Abstract The stability analysis of a natural circulation integrated self-pressurized water reactor is investigated by the Lyapunov approach. The analysis of the pressurized water reactors (PWRs), particularly the integrated self-pressurized water reactors, is essential in keeping the neutronic and thermal-hydraulic parameters of the system stable. An appropriate nonlinear dynamic model is introduced based on conservation of mass, momentum and energy which is then linearized, in a state-space model. The Lyapunov approach and Routh-Hurwitz criterion are applied to assess the stability of this linearized system over its entire power range. The analysis is done for the primary coolant circuit in the RPV by assuming the steam dome pressure as the fixed parameter. It is found that the system remains stable over its entire power range. The influence of different geometrical features is studied at nominal conditions. It has been found that by reducing the chimney height results in a decrease in the coolant flow rate and a downward motion of the onset of flashing while the average core coolant temperature rises. For lower values of friction losses coefficient, the coolant flow rate increases, and the onset of flashing moves upward and the average core coolant temperature decreases. A change in independent parameters, which are effective in generating the natural circulation of the coolant, can influence the inherent safety of the system: An increase in reactor power and chimney height and a decrease in friction losses coefficient improve the system inherent safety. Two input functions as extra reactivity for increasing and decreasing the power from the nominal state are implemented into the dynamic model and the model response is therefore assessed by considering the lack of two phase flow entry to the core restriction. The boundary of the system stability lies in the range 32–107 MWt and using the system outside this range the system pressure needs to be controlled through spray and heater systems. The obtained results are based on the initial information, data and primary design of these types of reactors. Determining a more accurate boundary requires more detailed design and assessment together with experimental test facilities with respect to other restricting parameters of the system. The results presented in this paper can be implemented in further research on this type of reactors, particularly for nonlinear stability analysis and finding nonlinear Lyapunov function.

中文翻译：

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自然循环一体化自压水堆稳定性分析与参数研究

摘要 采用李雅普诺夫方法研究了自然循环一体化自压水堆的稳定性分析。压水反应堆 (PWR)，特别是集成自压水反应堆的分析对于保持系统的中子和热工水力参数稳定至关重要。基于质量、动量和能量守恒引入了一个合适的非线性动力学模型，然后在状态空间模型中将其线性化。应用 Lyapunov 方法和 Routh-Hurwitz 准则来评估该线性化系统在其整个功率范围内的稳定性。通过假设蒸汽圆顶压力作为固定参数，对 RPV 中的主冷却剂回路进行了分析。发现系统在其整个功率范围内保持稳定。在标称条件下研究了不同几何特征的影响。已经发现，通过降低烟囱高度会导致冷却剂流速的降低和闪蒸开始的向下运动，同时平均堆芯冷却剂温度升高。对于较低的摩擦损失系数值，冷却剂流速增加，闪蒸的开始向上移动，平均堆芯冷却剂温度降低。影响冷却剂自然循环的独立参数的变化会影响系统的固有安全性：反应堆功率和烟囱高度的增加以及摩擦损失系数的降低可提高系统的固有安全性。两个输入函数作为用于从标称状态增加和减少功率的额外反应性被实施到动态模型中，因此通过考虑缺乏进入核心限制的两相流来评估模型响应。系统稳定性的边界在 32-107 MWt 范围内，使用此范围之外的系统，系统压力需要通过喷雾和加热器系统进行控制。获得的结果基于这些类型反应堆的初始信息、数据和初步设计。确定更准确的边界需要更详细的设计和评估以及与系统其他限制参数相关的实验测试设施。本文提出的结果可用于对此类反应堆的进一步研究，