Thermo-Hydrodynamics of Internally Heated Molten Salts for Innovative Nuclear Reactors

The problem of heat transfer in pipe flow has been extensively investigated in the past. Many different models have been proposed and adopted to predict the velocity profile, the eddy diffusivity, the temperature distributions, the friction factor and the heat transfer coefficient (Kays et al., 2004; Schlichting & Gersten, 2000). However, the majority of such studies give a description of the problem for non-internally heated fluids. Models regarding fluids with internal heat generation have been developed more than 50 years ago (Kinney & Sparrow, 1966; Poppendiek, 1954; Siegel & Sparrow, 1959), giving in most cases a partial treatment of the problem in terms of boundary conditions and heat source distribution, and relying on a turbulent flow treatment that does not seem fully satisfactory in the light of more recent investigations (Churchill, 1997; 2002; Kays, 1994; Zagarola & Smits, 1997). Internally heated fluids are of great interest in the current development of Molten Salt Reactors (MSR) (LeBlanc, 2010), included as one of the six innovative nuclear reactors selected by the Generation IV International Forum (GIF-IV, 2002) for a more sustainable version of nuclear power. MSRs are circulating fuel reactors (Nicolino et al., 2008), which employ a non-classical (fluid-type) fuel constituted by a molten halide (fluoride or chloride) salt mixture playing the distinctive role of both heat source and coolant. By adopting classical correlations for the Nusselt number (e.g., Dittus-Boelter), the heat transfer coefficient of the MSR fuel can be overestimated by a non-negligible amount (Di Marcello et al., 2008). In the case of thermal-neutron-spectrum (graphite-moderated) MSRs (LeBlanc, 2010), this has significant consequences on the core temperature predictions and on the reactor dynamic behaviour (Luzzi et al., 2011). Such influence of the heat source within the fluid cannot be neglected, and thus required proper investigation. The present chapter deals with this critical issue, first summarizing the main modelling efforts carried out by the authors (Di Marcello et al., 2010; Luzzi et al., 2010) to investigate the thermo-hydrodynamics of internally heated fluids, and then focusing on the heat transfer coefficient prediction that is relevant for analysing the molten salt behaviour encountered in MSRs. The chapter is organized as follows. Section 2 provides a brief description of the Molten Salt Reactors, focusing on their distinctive features, in terms of both sustainability (i.e., reduced radioactive waste generation, effective use of natural resources) and safety, with respect to the traditional configuration of nuclear reactors. Section 3 deals with the study of molten salt heat transfer characteristics, which represent a key issue in the current development of MSRs. In particular, a "generalized approach" to evaluate the steady-state temperature distribution in a representative power channel of the reactor core is presented. This approach incorporates recent formulations of turbulent flow and convection (Churchill, 1997; 2002), and is built in order to carefully take into account the molten salt mixture specificities, the reactor core power conditions and the heat transfer in the graphite core structure. In Section 4, a preliminary correlation for the Nusselt number prediction is advanced in the case of simultaneous uniform wall heat flux and internal heat generation, on the basis of the results achieved by means of the presented generalized approach. In Section 5, the main conclusions of the present study are summarized.