Numerical analysis of single-phase, natural circulation in a simple closed loop

The inherent numerical properties of large thermal-hydraulic system codes may be usually verified by means of simpler codes, dealing with selected cases of restricted practical application. The problem considered was the single-phase, natural circulation flow in a simple loop, under unstable flow conditions. Neutral stability curves were derived for the system and effect of nodes number in the expected system behavior analyzed. The codes developed in a previous work have been further refined to analyze the problem under two approaches: nodal one, based on a finite-difference approximation and a modal one, based in a modal decomposition of the governing equations in Fourier series. Theoretical values for the steady state parameters are obtained for both approximations. The nodal code was used as the standard approximation and different schemes or different order have been used. The modal code, with the modes number ranging from 30 to 100, was used as an free approximation of numerical diffusion. In this case, the energy equation was solved considering also a constant diffusion term, allowing a partial simulation of the nodal approximation numerical diffusion. Results show that the inclusion of this diffusion reasonably accounts for the solution damping, allowing a qualitative recovering of the nodal behavior. System non-linearity naturally precludes the exact coincidence of the obtained results. A similar analysis may be used to assess the effect of a given discretization nodes number on the dynamics of more complex thermal-hydraulic systems. (author). 6 refs., 4 figs