5.4 CFD-DEM Coupled Simulation and Development
323
cooled reactor. The particle motion, heat conduction, and particle thermal radiation
are modeled in the Lagrangian approach.
A diffusion function is obtained analytically as a spatial distribution function of
the particle volume in SVFM, which converges to the step-function-type distribution
of particle volume in the sub-particle-scale particle-Divided Finite Volume Method
(DFVM) when the smoothing degree goes to 0. The fluid flow and heat transfer are
solved in the Eulerian approach, and the sub-particle scale fluid–particle interactions
and convection are also taken into account. In the validation by a spout fluidized
bed when the cell size is less than the particle diameter, it is shown that SVFM is
preferable to DFVM for the CFD-DEM simulation since it is in better agreement
with the experimental measurements. Moreover, the CFD-DEM simulation using
the SVFM on sub-particle scale meshes is performed for the benchmark problem
of the HTR-10 reactor. The numerical results at the smoothing degree of η = 0.5
are in good agreement with the empirical code of THERMIX—which is based on
experimental measurements. In addition, the discussion indicates that the smoothing
degree in SVFM is recommended to be 0.5–0.7 based on the void fraction distribution
of Voronoï tessellation.
5.4.3.1 Particle-Divided Finite Volume Method (DFVM) and
Drawbacks
The basic governing equations under the CFD-DEM framework have been discussed
in Sect. 5.4.1 and Ref. [7]. For the fluid phase, the Navier–Stokes equations for packed
pebble beds are expressed by Eq. (5.145) [8, 118, 119]. Let the momentum and
energy source terms for particle–fluid interactions, i.e., S m and S e in Eq. (5.145) be
expressed by Eqs. (5.156) and (5.160), respectively. The KTA 3102.2 standard [120]
is recommended for the heat convection in packed pebble beds (Table 5.2).
Particle motion and heat transfer are solved by the Discrete Element Method
(DEM) (Eq. (5.146), [109]) considering particle–particle and particle–fluid heat
transfer by Eqs. (5.151)–(5.160). Different models for calculating the contact forces
and torques are discussed in [74, 75]. The Hertz–Mindlin contact model and the directional constant torque model are applied for the CFD-DEM simulations of packed
pebble beds [7]. The models of particle–particle contact conduction are described
in [79]. The Short-range Radiation Model (SRM) is developed for particle thermal
radiation in packed pebble beds (Sect. 5.3.2) [5, 7]).
In general, the void fraction in a CFD cell (Fig. 5.69) is calculated as follows
α f = 1 − α s ,
α s =
V solid
V cell
(5.166)
323
cooled reactor. The particle motion, heat conduction, and particle thermal radiation
are modeled in the Lagrangian approach.
A diffusion function is obtained analytically as a spatial distribution function of
the particle volume in SVFM, which converges to the step-function-type distribution
of particle volume in the sub-particle-scale particle-Divided Finite Volume Method
(DFVM) when the smoothing degree goes to 0. The fluid flow and heat transfer are
solved in the Eulerian approach, and the sub-particle scale fluid–particle interactions
and convection are also taken into account. In the validation by a spout fluidized
bed when the cell size is less than the particle diameter, it is shown that SVFM is
preferable to DFVM for the CFD-DEM simulation since it is in better agreement
with the experimental measurements. Moreover, the CFD-DEM simulation using
the SVFM on sub-particle scale meshes is performed for the benchmark problem
of the HTR-10 reactor. The numerical results at the smoothing degree of η = 0.5
are in good agreement with the empirical code of THERMIX—which is based on
experimental measurements. In addition, the discussion indicates that the smoothing
degree in SVFM is recommended to be 0.5–0.7 based on the void fraction distribution
of Voronoï tessellation.
5.4.3.1 Particle-Divided Finite Volume Method (DFVM) and
Drawbacks
The basic governing equations under the CFD-DEM framework have been discussed
in Sect. 5.4.1 and Ref. [7]. For the fluid phase, the Navier–Stokes equations for packed
pebble beds are expressed by Eq. (5.145) [8, 118, 119]. Let the momentum and
energy source terms for particle–fluid interactions, i.e., S m and S e in Eq. (5.145) be
expressed by Eqs. (5.156) and (5.160), respectively. The KTA 3102.2 standard [120]
is recommended for the heat convection in packed pebble beds (Table 5.2).
Particle motion and heat transfer are solved by the Discrete Element Method
(DEM) (Eq. (5.146), [109]) considering particle–particle and particle–fluid heat
transfer by Eqs. (5.151)–(5.160). Different models for calculating the contact forces
and torques are discussed in [74, 75]. The Hertz–Mindlin contact model and the directional constant torque model are applied for the CFD-DEM simulations of packed
pebble beds [7]. The models of particle–particle contact conduction are described
in [79]. The Short-range Radiation Model (SRM) is developed for particle thermal
radiation in packed pebble beds (Sect. 5.3.2) [5, 7]).
In general, the void fraction in a CFD cell (Fig. 5.69) is calculated as follows
α f = 1 − α s ,
α s =
V solid
V cell
(5.166)