Research and Validation of Accurate Temperature Calculation Method for Fuel Pebble in Pebble-bed High Temperature Gas-cooled Reactor

The fuel pebble elements in pebble-bed high temperature gas-cooled reactors (PB-HTGR) contain thousands of tri-structural isotropic (TRISO) particles randomly distributed in the graphite matrix. Each TRISO particle consists of a UO₂ kernel surrounded by multiple coating layers, including a porous buffer layer, inner and outer pyro-carbon layers, and a silicon carbide layer, each with distinct thermal properties. Due to the significant thermal conductivity differences between these layers and the graphite matrix, coupled with the fact that most fission heat is released within the UO₂ kernel, the temperature field within the fuel pebble exhibits strong local heterogeneity. The accurate prediction of temperature distribution in the UO₂ kernel of TRISO particles and graphite matrix is essential for reactor safety analysis and neutronics calculations, as it affects both fission product retention and neutron cross-section interpolation. This research aims to present an improved temperature calculation method based on two-temperature model for fuel pebble elements in PB-HTGR, with enhancements in both the effective thermal conductivity (ETC) model and the boundary condition formulation for the TRISO particle heat conduction equation. The conventional ETC models, derived under external heat flux assumptions following Fourier’s law, fail to account for the perturbation of heat flow caused by distributed internal heat sources. To overcome this limitation, an analytical ETC model considering internal heat source effects was derived based on the principle of graphite matrix average temperature conservation. This model was applied to the homogenized fuel pebble to obtain the matrix temperature distribution. Subsequently, the temperature perturbation method was used to establish the boundary condition for the TRISO particle heat conduction equation. And the UO₂ kernel temperatures were calculated through the boundary condition. A full-scale fuel pebble model including the fuel zone and outer graphite shell was constructed using COMSOL Multiphysics code with explicit modeling of randomly distributed TRISO particles and their multilayer structures to validate the proposed method. The results indicate that the ETC shows negligible dependence on fuel pebble power but decreases significantly with increasing TRISO packing fraction, which is attributed to the growing volume fraction of low-conductivity particle layers relative to the high-conductivity graphite matrix. The two-temperature model based on the temperature perturbation model achieves good accuracy: the maximum UO₂ kernel temperature deviation is 6.2 K at 0.05 packing fraction, reducing to 2.4 K at 0.15 packing fraction. Matrix temperature deviation reaches 3.8 K maximum. The proposed ETC model effectively captures the influence of distributed heat sources on fuel element heat transfer characteristics, providing an accurate temperature distribution of the graphite matrix for the calculation. Based on this matrix temperature field, the temperature perturbation model provides a reliable boundary condition for the predictions of UO₂ kernel average temperatures. The combination of the ETC model and temperature perturbation model offers a computationally efficient and accurate tool for coupled neutronic-thermal analysis of PB-HTGR, with potential applications in core design optimization and safety evaluation.