The 10th International Topical Meeting on Nuclear Thermal-Hydraulics, Operation and Safety (NUTHOS-10) NUTHOS10-1074 Okinawa, Japan, December 14-18, 2014 1/13 Linear and Nonlinear Analysis of the Dynamic Behaviour of Natural Circulation with Internally Heated Fluids Alessandro Pini, Antonio Cammi and Lelio Luzzi Politecnico di Milano - Department of Energy, CeSNEF (Enrico Fermi Center for Nuclear Studies) Via La Masa 34, 20156 Milano, Italy alessandro.pini@polimi.it, antonio.cammi@polimi.it, lelio.luzzi@polimi.it Daniel E. Ruiz Princeton University - Department of Astrophysical Sciences, 08544 Princeton, NJ, USA druiz@pppl.gov ABSTRACT 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. KEYWORDS Natural circulation, internal heat generation, stability/instability modelling, thermal hydraulics, molten salts. 1. INTRODUCTION Volumetric heat generation effects on natural circulation represent a little-explored field of thermo-fluid dynamics, and filling this gap is of interest not only from a scientific point of view but also for engineering applications that involve internally heated fluids. The main example is the Gen IV Molten Salt Reactor (MSR) [1,2], in which the nuclear fuel is directly dissolved in a molten salt that also serves as coolant. In MSRs, the heat production inside the fluid takes place through fission reactions in the reactor core and through nuclear decays of the fission products inside the primary circuit. Such decay heat distributed along the circuit may modify the dynamics of natural circulation and may lead to a critical behaviour of the reactor, which is an occurrence that needs to be carefully investigated. Therefore, it is clear how the study of the