INVESTIGATION OF CRITICAL TEMPERATURES FOR THERMAL EXPLOSION OF SODIUM DROPLET WITH VARIABLE THERMO-PHYSICAL PROPERTIES AND THERMAL RADIATIONS

Abstract

In many industrial and engineering nuclear plants, sodium droplet is of great im- portance because of its extensive use as a working uid in nuclear reactor. In this study, the problem of thermal explosion of a sodium droplet with variable thermo-physical properties in the presence of di_erent thermal radiation models are investigated. This study extends previous works on thermal explosion of a sodium droplet taking into account temperature dependent thermal conductivity and pre-exponential factor with convective and radiative heat losses. The contribu- tions of thermal radiation are based on three approximation models, which are P-1, Cogley et al. and Sohrab et al. approximations. The P-1 approximation model is used for optically thick gas while Cogley et al. and Sohrab et al. approximation models are for optically thin gas. Extension of analytical expressions for critical temperatures and disappearance of criticality based on di_erent thermal radiation models are obtained. It is worth noting that both P-1 and Cogley et al. approxi- mation models do not have disappearance of criticality under the condition of large activation energy since sodium droplet undergo high exothermic reaction. Under this condition, the ignition times are also presented for the three approximation models. Thermal explosion behaviour of the models are investigated numerically using a _nite di_erence method. Consequently, comparative analysis of the radiation approximation models are presented.