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5 Numerical Models for Pebble-Bed Heat Transfer
5.2.3 Short Summary
A continuum model is proposed here to derive the effective thermal conductivity,
which incorporates the conductive and radiative heat transfers of a nuclear pebble bed together. Analytical expressions are derived for computing conductive and
radiative Effective Thermal Conductivities (ETCs) of the nuclear pebble bed. It is
determined by the temperature, number density, heat transfer coefficient, and radial
distribution function. In this model, the governing equation of energy is presented
in a uniform framework to solve the conduction and thermal radiation of the nuclear
pebble bed. For the radiation cases without heat sources, the solution indicates that
local temperature is determined by all possible surrounding particles weighted by
the radiative kernel function. Detailed DEM results are in good agreement with the
solution obtained by the continuum model. At size factor μ 1, both the conductive
and the radiative continuum equation converge to the heat conduction in continuum
mechanics.
Radiative heat transfer is surface-to-surface radiation, and the radiation exchange
factor is determined by surface emissivity and particle-scale packing structures,
including porosity, Radial Distribution Function (RDF), and Radiation Interaction
Function (RIF). Since traditional Radiative Transfer Equation (RTE) cannot provide a good prediction of radiative heat transfer in densely packed bed of particles,
the Approximation Function Model (AFM) is proposed here based on the continuum media assumptions. In the approximation function model, a generic physical
expression for the radiation exchange factor is given for the packed bed.
Moreover, it is also feasible to apply the current expression to analyze other radiation models. The approximation function model is potentially a reasonable replacement of the conventional radiative transfer equation for a packed bed study. Without
heat source, local temperature is determined by all possible surrounding particles
weighted by the kernel function. It is proven that radiation in a packed bed is equivalent to that of heat conduction at size parameter ξ 1. In the AFM, the effective
thermal conductivity in central region far away from the walls is higher than that
of the whole bed. The approximation function model with radiative and conductive
heat transfer is developed here, and its demonstrative application to the pebble-bed
experiments (TF-PBEC and HTTU) shows that the solutions by the current model
are in a good agreement with the experimental measurements.
5.3 Discrete Modeling of Pebble Radiation
5.3.1 Voronoï Cells and Cutoff Scales
For heat transfer of the High-Temperature Gas-cooled Reactors (HTGRs), the particle
thermal radiation is an essential part of engineering and research purposes, which
is still poorly understood. The present section analyzes the effect of spatial scale
5 Numerical Models for Pebble-Bed Heat Transfer
5.2.3 Short Summary
A continuum model is proposed here to derive the effective thermal conductivity,
which incorporates the conductive and radiative heat transfers of a nuclear pebble bed together. Analytical expressions are derived for computing conductive and
radiative Effective Thermal Conductivities (ETCs) of the nuclear pebble bed. It is
determined by the temperature, number density, heat transfer coefficient, and radial
distribution function. In this model, the governing equation of energy is presented
in a uniform framework to solve the conduction and thermal radiation of the nuclear
pebble bed. For the radiation cases without heat sources, the solution indicates that
local temperature is determined by all possible surrounding particles weighted by
the radiative kernel function. Detailed DEM results are in good agreement with the
solution obtained by the continuum model. At size factor μ 1, both the conductive
and the radiative continuum equation converge to the heat conduction in continuum
mechanics.
Radiative heat transfer is surface-to-surface radiation, and the radiation exchange
factor is determined by surface emissivity and particle-scale packing structures,
including porosity, Radial Distribution Function (RDF), and Radiation Interaction
Function (RIF). Since traditional Radiative Transfer Equation (RTE) cannot provide a good prediction of radiative heat transfer in densely packed bed of particles,
the Approximation Function Model (AFM) is proposed here based on the continuum media assumptions. In the approximation function model, a generic physical
expression for the radiation exchange factor is given for the packed bed.
Moreover, it is also feasible to apply the current expression to analyze other radiation models. The approximation function model is potentially a reasonable replacement of the conventional radiative transfer equation for a packed bed study. Without
heat source, local temperature is determined by all possible surrounding particles
weighted by the kernel function. It is proven that radiation in a packed bed is equivalent to that of heat conduction at size parameter ξ 1. In the AFM, the effective
thermal conductivity in central region far away from the walls is higher than that
of the whole bed. The approximation function model with radiative and conductive
heat transfer is developed here, and its demonstrative application to the pebble-bed
experiments (TF-PBEC and HTTU) shows that the solutions by the current model
are in a good agreement with the experimental measurements.
5.3 Discrete Modeling of Pebble Radiation
5.3.1 Voronoï Cells and Cutoff Scales
For heat transfer of the High-Temperature Gas-cooled Reactors (HTGRs), the particle
thermal radiation is an essential part of engineering and research purposes, which
is still poorly understood. The present section analyzes the effect of spatial scale