A low diffusion numerical scheme for the stability analysis of natural circulation loops containing fluids at supercritical pressure

This paper reports the latest results of a research concerning the development of a computer programme aimed to be a tool based on 1D balance equations for the linear and the nonlinear stability analysis of natural circulation loops, with main attention to those equipped with fluids at supercritical pressure. With respect to available models, the programme has the useful feature to make use of a brute force numerical linearization of transient equations, aiming at setting up stability maps of loops with realistic features, something going beyond the state of the art of present 1D system codes, while providing data with similar accuracy. Moreover, unlike what is normally found in the literature for the analysis of stability of natural circulation with supercritical pressure fluids, allowance for the presence of heating structures is made, pointing out the strong effect that wall heat capacitance has on stability in the conditions addressed in many previous works. The further step reported herein addresses in particular the inclusion in the computer programme of a low diffusion numerical scheme that is capable to rule out most of the truncation error effects experienced with similar codes. As in earlier works related to singlephase natural circulation, a second order upwind scheme has been adapted in a “donor cell” form to the case of supercritical pressure fluids, to be included in the conservation law form of the discretised energy balance equations, thus achieving a very low impact of numerical diffusion even with relatively coarse nodalizations. The resulting programme has been applied with success to relevant available data, from both theoretical and experimental analyses. Owing to this step, the programme can be now used as a tool for discussing the important issues of the selection of the most appropriate correlations for heat transfer and friction in natural circulation conditions with supercritical pressure fluids, allowing for excluding a priori a too large effect of the numerical effects on the obtained results