A thermal resistance model of conduction–thermal radiation heat transfer in pebble-bed nuclear reactors

The pebble-bed high-temperature gas-cooled reactor (HTGR) is an advanced nuclear system with inherent safety. The nuclear reactor is operated in high-temperature ranges and its design temperature limit is 1600 °C. It is important to discuss the conduction–radiation heat transfer in the nuclear pebble bed during the thermal hydraulics analysis. Until now, the investigation mainly focuses on large-scale experimental tests, such as the Selbsttätige Abfuhr der Nachwärme (SANA) test by the International Atomic Energy Agency (IAEA), high temperature test unit (HTTU) under low gas pressure by North-West University of South Africa, and the pebble bed equivalent conductivity measurement (PBEC) under vacuum conditions for the high temperature gas-cooled reactor pebble bed module (HTR-PM) project by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University. In this work, a thermal resistance model was developed to calculate the conduction–radiation effective thermal conductivity of nuclear pebble beds. With the constitutive continuum modeling for conduction, contact resistance, coordination number, and void fraction are considered for physical expressions, and heat conduction in the packed bed will be enhanced directly by higher packing density and more contact. For thermal radiation dominated by the heat transfer process under high temperatures, a sub-cell model with an equivalent resistance network is developed to calculate the radiative exchange factor, and the void fraction effect is implemented by a modification term with thermal ray tracing results. At low packing density, because the thermal rays from the local pebble will travel a further distance until reaching the surrounding pebbles, the local sphere will be in contact with more particles by thermal radiation, and the heat transfer is enhanced. Compared with the empirical correlations, the present model is proven to be applicable for both dense and dilute cases. In the nuclear pebble bed, the present conduction–thermal radiation model agrees generally with experimental data under different temperatures and can be applied in the particle-scale CFD-DEM simulations. The present work provides a meaningful approach for conduction–thermal radiation heat transfer for engineering and nuclear pebble-bed design.