Linear stability analysis of flashing instability based on the homogeneous equilibrium model

Flashing instability is a two-phase flow instability widely reported in low-pressure natural circulation that induces undesirable flow oscillations with large magnitudes challenging the operation of facilities. The current study performs linear stability analysis on the flashing instability using a homogenous equilibrium model developed for a typical natural circulation configuration. Physical simplifications are performed, and the governing equations are analytically solved lumping the dynamics of the flow into the evolution of the inlet flow rate governed by a linear ordinary integro-differential equation. Similarity groups governing the dynamics is extracted from the non-dimensionalization. Static stability of the flow is checked based on the classic criterion of the excursive instability, which confirms negligible potential of the static instability and proves the dynamic nature of the flashing instability. The Laplace transformation is performed providing the characteristic function governing the dynamic stability, and the D-partition method is implemented producing the stability boundaries. Through reviewing the characteristic function, a simplified model is obtained around the stability boundary with the low exit flow quality, revealing three dominant feedback effects. For conditions with a short two-phase region near the top of the chimney, the flashing is found to introduce a strong delayed feedback between the gravitational driving force and the inlet flow rate, which essentially triggers the instability under favorable oscillation frequencies properly shifting the phase differences. The extracted dominant dynamics explains the parametric effect on the stability, and analytically predicts a proportional relation between oscillation period and the fluid residence time in the hot leg. The modeling and analysis in the current study supplements the analytical basis for understanding the flashing instability and provides valuable reference for further analytical studies.