具导热时滞的核反应堆模型的Hopf分支

发布时间：2018-05-01 09:40

本文选题：核反应堆 + 时滞　；参考：《哈尔滨工业大学》2015年硕士论文

【摘要】：核电作为一种高效、环保能源,可大幅减少空气污染、促进我国能源独立。核电产业的发展离不开核安全问题,核反应堆运行务必要保障反应堆堆芯的安全性,核电控制系统可担此任。该系统主要通过测量冷却剂平均温度,控制反应堆功率来保证核电站正常运转。因此,温度与功率是研究核反应堆运行安全的两个关键变量。本文对Kostas Bucys建立的具时滞的二维点堆模型进行了动力学性质分析。这里引入时滞,即冷却剂通过管道所需要的时间来刻画核电站控制系统对堆内温度的测量控制。首先,考虑了时滞?对系统平衡点稳定性的影响,并得到了在正平衡点处存在局部Hopf分支的充分条件。在Hassard等人提出的中心流形约化方法和规范型理论的基础上,研究了正平衡点处的Hopf分支方向和分支周期解稳定性,并推导了显示公式。其次,利用吴建宏等人建立的全局Hopf分支理论研究了分支周期解的大范围存在性。通过这些理论分析,我们得到了冷却剂通过管道所需的时间的长短(即时滞的大小)对反应堆堆芯安全的影响。当时滞的大小在一定范围内,并且模型中的相关参数满足一定条件时,反应堆的温度和功率都将被限制在一个区间内。最后,使用MATLAB软件进行数值模拟,得到了当参数满足一定条件时确实可以防止反应堆的功率和温度升高到不可接受的程度,因此数值模拟结果例证了理论分析结果的正确性。
[Abstract]:Nuclear power, as an efficient and environmentally-friendly energy, can greatly reduce air pollution and promote energy independence in China. The development of nuclear power industry can not do without nuclear safety, nuclear reactor operation must ensure the safety of reactor core, nuclear power control system can assume this role. The system ensures the normal operation of the nuclear power plant by measuring the coolant average temperature and controlling the reactor power. Therefore, temperature and power are two key variables to study the safety of nuclear reactor operation. In this paper, the dynamical properties of a two dimensional point heap model with time delay established by Kostas Bucys are analyzed. Time delay is introduced to describe the measurement and control of the temperature in the reactor by the control system of the nuclear power plant in terms of the time required for the coolant to pass through the pipeline. First, time delay is considered? The sufficient conditions for the existence of local Hopf bifurcation at the positive equilibrium point are obtained. Based on the center manifold reduction method and normal form theory proposed by Hassard et al, the direction of Hopf bifurcation and the stability of bifurcation periodic solution at positive equilibrium point are studied, and the display formula is derived. Secondly, using the global Hopf bifurcation theory established by Wu Jian-hong and others, we study the existence of the periodic solutions in a large range. Based on these theoretical analyses, we have obtained the influence of the length of time required for the coolant to pass through the pipeline (i.e., the size of the time lag) on the reactor core safety. When the hysteresis is within a certain range and the parameters in the model satisfy certain conditions, the temperature and power of the reactor will be confined to a certain range. Finally, the numerical simulation with MATLAB software shows that the power and temperature of the reactor can be prevented from rising to an unacceptable level when the parameters meet certain conditions, so the numerical simulation results illustrate the correctness of the theoretical analysis results.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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