Prediction of stability of one-dimensional natural circulation with a low diffusion numerical scheme

This paper presents the results obtained in the analysis of stability of flow in single-phase natural circulation loops by a computer program incorporating two different numerical schemes for the discretisation of the energy balance equation. In particular, in addition to an usual first order upwind scheme, a low diffusion numerical method, devised as an application of a classical second order explicit upwind scheme, has been introduced by simply using an appropriate definition of the “donor cell rule”. Both transient behaviour and linear stability are addressed, the latter obtained by a numerical perturbation technique providing full consistency with the transient algorithm. The behaviour of heat structures is also accounted for both in the non-linear transient program and in its linearised counterpart. After a detailed description of the adopted models, examples of their application are provided in the paper, addressing single-phase natural circulation loop behaviour. The results obtained by the low diffusion scheme are compared with those provided by the first order numerical scheme and with available information from a previous work on experimental loop behaviour, showing a remarkable improvement in the reliability of stability predictions.