20
1 Introduction
Due to the essential heat transfer process in the reactor core, the accurate knowledge about effective thermal diffusivity and conductivity of pebble bed, packed by
420,000 spherical fuel elements inside one reactor core, is significant to assure the
correct design and inherent safety. Notably, the effective thermal conductivity is a
vital parameter to determine whether the core of HTGR will melt and remove residual
heat without any active emergency system under accident conditions [196]. With the
porous structure in the pebble bed, the effective thermal diffusivity and conductivity,
in this case, represent the combination of heat conduction between adjacent spheres,
solid heat conduction inside fuel elements, and radiation heat transfer between the
surfaces of adjacent spheres. It should be noted here that this radiation effect would
account for more than 50 % of total heat transfer at moderate temperatures in some
porous media [27]. A useful review of the heat and flow characteristics of pebble
beds was given by Achenbach [197]. Zehner and Schlüünder proposed cell model to
treat effective thermal conductivity of pebble bed [198]. Du Toit [199] and Rousseau
[200] used the two values to simulate the steady-state, as well as transient heat transfer process, in the integral power plant with the network simulation code, flownex.
The heat transfer in this simulation is split into two components. The first is solid
thermal conduction and radiation processes. The second is the thermal diffusion due
to the helium flow in the voids between the pebbles surfaces. Therefore, two energy
equations refer to the pebble surface temperature and the fluid temperature. These
two solutions are linked by the heat convection between pebble surfaces and fluid.
Two experiments on measuring thermal properties of pebble bed had been conducted
by the SANA (composed of the German words for Secure Decay Heat Removal) test
facility in Germany, in 1996 [29] and the non-nuclear High-Temperature Test Unit
(HTTU) in South Africa, in 2008 [31]. Some further analyses were presented in
literature [30, 201, 202].
For pebble flow, the discrete element method is regarded as an excellent approach
for simulating particle motions [123, 203], and the CFD-DEM coupled simulations
have been widely applied for gas-particle flows. Comparing to the homogeneous
equilibrium model [204, 205], in the traditional empirical approach, the CFD-DEM
framework based on physical mechanisms provides the possibility to investigate
the flow and heat transfer of packed pebble beds in particle scale [206, 207]. In
this framework, the computational fluid dynamics and discrete element method are
utilized for solving the continuous phase and particle phase. However, there are still
two significant challenges for the CFD-DEM coupling algorithm to be applied for
the packed pebble beds. First, when the cell size of CFD mesh is close to particle
size, it is rather difficult to converge in computing the void fraction distribution in the
divided finite volume method (DFVM) [208–210]. Second, for the high-temperature
gas-particle system, it also brings difficulty to the incorporation of particle thermal
radiation in the CFD-DEM simulations, particularly for the packed beds of large
pebbles [211]. In short, the essential tasks of the CFD-DEM simulation for the
packed pebble beds are to model the heat transfer at high-temperature and to mesh
the computational domain in sizes close to particle diameter.
Even though many researches on the CFD-DEM simulations of various fluidparticle systems are available [212–216], the particles in the conventional granular
1 Introduction
Due to the essential heat transfer process in the reactor core, the accurate knowledge about effective thermal diffusivity and conductivity of pebble bed, packed by
420,000 spherical fuel elements inside one reactor core, is significant to assure the
correct design and inherent safety. Notably, the effective thermal conductivity is a
vital parameter to determine whether the core of HTGR will melt and remove residual
heat without any active emergency system under accident conditions [196]. With the
porous structure in the pebble bed, the effective thermal diffusivity and conductivity,
in this case, represent the combination of heat conduction between adjacent spheres,
solid heat conduction inside fuel elements, and radiation heat transfer between the
surfaces of adjacent spheres. It should be noted here that this radiation effect would
account for more than 50 % of total heat transfer at moderate temperatures in some
porous media [27]. A useful review of the heat and flow characteristics of pebble
beds was given by Achenbach [197]. Zehner and Schlüünder proposed cell model to
treat effective thermal conductivity of pebble bed [198]. Du Toit [199] and Rousseau
[200] used the two values to simulate the steady-state, as well as transient heat transfer process, in the integral power plant with the network simulation code, flownex.
The heat transfer in this simulation is split into two components. The first is solid
thermal conduction and radiation processes. The second is the thermal diffusion due
to the helium flow in the voids between the pebbles surfaces. Therefore, two energy
equations refer to the pebble surface temperature and the fluid temperature. These
two solutions are linked by the heat convection between pebble surfaces and fluid.
Two experiments on measuring thermal properties of pebble bed had been conducted
by the SANA (composed of the German words for Secure Decay Heat Removal) test
facility in Germany, in 1996 [29] and the non-nuclear High-Temperature Test Unit
(HTTU) in South Africa, in 2008 [31]. Some further analyses were presented in
literature [30, 201, 202].
For pebble flow, the discrete element method is regarded as an excellent approach
for simulating particle motions [123, 203], and the CFD-DEM coupled simulations
have been widely applied for gas-particle flows. Comparing to the homogeneous
equilibrium model [204, 205], in the traditional empirical approach, the CFD-DEM
framework based on physical mechanisms provides the possibility to investigate
the flow and heat transfer of packed pebble beds in particle scale [206, 207]. In
this framework, the computational fluid dynamics and discrete element method are
utilized for solving the continuous phase and particle phase. However, there are still
two significant challenges for the CFD-DEM coupling algorithm to be applied for
the packed pebble beds. First, when the cell size of CFD mesh is close to particle
size, it is rather difficult to converge in computing the void fraction distribution in the
divided finite volume method (DFVM) [208–210]. Second, for the high-temperature
gas-particle system, it also brings difficulty to the incorporation of particle thermal
radiation in the CFD-DEM simulations, particularly for the packed beds of large
pebbles [211]. In short, the essential tasks of the CFD-DEM simulation for the
packed pebble beds are to model the heat transfer at high-temperature and to mesh
the computational domain in sizes close to particle diameter.
Even though many researches on the CFD-DEM simulations of various fluidparticle systems are available [212–216], the particles in the conventional granular