETC) at high-temperatures
(over 1000
◦ C) for the experimental pebble beds [30, 196]. Besides, thermal radiation
is much more complicated for numerical computation because of its non-contact and
long-range interactions. Therefore, thermal radiation is an essential issue of heat
transfer for HTGR, and modeling ETC of thermal radiation is a fundamental task for
researchers and engineers in the fields of nuclear reactor-packed pebble beds.
Due to its negative temperature coefficient of reactivity and thermal-hydraulics
design, the maximum fuel element temperature in reactor core will always be under
the limiting temperature 1600
◦ C without employing any dedicated emergency system in the conceivable severe accident scenarios. In the loss-of-coolant and depressurized accident, the transient temperature of the reactor core will increase temporarily
but decay later, which is determined by effective thermal diffusivity in heat transfer.
Furthermore, the effective thermal conductivity of the pebble bed and steady-state
decay heat of fuel elements will construct a steady temperature distribution along the
radial direction of the reactor core, and the residual heat of the reactor is extracted
by the outside natural circulation. Therefore, effective thermal diffusivity and conductivity of pebble bed are two crucial parameters to determine the inherent safety.
Comparing to conduction [249] and convection [250], the radiation of particles
increases significantly with temperature. Experimental tests of packed nuclear pebble
beds, such as SANA [196], HTTU [30], and TF-PBEC [248], were carried out for
the HTGR in high-temperature ranges. Most efforts contributing to the modeling of
thermal radiation in densely packed bed have focused on using empirical correlations
and developing continuous porous models [251]. From the experiments operated in
medium temperatures (less than 1000
◦ C) [252], it is shown that ZBS correlation
[196] and Kunii-Smith correlation [237], are in good agreement with experimental
data.
Moreover, as a kind of discrete particle model, the short-range models are always
based on one essential assumption to cut off the long-range parts of thermal radiation
to simplify the calculation of the view factors between spheres [253, 254]. The
classical short-range model can be seen in the literature [255], which was applied to
the packed beds and fluidized beds. It only considered the radiation pairs within the
short-ranges of 1.5 times of particle diameter. In the work of Ref. [256], a numerical
model was reported, which only calculated the radiative flux within a single layer
of Voronoï neighbors in the bed. With the physically reasonable simplification, the
23
bed composed of large quantities of randomly packed mono-sized TRI-structural
ISOtropic (TRISO) spherical particles,such as 420,000 spheres in one reactor of
HTR-PM [20, 246]. Each fuel sphere uses 6-cm-diameter pebbles made of pyrolytic
graphite. The packed pebble bed operates at about 800
◦ C under normal conditions
[247]. The highest temperature in expected accidents of HTGR is about 1600
◦ C
[248].
As temperature rises, the amount of heat conduction almost remains constant,
while the amount of thermal radiation heat exchange between particles will increase
rapidly. It is estimated that particle radiation contributes to the dominant part (more
than 80%) of the total effective Thermal Conductivity (ETC) at high-temperatures
(over 1000
◦ C) for the experimental pebble beds [30, 196]. Besides, thermal radiation
is much more complicated for numerical computation because of its non-contact and
long-range interactions. Therefore, thermal radiation is an essential issue of heat
transfer for HTGR, and modeling ETC of thermal radiation is a fundamental task for
researchers and engineers in the fields of nuclear reactor-packed pebble beds.
Due to its negative temperature coefficient of reactivity and thermal-hydraulics
design, the maximum fuel element temperature in reactor core will always be under
the limiting temperature 1600
◦ C without employing any dedicated emergency system in the conceivable severe accident scenarios. In the loss-of-coolant and depressurized accident, the transient temperature of the reactor core will increase temporarily
but decay later, which is determined by effective thermal diffusivity in heat transfer.
Furthermore, the effective thermal conductivity of the pebble bed and steady-state
decay heat of fuel elements will construct a steady temperature distribution along the
radial direction of the reactor core, and the residual heat of the reactor is extracted
by the outside natural circulation. Therefore, effective thermal diffusivity and conductivity of pebble bed are two crucial parameters to determine the inherent safety.
Comparing to conduction [249] and convection [250], the radiation of particles
increases significantly with temperature. Experimental tests of packed nuclear pebble
beds, such as SANA [196], HTTU [30], and TF-PBEC [248], were carried out for
the HTGR in high-temperature ranges. Most efforts contributing to the modeling of
thermal radiation in densely packed bed have focused on using empirical correlations
and developing continuous porous models [251]. From the experiments operated in
medium temperatures (less than 1000
◦ C) [252], it is shown that ZBS correlation
[196] and Kunii-Smith correlation [237], are in good agreement with experimental
data.
Moreover, as a kind of discrete particle model, the short-range models are always
based on one essential assumption to cut off the long-range parts of thermal radiation
to simplify the calculation of the view factors between spheres [253, 254]. The
classical short-range model can be seen in the literature [255], which was applied to
the packed beds and fluidized beds. It only considered the radiation pairs within the
short-ranges of 1.5 times of particle diameter. In the work of Ref. [256], a numerical
model was reported, which only calculated the radiative flux within a single layer
of Voronoï neighbors in the bed. With the physically reasonable simplification, the