1.4 Pebble Bed Heat Transfer
25
particle diameter [255, 273] or only single neighboring Voronoï cells [211, 257],
are considered in these numerical radiation models. The accumulated view factor in
SRM is only about 0.83, which is smaller than that in the models considering the
long-distance radiation. The numerical results showed that the local average model
and the SRM underestimated the radiation exchange factor of black radiation [274].
In contrast, for the long-range radiation, numerical computation of the view factor between every pair of particles and all their possible surrounding particles are
necessary for the diffuse-gray radiosity method [211, 275, 276].
1.4.3 Effective Thermal Diffusivity and Conductivity
As one of the main approaches of energy transportation, thermal conduction exists
widely in a variety of particle systems, such as the nuclear pebble bed in hightemperature gas-cooled reactor (HTGR) [33, 277], the granular bed [278, 279], and
the suspensions of nanoparticles [280, 281]. In most cases, measuring or modeling
the effective thermal conductivity and the contact thermal resistance is one of the
critical issues [235, 282, 283].
Effective thermal diffusivity and conductivity in porous pebble bed represent a
combined heat transfer effect of solid heat conduction inside or between fuel elements, thermal radiation between surfaces of adjacent spheres, and helium gas heat
convection [263]. Although various researches proposed empirical correlations to
describe the effective thermal conductivity of pebble bed, the practical application
of heat transfer in pebble bed should be based on experimental data to give a reliable
result. In early researches, two experiments on the effective conductivity of graphite
pebble bed were conducted with the steady-state method by the SANA facility in
Germany, in 1996 [29], and the HTTU facility in South Africa, in 2012 [30, 31].
However, with the steady-state method, heat loss in other directions and heat flow in
the radial direction are difficult to determine accurately at high-temperature, which
brings unpredictable perplexity in its higher-temperature application. Also, the severe
carbon-reducing atmosphere in these tests can make thermocouples invalid, so the
special sheathed thermocouples should be designed for higher-temperature applications [161]. Due to the limitation of the experimental method and thermocouples at a
higher temperature, the effective thermal conductivities obtained by the steady-state
method were just up to approximate 900
◦ C in SANA and 1200
◦ C in HTTU (the
valid highest temperature is 1000
◦ C in HTTU).
Up to date, many experiments have been conducted on the particle radiation in
various types of granular systems [30, 252, 284]. There appears to be a scarcity of
distinct descriptions of significant drastic growth of effective thermal conductivity
caused by radiation heat transfer at a higher temperature. Therefore, the INET at
Tsinghua University constructed a full-radius-scale heat test facility designed to
measure effective thermal diffusivity and conductivity up to 1600
◦ C [32, 285, 286].
In early works [161, 287], the availability, robustness and accuracy of the inverse
method were focused on by comparing the experimental data (the vacuum test) with
25
particle diameter [255, 273] or only single neighboring Voronoï cells [211, 257],
are considered in these numerical radiation models. The accumulated view factor in
SRM is only about 0.83, which is smaller than that in the models considering the
long-distance radiation. The numerical results showed that the local average model
and the SRM underestimated the radiation exchange factor of black radiation [274].
In contrast, for the long-range radiation, numerical computation of the view factor between every pair of particles and all their possible surrounding particles are
necessary for the diffuse-gray radiosity method [211, 275, 276].
1.4.3 Effective Thermal Diffusivity and Conductivity
As one of the main approaches of energy transportation, thermal conduction exists
widely in a variety of particle systems, such as the nuclear pebble bed in hightemperature gas-cooled reactor (HTGR) [33, 277], the granular bed [278, 279], and
the suspensions of nanoparticles [280, 281]. In most cases, measuring or modeling
the effective thermal conductivity and the contact thermal resistance is one of the
critical issues [235, 282, 283].
Effective thermal diffusivity and conductivity in porous pebble bed represent a
combined heat transfer effect of solid heat conduction inside or between fuel elements, thermal radiation between surfaces of adjacent spheres, and helium gas heat
convection [263]. Although various researches proposed empirical correlations to
describe the effective thermal conductivity of pebble bed, the practical application
of heat transfer in pebble bed should be based on experimental data to give a reliable
result. In early researches, two experiments on the effective conductivity of graphite
pebble bed were conducted with the steady-state method by the SANA facility in
Germany, in 1996 [29], and the HTTU facility in South Africa, in 2012 [30, 31].
However, with the steady-state method, heat loss in other directions and heat flow in
the radial direction are difficult to determine accurately at high-temperature, which
brings unpredictable perplexity in its higher-temperature application. Also, the severe
carbon-reducing atmosphere in these tests can make thermocouples invalid, so the
special sheathed thermocouples should be designed for higher-temperature applications [161]. Due to the limitation of the experimental method and thermocouples at a
higher temperature, the effective thermal conductivities obtained by the steady-state
method were just up to approximate 900
◦ C in SANA and 1200
◦ C in HTTU (the
valid highest temperature is 1000
◦ C in HTTU).
Up to date, many experiments have been conducted on the particle radiation in
various types of granular systems [30, 252, 284]. There appears to be a scarcity of
distinct descriptions of significant drastic growth of effective thermal conductivity
caused by radiation heat transfer at a higher temperature. Therefore, the INET at
Tsinghua University constructed a full-radius-scale heat test facility designed to
measure effective thermal diffusivity and conductivity up to 1600
◦ C [32, 285, 286].
In early works [161, 287], the availability, robustness and accuracy of the inverse
method were focused on by comparing the experimental data (the vacuum test) with