Experimental study of the multi-factor coupling effect of coal dust explosion intensity based on Box-Behnken response surface
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摘要: 为分析煤尘瞬态爆炸反应过程中多因素耦合效应对爆炸强度的影响，采用Box-Behnken试验设计方法在20 L球形爆炸测试系统中进行了45组爆炸试验，观察了煤尘质量浓度（ρ）、煤尘粒径（D）、煤挥发分质量分数（w）、点火能量（E）和点火延迟（td）5个因素耦合作用下煤尘爆炸强度的宏观特征。通过测量压力变化来监控爆炸过程，并从压力-时间曲线确定最大爆炸压力（pmax）及最大爆炸压力上升速率（$ {\dot{p}}_{\max } $）。使用Design-Expert软件分析实验结果，建立了响应量pmax和$ {\dot{p}}_{\max } $的二次回归模型。结果显示，在方差分析中，pmax和$ {\dot{p}}_{\max } $的决定系数R2分别为
0.9771 和0.9258 ，表明模型和实验数据良好拟合。在模型中，对煤尘最大爆炸压力（$ {\dot{p}}_{\max } $）影响最大的单因素是点火能量（E）和点火延迟（td），对最大爆炸压力上升速率（$ {\dot{p}}_{\max } $）影响最大的单因素是煤尘粒径（D）和点火延迟（td）。影响pmax的显著双因素交互作用是ρD、ρE、ρtd、Dw、wE、wtd和Etd，而影响$ {\dot{p}}_{\max } $的显著双因素交互作用是ρtd、Dw、Dtd、wtd和Etd。其中，点火延迟（td）在响应量pmax和$ {\dot{p}}_{\max } $中起决定性作用。-
关键词:
- 煤尘爆炸 /
- 爆炸强度 /
- Box-Behnken试验设计 /
- 响应面法
Abstract: Using the Box-Behnken experimental design method, the influence of multi-factor coupling effects on the intensity of coal dust explosion during the transient explosion reaction process was studied. Forty-five sets of explosion tests were carried out in a 20L spherical explosion test system, examining the macroscopic characteristics of the coal dust explosion intensity under the coupling effects of five factors: coal dust concentration (ρ), coal dust particle size (D), coal volatile matter (w), ignition energy (E), and ignition delay (td). The explosion process was monitored by measuring pressure changes, and the maximum explosion pressure (response value pmax) and the maximum explosion pressure rise rate (response value $ {\dot{p}}_{\max } $) were determined from the pressure-time curve. The Design-Expert software was used to analyze the experimental results to establish a quadratic regression model for response values pmax and $ {\dot{p}}_{\max } $, and the models were verified by four different methods. The results show that in the variance analysis, the coefficient of determination R2 for pmax and $ {\dot{p}}_{\max } $ is0.9771 and0.9258 , respectively, indicating a good fit between the model and experimental data. The single factors with the greatest influence on the maximum explosion pressure (pmax) are ignition energy (E) and ignition delay(td), while the single factors with the greatest influence on the rise rate of the maximum explosion pressure ($ {\dot{p}}_{\max } $) is coal dust particle size(D) and ignition delay(E). In the quadratic regression model, the significant two-factor interaction affecting pmax are ρD, ρE, ρtd, Dw, wE, wtd, and Etd, wheras the significant two-factor interaction affecting $ {\dot{p}}_{\max } $ are ρtd, Dw, Dtd, wtd, and Etd. Among these, ignition delay (td) plays a decisive role in response values pmax and $ {\dot{p}}_{\max } $. -
图 4 响应量预测值-实际值图
Figure 4. Plot of Predicted Values vs. Actual Values for Response Variable
图 5 响应量残差-实验编号图
Figure 5. Plot of residuals vs. experiment number for Response Variable
图 6 响应量杠杆值-实验编号图
Figure 6. Plot of leverage vs. experiment number for Response Variable
图 8 响应量$ {\dot{p}}_{\max } $响应曲面图
Figure 8. Response value $ {\dot{p}}_{\max } $ response surface plot
表 1 煤样各组分及元素质量分数占比
Table 1. Mass Fraction of Components and Elements in Coal Samples
煤样编号 水分/% 挥发分/% 灰分/% 固定碳/% C/% H/% O/% N/% S/% 煤样1 6.41 34.47 3.59 55.53 73.78 4.68 19.49 1.58 0.47 煤样2 6.01 31.47 2.99 59.53 77.45 3.24 18.08 1.03 0.2 煤样3 1.17 28.63 13.18 57.02 76.70 3.84 15.95 1.36 1.15 
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表 2 试验影响因素及水平
Table 2. Factors and levels affecting the experiment
水平 ρ/(g·m−3) D/μm w/% E/kJ td/ms −1 200 58 28.6 4 60 0 300 119 31.5 5 80 1 400 180 34.4 6 100
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表 3 Box-Behnken试验方案及结果
Table 3. Box-Behnken experimental design and results
试验编号 ρ/(g·m−3) D/μm w/% E/kJ td/ms pmax/MPa pmax/(MPa·s−1) pmax相对误差/% ${\dot{p}}_{\max } $相对误差/% 1 300 58 31.5 5 60 0.6136 38.6899 3.1 2.3 2 300 119 34.4 4 80 0.5398 24.9074 1.7 4.7 3 300 119 31.5 5 80 0.5639 25.8196 4.3 0.8 4 300 119 28.6 5 100 0.5196 16.4131 0.5 3.4 5 200 119 31.5 5 100 0.5023 12.5697 2.8 5.0 6 200 119 31.5 4 80 0.5541 24.4600 2.1 1.6 7 300 180 31.5 5 60 0.6099 36.1483 3.9 4.1 8 300 58 31.5 6 80 0.5808 31.4863 2.4 2.9 9 300 119 34.4 6 80 0.5684 28.4717 1.2 0.2 10 300 119 34.4 5 100 0.5214 20.0977 4.8 3.7 11 300 58 28.6 5 80 0.5500 26.7969 0.9 1.1 12 400 180 31.5 5 80 0.5331 24.7871 3.5 4.9 13 400 119 34.4 5 80 0.5357 26.5759 2.1 2.0 14 300 119 31.5 5 80 0.5711 24.5424 4.6 0.5 15 300 58 31.5 5 100 0.5606 26.1586 1.0 3.8 16 200 119 34.4 5 80 0.5431 22.5871 0.3 4.3 17 200 119 28.6 5 80 0.5359 23.1011 4.0 1.9 18 300 119 31.5 5 80 0.5693 23.4408 2.7 0.7 19 300 180 34.4 5 80 0.5378 20.4326 3.2 2.6 20 400 119 31.5 5 60 0.5552 33.2927 4.7 2.9 21 300 180 31.5 5 100 0.5412 17.0977 1.8 3.0 22 300 119 28.6 4 80 0.5421 25.4424 0.7 1.4 23 300 119 28.6 5 60 0.5657 40.5894 2.9 4.6 24 400 119 31.5 6 80 0.5605 25.792 5.0 2.2 25 400 119 31.5 4 80 0.5319 24.1202 3.6 0.9 26 300 119 31.5 6 100 0.5752 23.4433 1.4 4.4 27 300 58 31.5 4 80 0.5784 32.2736 4.2 3.5 28 300 119 28.6 6 80 0.5469 27.4668 0.1 1.3 29 200 58 31.5 5 80 0.5632 25.4277 2.5 0.4 30 300 119 34.4 5 60 0.5948 36.5107 3.5 2.8 31 200 119 31.5 5 60 0.6067 35.3311 4.9 4.5 32 300 119 31.5 6 60 0.5787 33.9722 1.2 1.7 33 200 180 31.5 5 80 0.5637 19.7039 0.6 3.4 34 200 119 31.5 6 80 0.5560 25.4570 2.3 0.1 35 400 58 31.5 5 80 0.5548 27.4668 4.4 2.5 36 300 180 31.5 6 80 0.5761 26.7969 1.9 4.8 37 300 180 31.5 4 80 0.5650 23.4473 3.0 3.9 38 400 119 28.6 5 80 0.5262 26.1270 2.6 1.0 39 300 119 31.5 5 80 0.5657 24.7773 0.8 0.6 40 300 180 28.6 5 80 0.5635 26.1172 4.1 2.7 41 300 119 31.5 5 80 0.5668 23.7822 1.5 4.0 42 300 119 31.5 4 60 0.6097 42.2051 1.5 1.8 43 300 119 31.5 4 100 0.5224 18.1277 3.7 3.2 44 400 119 31.5 5 100 0.5366 20.0436 2.2 0.3 45 300 58 34.4 5 80 0.5808 33.1611 0.4 4.8
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表 4 各模型方差分析结果
Table 4. ANOVA results for each model
方差来源 顺序P值 缺失拟合P值 决定系数R2 修正后R2 预测系数R² pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ 线性 < 0.0001 < 0.0001 0.0010 0.0146 0.5306 0.8069 0.4704 0.7821 0.3594 0.7391 2FI 0.0998 0.0804 0.0013 0.0207 0.7121 0.8842 0.5632 0.8244 0.2328 0.7056 二次 < 0.0001 < 0.0001 0.1051 0.2084 0.9771 0.9258 0.9580 0.9543 0.9112 0.9050 三次 0.4117 0.2115 0.0854 0.2798 0.9923 0.9751 0.9623 0.9683 0.5794 0.7054
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表 5 二次回归分析模型方差分析表
Table 5. ANOVA model for quadratic regression analysis
来源 自由度 平方和 均方 F值 显著性p值 pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ pmax $ {\dot{p}}_{\max } $ 模型整体 20 0.0275 1739.93 0.0014 87 51.19 46.95 < 0.0001 < 0.0001 ρ 1 0.0005 23.93 0.0005 23.93 19.28 12.92 0.0002 0.0015 D 1 0.0005 137.65 0.0005 137.65 19.67 74.29 0.0002 < 0.0001 w 1 0.0003 0.0298 0.0003 0.0298 12.04 0.0161 0.002 0.9002 E 1 0.0006 3.9 0.0006 3.9 22.92 2.11 < 0.0001 0.1596 td 1 0.0129 1274.28 0.0129 1274.28 482.08 687.76 < 0.0001 < 0.0001 ρD 1 0.0001 2.32 0.0001 2.32 4.59 1.25 0.0425 0.2746 ρw 1 0.0001 0.2318 0.0001 0.2318 0.0493 0.1251 0.8262 0.7267 ρE 1 0.0002 0.1138 0.0002 0.1138 6.64 0.0614 0.0165 0.8063 ρtd 1 0.0018 22.62 0.0018 22.62 68.57 12.21 < 0.0001 0.0019 Dw 1 0.0008 36.29 0.0008 36.29 29.73 19.59 < 0.0001 0.0002 DE 1 0 4.28 0 4.28 0.705 2.31 0.4094 0.1417 Dtd 1 0.0001 10.63 0.0001 10.63 2.3 5.73 0.1428 0.0248 wE 1 0.0001 0.5928 0.0001 0.5928 5.28 0.32 0.0306 0.5769 wtd 1 0.0002 15.07 0.0002 15.07 6.94 8.13 0.0145 0.0088 Etd 1 0.0018 45.89 0.0018 45.89 65.41 24.77 < 0.0001 < 0.0001 ρ2 1 0.0027 18.85 0.0027 18.85 102.35 10.17 < 0.0001 0.0039 D2 1 0.0005 24.64 0.0005 24.64 18.2 13.3 0.0003 0.0013 w2 1 0.0024 5.3 0.0024 5.3 90.9 2.86 < 0.0001 0.1036 E2 1 0.0001 29.27 0.0001 29.27 0.0887 15.8 0.7684 0.0006 td2 1 0.0001 71.53 0.0001 71.53 2.45 38.61 0.1309 < 0.0001 残差 24 0.0006 44.47 0 1.85 失拟项 20 0.0006 41.01 0 2.05 3.73 2.38 0.1051 0.2084 纯误差 4 0 3.45 0.0001 0.8633 校正总平方和 44 0.0281 1784.4
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