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.

闪蒸不稳定性是低压自然循环中广泛报道的两相流不稳定性，它会引起不希望有的大幅度流动扰动，对设施的运行提出挑战。当前的研究使用针对典型自然循环构造开发的均质平衡模型对闪蒸不稳定性进行线性稳定性分析。进行物理简化，然后解析地解析控制方程，将流动的动力学集中到由线性普通积分微分方程控制的入口流量的演变过程中。从无量纲化中提取控制动力学的相似性组。根据漂移不稳定性的经典标准检查流体的静态稳定性，证实了静态不稳定性的可能性可以忽略不计，并且证明了闪烁不稳定性的动态性质。执行Laplace变换以提供控制动态稳定性的特征函数，并实施D分区方法以产生稳定性边界。通过回顾特征函数，在出口水流质量较低的稳定边界附近获得了简化模型，揭示了三个主要的反馈效应。对于烟囱顶部附近两相区域较短的情况，发现闪烁会在重力驱动力和入口流速之间引入强烈的延迟反馈，这在适当的振荡频率下会触发不稳定，从而适当地移动相位差异。提取的主要动力学解释了对稳定性的参数影响，并分析性地预测了振荡周期和热段中流体停留时间之间的比例关系。当前研究中的建模和分析补充了理解闪烁不稳定性的分析基础，并为进一步的分析研究提供了有价值的参考。