Asymmetrical operation characteristics of natural circulation lead-bismuth reactor under ocean conditions
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摘要: 基于二次开发RELAP5/MOD3.1程序，分析了典型海洋条件下的10 MW自然循环铅铋反应堆偏环运行特性。分析结果表明：反应堆在倾斜条件下偏环运行时，其系统参数对倾角变化敏感性较弱；起伏条件下，偏环运行导致流量的波动幅度降低为9%，出口温度降低约16 K。起伏幅度越大、流量波动越剧烈；起伏周期越大、流量震荡越明显，但影响效果也在减弱；摇摆条件下，堆芯流量、出口温度降低，反应堆引入更高的安全裕量；摇摆幅度越大、摇摆周期越小，流量波动幅度越大，且堆芯出口温度对周期变化敏感性明显高于摇摆幅度变化。Abstract: To ensure the vitality of naval nuclear power at all times, the natural cycle lead-bismuth reactor loop will take partial loop operation when it fails under marine conditions. However, there are few studies on the partial loop operation characteristics of lead-bismuth reactor under marine conditions. Based on the secondary development of RELAP5/MOD3.1 program, the off-loop operation characteristics of a 10 MW natural cycle lead-bismuth reactor under typical oceanic conditions are analyzed. The analysis results show that the system parameters of the reactor are less sensitive to the change of tilt angle when the reactor is operating under inclined conditions. Under undulating conditions, the fluctuation of flow rate is reduced by 9% and the outlet temperature is reduced by about 16 K. The larger the undulating amplitude, the more drastic the flow rate fluctuation; the larger the undulating period, the more obvious the flow rate oscillation, but the effect is also weakening. Under rocking conditions, the core flow and outlet temperature are reduced and the reactor introduces higher safety margins. The larger the swing amplitude and the smaller the swing period, the larger the flow fluctuation, and the core outlet temperature is significantly more sensitive to the cycle change than the swing amplitude change.
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Key words:
- ocean conditions /
- lead-bismuth reactor /
- RELAP5 /
- natural circulation /
- asymmetric loop operation
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图 1 TALL-3D实验装置图（a）与节点图（b）
Figure 1. Schematic diagram of TALL-3D experimental device (a) and node diagram (b)
图 4 SNCLFR-10反应堆结构简图（a）与节点图（b）
Figure 4. SNCLFR-10 reactor structure sketch (a) and node diagram (b)
图 10 不同倾角下堆芯流量（a）、出口温度（b）变化
Figure 10. Effect of inclination angle on core flow (a) and outlet temperature(b)
图 12 起伏周期（a）、幅度（b）对流量的影响
Figure 12. Effect of heaving period (a) and amplitude(b) on flow
图 13 堆芯温度（a）和自然循环流量（b）变化
Figure 13. Variation of core temperature (a) and natural circulation flow (b)
图 14 起伏周期（a）和幅度（b）对流量的影响
Figure 14. Effect of heaving period (a) and amplitude(b) on flow
图 16 摇摆幅度（a）和周期（b）对流量的影响
Figure 16. Effect of rolling amplitude (a) and period (b) on flow
图 17 堆芯温度（a）和自然循环流量（b）变化
Figure 17. Variation of core temperature (a) and natural circulation flow (b)
图 18 摇摆幅度（a）和周期（b）对流量的影响
Figure 18. Effect of rolling amplitude (a) and period (b) on flow
图 19 摇摆周期（a）和幅度（b）对堆芯出口温度的影响
Figure 19. Effect of rolling period (a) and amplitude (b) on core outlet temperature
表 1 RELAP5中的液相铅铋物性关系式
Table 1. Formula of RELAP5 program for liquid LBE
parameter thermodynamic properties density ${\rho _{{\rm{LBE}}} }[{\rm{kg}} \cdot {{\rm{m}}^{ - 3} }] = 11\;096.0 - 1.303\;6 \times {T_{{\rm{LBE}}} }$ saturation vapor pressure ${p_s}_{({\rm{LBE}})}[{\rm{Pa}}] = 1.11 \times {10^{10}} \cdot \exp \Bigg( - \dfrac{{22\;552.0}}{{{T_{{\rm{LBE}}}}}}\Bigg)$ heat capacity ${c_p}_{({\rm{LBE}})}[{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}] = 159.0 - 2.72 \times {10^{ - 2}} \times {T_{{\rm{LBE}}}} + 7.12 \times {10^{ - 6}} \times T_{{\rm{LBE}}}^2$ internal energy ${U_{({\rm{LBE}})}}[{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}}] = 159.0({T_{{\rm{LBE}}}} - {T_{\rm{M}}}) + \dfrac{{2.72 \times {{10}^{ - 2}}({T^2}_{{\rm{LBE}}} - {T^2}_{\rm{M}})}}{2} + \dfrac{{7.12 \times {{10}^{ - 6}}({T^3}_{{\rm{LBE}}} - {T^3}_{\rm{M}})}}{3}$
${T_{\rm{M}}} = 398.15K$enthalpy ${h_{({\rm{LBE}})}}[{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}}] = U + pv$ entropy ${{{S}}_{({\rm{LBE}})}}[{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}] = 159.0\ln \dfrac{{{T_{{\rm{LBE}}}}}}{{{T_{\rm{M}}}}} + 2.72 \times {10^{ - 2}}({T_{{\rm{LBE}}}} - {T_{\rm{M}}}) + \dfrac{{7.12 \times {{10}^{ - 6}}({T^2}_{{\rm{LBE}}} - {T^2}_{\rm{M}})}}{2}$ thermal coefficient of expansion ${\beta _{({\rm{LBE}})}}[{{\rm{K}}^{ - 1}}] = \dfrac{1}{{(8\;383.2 - {T_{{\rm{LBE}}}})}}$ pressure coefficient of expansion ${\kappa _{({\rm{LBE}})}}[{\rm{P}}{{\rm{a}}^{ - 1}}] = \dfrac{1}{{(11\;096.0 - 1.303\;6{T_{{\rm{LBE}}}}){{(1\;773.0 + 0.104\;9{T_{{\rm{LBE}}}} + 2.87 \cdot {{10}^{ - 4}}T_{{\rm{LBE}}}^{ - 4})}^2}}}$ viscosity ${\eta _{({\rm{LBE}})}}[{\rm{Pa}} \cdot {\rm{s}}] = 4.94 \times {10^{ - 4}} \times \exp \left( {\dfrac{{754.1}}{{{T_{{\rm{LBE}}}}}}} \right)$ surface tension ${\sigma _{({\rm{LBE}})}}[{\rm{N}} \cdot {{\rm{m}}^{ - 1}}] = 0.367 - 5.5 \cdot {10^{ - 5}}\left( {{T_{{\rm{LBE}}}} - 1\;073.15} \right)$ thermal conductivity ${\lambda _{({\rm{LBE}})}}[{\rm{W}} \cdot {{\rm{m}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}] = 3.61 + 1.517 \times {10^{ - 2}}{T_{{\rm{LBE}}}} - 1.741 \times {10^{ - 6}}T_{{\rm{LBE}}}^2$ 
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表 2 自然循环实验值与计算值对比
Table 2. Comparison of experimental value and calculated value of natural circulation
parameter MH flow/(kg/s) TS flow/(kg/s) total flow/(kg/s) MH inlet temperature/K MH outlet temperature/K TS inlet temperature/K TS outlet temperature/K experiment 0.238 0.293 0.533 473.28 556.63 457.53 567.14 extension 0.242 0.29 0.533 473.19 559.99 473.19 565.44 error/% −1.68 1.023 0 0.019 −0.603 0.492 0.300 RELAP5-3D 0.238 0.296 0.534 473.2 561.23 473.2 561.75 error/% 0 −1.023 −0.187 0.017 −0.826 0.490 0.950
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表 3 堆芯关键参数设计值与计算值对比
Table 3. Comparison of design values and calculated values of key parameters in core
parameter power/MW inlet temperature/K outlet temperature/K flow/(kg/s) flow rate(m/s) design value 10 533 663 529.4 0.12356 extension 10 533.52 659.63 529.28 0.12133 error/% 0 −0.098 0.508 0.022 1.804 RELAP5-3D 10 533.34 659.1 529.84 0.12123 error/% 0 −0.064 0.588 −0.083 1.886
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