Linear and Nonlinear Analysis of the Dynamic Behaviour of Natural Circulation with Internally Heated Fluids

In this paper, the study of the dynamic behaviour of single-phase natural circulation with internal heat generation for a rectangular loop is presented. In order to predict natural circulation stability, two different methods of analysis are developed and compared. The first approach is a linear analysis in which the Navier-Stokes equation is linearized around a steady-state solution of the system. This strategy is adopted to calculate transient evolutions and dimensionless stability maps for several system configurations in case of small perturbations, outlining the geometrical parameters that mainly affect the natural circulation behaviour when internal heat generation is also considered. The second approach consists in directly solving the nonlinear governing equations and it is used to confirm the results of the linear analysis. In this case, the hypothesis that the perturbations on the stationary state variables are negligible is removed. Stability maps and time-dependent simulations represent very useful tools of investigation not only from a theoretical point of view but also in practice. As a matter of fact, stability maps may be used to optimize the configuration of natural circulation loops, while time-dependent simulations allow to completely evaluate the system dynamics showing mass flow and temperature transients.