A moving-boundary nodal model for the analysis of the stability of boiling channels

Abstract

A moving-boundary nodal model has been derived for the linear and non-linear stability analysis of boiling channels. This model is based on the integration of the conservation (partial differential) equations in space and an approximation of the integral with a weighted average of the integrated variable evaluated at the boundaries of the nodes. The resulting system of ODEs has been used to evaluate the linear stability of a boiling vertical channel. The results obtained with this model, using a relatively small number of nodes, compare favorably with experimental results and calculations obtained with distributed parameter and fixed node models, which require the use of many axial nodes. Supercritical and subcritical Hopf bifurcations have been identified, and the frequency response of the model has been evaluated. These results have been used as the criteria for the determination of the number of single-phase nodes needed for a given frequency range.