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1 Introduction
Based on the experimental results of pebble bed [196] and packed bed [233–235],
composed of different particles and fluids with different void fractions, theoretical
models and empirical correlations of conductive effective thermal conductivity [236],
have been developed, e.g., the Kunii-Smith equation [237], the Zehner-Schlunder
correlation [238], and the Krupiczka correlation [239]. It indicates that the conductive
heat transfer is driven by the gas-solid conduction near the contact point and the
effective thermal conductivity is a function of void fraction and thermal conductivity
ratio of the particle to the stagnant fluid.
According to the empirical correlations [237, 240], the ETC of radiation is affected
by pebble size, temperature, material properties and porosity. In physical, the ETC of
thermal radiation increases with particle size greatly [241]. Commonly, the particle
size in various cases of the packed beds is about 1.0–10.0 mm and it is much smaller
than the pebbles of 60 mm in diameter in nuclear beds. As for the temperature, the
measurements of pebble beds operated under similar conditions of the nuclear reactor
were conducted in the high-temperature test unit (HTTU) [30], and the test facility
for pebble bed equivalent conductivity measurement (TF-PBEC) by the institute of
nuclear and new energy technology at Tsinghua university [161]. The experimental
data showed that the ETC in the pebble bed significantly increases by thermal radiation at high-temperatures. The radiation exchange factor is now widely accepted as
a primary non-dimensional parameter in the discussion of particle radiations [242].
Theoretically, it is determined by the structure parameters of the beds and the surface
optical properties of the pebbles. For the opaque particles, the radiation exchange
factor is a function of the average porosity of the bed and the surface emissivity
[243–245]. For the dense bed of spheres, it reduces to a continuous monotonically
increasing function of the emissivity [231, 252]
Many studies have been performed to improve the understanding of heat transfer
in packed pebble bed. For example, for experimental investigations, SANA-I was a
classic experiment of packed pebble bed, which was filled with about 9500 graphite
particles of 60 mm in diameter and heated by electrical resistance heating elements
[196]. The bed was operated in an inert gas (helium or nitrogen) atmosphere and
the effect of natural convection could not be neglected under lower heating power.
The HTTU test was another new experiment with negligible natural convection [30].
The facility was filled with nitrogen as interstitial gas and operated under very low
pressures. There were about 25000 machined graphite spheres of 60 mm in diameter. The annular core of the bed was 0.6 and 2.3 m in inner and outer diameters
respectively, and 1.2 m in height.
1.4.2 Pebble Thermal Radiation
Thermal radiation exists widely in granular systems and is an essential part of the
heat transfer in high-temperature systems, such as the pebble-bed high-temperature
gas-cooled reactor (HTGR) [23, 230]. The reactor core of HTGR is a packed pebble
1 Introduction
Based on the experimental results of pebble bed [196] and packed bed [233–235],
composed of different particles and fluids with different void fractions, theoretical
models and empirical correlations of conductive effective thermal conductivity [236],
have been developed, e.g., the Kunii-Smith equation [237], the Zehner-Schlunder
correlation [238], and the Krupiczka correlation [239]. It indicates that the conductive
heat transfer is driven by the gas-solid conduction near the contact point and the
effective thermal conductivity is a function of void fraction and thermal conductivity
ratio of the particle to the stagnant fluid.
According to the empirical correlations [237, 240], the ETC of radiation is affected
by pebble size, temperature, material properties and porosity. In physical, the ETC of
thermal radiation increases with particle size greatly [241]. Commonly, the particle
size in various cases of the packed beds is about 1.0–10.0 mm and it is much smaller
than the pebbles of 60 mm in diameter in nuclear beds. As for the temperature, the
measurements of pebble beds operated under similar conditions of the nuclear reactor
were conducted in the high-temperature test unit (HTTU) [30], and the test facility
for pebble bed equivalent conductivity measurement (TF-PBEC) by the institute of
nuclear and new energy technology at Tsinghua university [161]. The experimental
data showed that the ETC in the pebble bed significantly increases by thermal radiation at high-temperatures. The radiation exchange factor is now widely accepted as
a primary non-dimensional parameter in the discussion of particle radiations [242].
Theoretically, it is determined by the structure parameters of the beds and the surface
optical properties of the pebbles. For the opaque particles, the radiation exchange
factor is a function of the average porosity of the bed and the surface emissivity
[243–245]. For the dense bed of spheres, it reduces to a continuous monotonically
increasing function of the emissivity [231, 252]
Many studies have been performed to improve the understanding of heat transfer
in packed pebble bed. For example, for experimental investigations, SANA-I was a
classic experiment of packed pebble bed, which was filled with about 9500 graphite
particles of 60 mm in diameter and heated by electrical resistance heating elements
[196]. The bed was operated in an inert gas (helium or nitrogen) atmosphere and
the effect of natural convection could not be neglected under lower heating power.
The HTTU test was another new experiment with negligible natural convection [30].
The facility was filled with nitrogen as interstitial gas and operated under very low
pressures. There were about 25000 machined graphite spheres of 60 mm in diameter. The annular core of the bed was 0.6 and 2.3 m in inner and outer diameters
respectively, and 1.2 m in height.
1.4.2 Pebble Thermal Radiation
Thermal radiation exists widely in granular systems and is an essential part of the
heat transfer in high-temperature systems, such as the pebble-bed high-temperature
gas-cooled reactor (HTGR) [23, 230]. The reactor core of HTGR is a packed pebble