On the analysis of thermal-fluid-dynamic instabilities via numerical discretization of conservation equations Original Research Article

The numerical aspects involved in the prediction of fluid-dynamic instabilities are shortly reviewed, mainly addressing single-phase natural circulation flows. In particular, some open literature, produced since the pioneering work of Welander [J. Fluid Mech. 29 (1967) 17–30] and related to single-phase thermosyphon loops, is firstly considered; then the analysis turns to summarize some early calculations and examples of code verification results dealing with the prediction of single-phase natural circulation. The work previously performed by the Authors in relation to Welanderʹs problem and other relevant single-phase thermosyphon loop cases is reviewed, with main emphasis on the adopted methodology, based on numerical discretization of governing equations. These results serve to illustrate how time domain codes may be used to analyze such problems and also to highlight the effect of considering different constitutive laws in the computed linear stability map. Reference to the application of this methodology to boiling channel stability analysis is also made to demonstrate its generality. The results show both the qualitative and quantitative details of the changes that stability maps undergo as a consequence of numerical discretization of governing equations. The recent attempt to make easier the application of the methodology by the use of automatic fortran code differentiation tools is finally reported, showing quantitative results concerning calculation of the sensitivity of simulation results to physical and numerical parameters.