An explicit expression of empirical parameter in ZBS model for predicting pebble bed effective thermal conductivity

Abstract The pebble bed effective thermal conductivity is a key parameter in the design and safety analysis of the high temperature pebble bed reactor. The ZBS model is widely used to predict the pebble bed effective thermal conductivity. However, the predictive ability of the ZBS model is greatly affected by the selected values of the empirical parameter contact area fraction φ. In this paper, a semi-empirical formula is proposed to estimate the empirical parameter contact area fraction φ, which is related with the contact radius ratio γ and coordination number Nc. The stagnant effective thermal conductivities in the three types of ordered pebble beds are numerically studied to provide the values of φ with corresponding contact radius ratios γ and coordination numbers Nc. Then the multiple linear regression is performed and the proposed semi-empirical formula is determined as φ = 0.15 N c 1.1 γ . The predicted values by the improved ZBS model with the estimation of contact area fraction φ agree rather well with the numerical results of the random pebble bed. Compared with SANA experimental data, the improved ZBS model is proved to be better than other models. Compared with HTTU experimental data, the improved ZBS model is able to predict the effective thermal conductivity in the bulk region of pebble beds. However, the improved ZBS model needs to be further improved in the near-wall region.