Study on Orthogonal Experiments of Jet Breakup and its Modeling Based on MPS Method
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摘要: 为了研究堆芯熔融物射流破裂过程中射流破裂长度的主要影响因素及其作用程度评级，基于正交实验法设计了3因素5水平的25组实验，采用移动粒子半隐式仿真（MPS）得到各工况下的射流破裂长度，并对模拟结果进行极差与方差分析，结果表明，影响射流破裂长度的主要因素为射流与冷却剂密度比、射流速度和射流直径，三者的显著性均为二级（**），在同级别中的作用程度大小依次为：射流速度>射流与冷却剂密度比>射流直径。在此基础上使用模拟数据拟合出了新的预测射流破裂长度经验关系式，当射流与冷却剂密度比为1.1~13.6时，该关系式的预测误差控制在±30%范围内。Abstract: In order to study the primary influencing factors of jet breakup length during the core melt jet breakup process and their ranking, 25 sets of experiments with 3 factors and 5 levels were designed based on the orthogonal experimental method, and the jet breakup lengths were obtained for each condition by using the Moving Particle Semi-implicit method (MPS). The simulation results were analyzed by polarity and variance analysis, and it was concluded that the primary influencing factors of jet breakup length were jet to coolant density ratio, jet velocity and jet diameter, and all of them have a second level of significance (**). Their ranking in the same level was in the following order: jet velocity > jet to coolant density ratio > jet diameter. Moreover, a new empirical relationship for predicting jet breakup length was fitted using simulated data, and the error margin of the model was kept within ±30% when the ratio of jet to coolant density was 1.1~13.6.
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Key words:
- Jet breakup length /
- Influencing factors /
- Orthogonal experiments /
- Empirical correlation
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图 2 不同粒子直径和参考实验的射流穿透深度
Figure 2. Jet Penetration Depth for Different Particle Diameter Sizes and Reference Experiments
图 3 数值模拟和参考实验的伍德合金射流形态
红色区域—数值模拟结果，灰色区域—参考实验结果
Figure 3. Morphology of Wood’s Alloy Jet for Value Simulation and Reference Experiments
图 4 模拟数据与先前经验关系式的对比
$ \varOmega = {{\left( {{{{L_{{\text{brk}}}}} \mathord{\left/ {\vphantom {{{L_{{\text{brk}}}}} {{D_{{\text{jet}}}}}}} \right. } {{D_{{\text{jet}}}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{{{L_{{\text{brk}}}}} \mathord{\left/ {\vphantom {{{L_{{\text{brk}}}}} {{D_{{\text{jet}}}}}}} \right. } {{D_{{\text{jet}}}}}}} \right)} {{{\left( {{{{\rho _{{\mathrm{jet}}}}} \mathord{\left/ {\vphantom {{{\rho _{{\mathrm{jet}}}}} {{\rho _{\mathrm{c}}}}}} \right. } {{\rho _{\mathrm{c}}}}}} \right)}^{0.5}}}}} \right. } {{{\left( {{{{\rho _{{\mathrm{jet}}}}} \mathord{\left/ {\vphantom {{{\rho _{{\mathrm{jet}}}}} {{\rho _{\mathrm{c}}}}}} \right. } {{\rho _{\mathrm{c}}}}}} \right)}^{0.5}}}} \text{；} \beta = {\left( {{{V_{{\mathrm{jet}}}^2} \mathord{\left/ {\vphantom {{{V_{{\mathrm{jet}}}}^2} {g{D_{{\mathrm{jet}}}}}}} \right. } {g{D_{{\mathrm{jet}}}}}}} \right)^{0.5}} $
Figure 4. Comparison of Simulated Data with Previous Empirical Correlations
表 1 参考实验的材料物性参数
Table 1. Physical Parameters of Materials for Reference Experiment
参数 伍德合金 水 二氧化铀 钠 密度/(kg·m−3) 9400 1000 8756 856 参考温度/K 473.15 293.15 3273.15 673.15 表面张力/(N·m−1) 0.430 0.072 0.484 0.179 运动粘度/(m2·s−1) 2.95×10−7 1.09×10−6 7.41×10−7 3.24×10−7 射流与冷却剂的密度比 9.4 10.1 
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表 2 数值模拟的材料物性参数
Table 2. Physical Parameters of Materials for Numerical Simulation
实验材料 密度/
(kg·m−3)参考温
度/K运动粘度/
(m2·s−1)表面张力/
(N·m−1)原型材料
（UO2∶ZrO2=80%∶20%）7960 3273.15 5.65×10−7 0.450 二氧化铀 8756 3273.15 7.41×10−7 0.484 苯甲酸苄酯 1118 293.15 7.56×10−6 0.044 汞 13600 293.15 1.14×10−7 0.510 伍德合金 9400 493.15 2.95×10−7 0.430 水 1000 293.15 1.09×10−6 0.072
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表 3 研究因素和水平
Table 3. Research Factors and Levels
密度比（因素A） 速度（ 因素 B）/(m·s−1) 直径（因素 C）/mm 1(8.0) ① 1(0.5) 1(10.0) 2(1.1) 2(1.2) 2(20.0) 3(13.6) 3(2.5) 3(15.0) 4(8.8) 4(3.2) 4(5.0) 5(9.4) 5(1.8) 5(30.0) 注：① 1(8.0)表示水平数为1，密度比为8.0，下同
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表 4 L25(56)正交实验结果
Table 4. Results of L25(56) Orthogonal Experiments
密度比
（因素A）速度（因素B）/
(m·s−1)直径（因素C）/
mmD E F 射流破
裂长度/m1(8.0) 1(0.5) 1(10) 1 1 1 0.080 1(8.0) 2(1.2) 3(15) 4 5 2 0.122 1(8.0) 3(2.5) 5(30) 2 4 3 0.228 1(8.0) 4(3.2) 2(20) 5 3 4 0.230 1(8.0) 5(1.8) 4(5) 3 2 5 0.128 2(1.1) 1(0.5) 5(30) 4 3 5 0.062 2(1.1) 2(1.2) 2(20) 2 2 1 0.078 2(1.1) 3(2.5) 4(5) 5 1 2 0.107 2(1.1) 4(3.2) 1(10) 3 5 3 0.135 2(1.1) 5(1.8) 3(15) 1 4 4 0.090 3(13.6) 1(0.5) 4(5) 2 5 4 0.052 3(13.6) 2(1.2) 1(10) 5 4 5 0.126 3(13.6) 3(2.5) 3(15) 3 3 1 0.219 3(13.6) 4(3.2) 5(30) 1 2 2 0.338 3(13.6) 5(1.8) 2(20) 4 1 3 0.190 4(8.8) 1(0.5) 3(15) 5 2 3 0.085 4(8.8) 2(1.2) 5(30) 3 1 4 0.161 4(8.8) 3(2.5) 2(20) 1 5 5 0.202 4(8.8) 4(3.2) 4(5) 4 4 1 0.179 4(8.8) 5(1.8) 1(10) 2 3 2 0.142 5(9.4) 1(0.5) 2(20) 3 4 2 0.095 5(9.4) 2(1.2) 4(5) 1 3 3 0.103 5(9.4) 3(2.5) 1(10) 4 2 4 0.170 5(9.4) 4(3.2) 3(15) 2 1 5 0.214 5(9.4) 5(1.8) 5(30) 5 5 1 0.185
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表 5 正交实验结果的极差分析
Table 5. Polar Analysis of Results of Orthogonal Experiments
项目 密度比
（因素A）射流速度（因素B）/
(m·s−1)射流直径
（因素C）/mmD E F K1 0.788 0.374 0.653 0.813 0.752 0.741 K2 0.472 0.590 0.795 0.714 0.799 0.804 K3 0.925 0.926 0.730 0.738 0.756 0.741 K4 0.769 1.096 0.569 0.723 0.718 0.703 K5 0.767 0.735 0.974 0.733 0.696 0.732 R 0.453 0.722 0.405 0.099 0.103 0.101
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表 6 正交实验结果的方差分析
Table 6. Variance Analysis of Results of Orthogonal Experiments
方差来源 离差平方和 自由度 均方 统计量 显著性 A 0.0220 4 0.0055 18.39 ** B 0.0635 4 0.0159 53.21 ** C 0.0189 4 0.0047 15.84 ** 误差 0.0036 12 0.0003
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表 7 拟合组数据
Table 7. Fitting Group Data
密度比
（因素A）速度（因素B）/
(m·s−1)直径（因素C）/mm 射流破裂
长度/m1(8.0) 1(0.5) 1(10) 0.080 1(8.0) 3(2.5) 5(30) 0.228 1(8.0) 4(3.2) 2(20) 0.230 2(1.1) 3(2.5) 4(5) 0.107 2(1.1) 4(3.2) 1(10) 0.135 2(1.1) 5(1.8) 3(15) 0.090 3(13.6) 1(0.5) 4(5) 0.052 3(13.6) 4(3.2) 5(30) 0.338 3(13.6) 5(1.8) 2(20) 0.190 4(8.8) 1(0.5) 3(15) 0.085 4(8.8) 3(2.5) 2(20) 0.202 4(8.8) 4(3.2) 4(5) 0.179 5(9.4) 1(0.5) 2(20) 0.095 5(9.4) 2(1.2) 4(5) 0.103 5(9.4) 4(3.2) 3(15) 0.214
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表 8 验证组数据
Table 8. Validation Group Data
密度比
（因素A）速度（因素B）/
(m·s−1)直径（因素C）/mm 射流破裂
长度/m1(8.0) 2(1.2) 3(15) 0.122 1(8.0) 5(1.8) 4(5) 0.128 2(1.1) 1(0.5) 5(30) 0.062 2(1.1) 2(1.2) 2(20) 0.078 3(13.6) 2(1.2) 1(10) 0.126 3(13.6) 3(2.5) 3(15) 0.219 4(8.8) 2(1.2) 5(30) 0.161 4(8.8) 5(1.8) 1(10) 0.142 5(9.4) 3(2.5) 1(10) 0.170 5(9.4) 5(1.8) 5(30) 0.185
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表 9 参考实验信息
Table 9. Reference Experiment Information
研究机构 实验材料 密度比 速度/
（m·s−1）射流直
径/mm射流破裂
长度/mCityU 汞/水 13.6 2.16 5 0.152 POSTECH 伍德合金/水 8.8 3.35 35 0.490 JAERI ZAO/水① 3.4 7.80 35 0.800 注：①ZAO为ZrO2-Al2O3(49%∶51%)合金
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