Analytical and numerical investigation of the heat exchange effect on the dynamic behaviour of natural circulation with internally heated fluids

In this paper, the study of the heat exchange effect on the dynamic behaviour of single-phase natural circulation with internal heat generation is presented. In order to predict natural circulation instabilities, two different methods of analysis are developed and compared. The first approach is a linear analysis in which the governing equations are firstly linearized around a steady-state solution of the system and then treated by means of the Fourier transform. This strategy is adopted to compute, in a semi-analytical way, dimensionless stability maps for different system configurations, highlighting the heat exchange effect on the system dynamics. The second approach consists in numerically solving the nonlinear governing equations and allows investigating some transients of interest. For this purpose, an object-oriented one-dimensional model of natural circulation loops has been developed, and the corresponding results have been compared with RELAP5 and Computational Fluid-Dynamics (CFD) time-dependent simulations. The developed models have been applied to investigate the dynamic behaviour of two loop configurations characterized by large instability regions, namely the Horizontal Heater-Horizontal Cooler (HHHC) and the Vertical Heater-Horizontal Cooler (VHHC).