Stability Analysis of Double-Loop Natural Circulation under Asymmetric Conditions
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摘要: 为研究非对称条件下双环路自然循环稳定性的变化，以单环路自然循环载热系统为起点，采用无量纲分析方法，将单环路自然循环的无量纲控制方程组中关于位移项进行傅里叶展开，从而得到表征单环路自然循环载热系统的雅克比（Jacobi）矩阵，并进行验证。在此基础上，构建了双环路Jacobi矩阵分析模型，基于所构建的模型，分别开展不同负荷差和阻力差下双环路自然循环稳定性分析，以及回路几何特征对稳定性边界的影响。结果表明，对于某一双环路系统而言，存在2个临界雷诺数，当左、右环路引入负荷差大于这2个临界雷诺数时，系统将会变得不稳定。增大高径比、减少管道直径、增加加热段长度和减少冷却段长度可以增加回路稳定性区域范围，且反应堆回路稳定性边界对环路高径比、加热段长度较为敏感；此外，在自然循环回路形成的允许范围内，增加环路压降可以提高系统稳定性。
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关键词:
- 自然循环 /
- 雅克比（Jacobi）矩阵 /
- 非对称 /
- 双环路 /
- 稳定性边界
Abstract: In order to study the stability change of double loop natural circulation under asymmetric conditions, taking the single loop natural circulation heat carrying system as the starting point, the displacement term in the dimensionless governing equation set of single loop natural circulation is expanded by Fourier expansion, and the Jacobi matrix characterizing the single loop natural circulation heat carrying system is obtained, and verification is conducted. On this basis, the Jacobi matrix analysis model of double loop is constructed. Based on the constructed model, the stability analysis of double loop natural circulation under different load difference and resistance difference is carried out, and the influence of loop geometric characteristics on the stability boundary is carried out. The results show that for a double loop system, there are two critical Reynolds numbers. When the load difference between the left and right loops is greater than these two critical Reynolds numbers, the system will become unstable. Increasing the aspect ratio, reducing the pipe diameter, increasing the length of heating section and reducing the length of cooling section can increase the range of loop stability area, and the stability boundary of reactor loop is more sensitive to the aspect ratio and the length of heating section; Besides, within the allowable range of natural circulation loop formation, increasing the loop pressure drop can improve the system stability.-
Key words:
- Natural circulation /
- Jacobi matrix /
- Asymmetry /
- Double loop /
- Stability boundary
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图 1 简化的自然循环单环路模型
H—回路高度，m；L—回路宽度，m；Hh—加热段高度，m；Hc—冷却段高度，m
Figure 1. Simplified Single Loop Model of Natural Circulation
图 3 非对称负荷差下左右环路
$Re - Gr'$ 稳定性图Figure 3.
$Re - Gr' $ Stability Diagram of Left and Right Loops under Asymmetric Load Difference
图 4 非对称阻力差下左右环路
$Re - Gr'$ 稳定性图Figure 4.
$Re - Gr' $ Stability Diagram of Left and Right Loops under Asymmetric Resistance Difference表 1 ALLF回路主要参数
Table 1. Main Parameters of ALLF Loop
参数 数值 参数 数值 H/m 5 功率/MW 0.206 L/m 1.1 热段温度/K 627 Hh/m 1.52 冷段温度/K 542 Hc/m 1.52 温升/K 85 D/m 0.063 LBE流速/( m·s-1) 0.501 LBE—液态铅铋合金 
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表 2 不同尺寸自然循环回路几何参数 m
Table 2. Geometric Parameters of Natural Circulation Loop with Different Sizes
回路编号 Hn Hh Hc D L Lt 1 1.25 0.75 0.75 0.20 1.8 10 2 1.25 0.40 0.75 0.20 1.8 10 3 1.50 0.75 0.75 0.20 1.8 10 4 1.25 0.75 0.75 0.20 1.5 10 5 1.25 0.75 0.75 0.15 1.8 10 6 1.25 0.75 0.60 0.20 1.8 10 ${H_{\rm{n}}}$—回路循环高度
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表 3 对称条件下不同几何参数回路稳定性边界裕量
Table 3. Stability Margin of Circuits with Different Geometric Parameters under Symmetrical Condition
回路编号 1 2 3 4 5 6 稳定性裕量/109 1.93 −5.65 12 3.29 2.88 0.78
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