Abstract

Conventionally, the stability of xenon oscillations is estimated by solution of the time-dependent neutron diffusion equation, coupled with iodine and xenon equations, by finding out the damping ratios in each case. This is performed for different initial perturbations and core burnup conditions and is a very time-consuming and tedious process. Some earlier studies include linear stability estimation, which is valid for small perturbations, but not much work has been done in nonlinear stability analysis for spatial xenon oscillations in particular. In this paper, an approach for carrying out bifurcation analysis of xenon oscillations in large pressurized heavy water reactors (PHWRs) is demonstrated using reduced-order models. The reduced-order model for studying spatial xenon oscillations consists of multipoint kinetic equations coupled with xenon and iodine equations along with explicit fuel and coolant temperature feedback. Both subcritical Hopf bifurcation and supercritical Hopf bifurcation in different parameter planes exist, which leads to unstable limit cycles in the linearly stable region (subcritical Hopf bifurcation) and stable limit cycles in the linearly unstable region (supercritical Hopf bifurcation). The stability map provides a total picture of the stability of the out-of-phase oscillations in a PHWR. Depending on the value of the fuel temperature coefficient of reactivity and coolant temperature coefficient of reactivity, one can determine the operating power level above which the out-of-phase xenon oscillations start to grow. This model can be used to analyze nonlinear stability characteristics without spatial power control, which is helpful in identification of stable/unstable regimes in different parameter spaces and is likely to aid in reactor design.

摘要

传统上，氙振荡的稳定性是通过求解与时间相关的中子扩散方程，再加上碘和氙方程，通过找出每种情况下的阻尼比来估计的。这是针对不同的初始扰动和核心燃耗条件执行的，并且是一个非常耗时且乏味的过程。一些早期的研究包括线性稳定性估计，这对于小扰动是有效的，但在非线性稳定性分析中，尤其是空间氙气振荡的非线性稳定性分析没有做太多工作。在本文中，使用降阶模型演示了一种对大型加压重水反应堆 (PHWR) 中的氙气振荡进行分岔分析的方法。用于研究空间氙气振荡的降阶模型由多点动力学方程、氙气和碘方程以及显式燃料和冷却剂温度反馈组成。不同参数平面上的亚临界Hopf分岔和超临界Hopf分岔都存在，导致线性稳定区（亚临界Hopf分岔）的极限环不稳定，而线性不稳定区（超临界Hopf分岔）的极限环稳定。稳定性图提供了 PHWR 中异相振荡稳定性的总体情况。根据燃料反应温度系数和冷却剂反应温度系数的值，可以确定运行功率水平，高于该水平异相氙振荡开始增长。