基于Box-Behnken响应面的煤尘爆炸强度多因子耦合效应的实验研究

郭宏泽; 陈曦; 杨恒一

doi:10.11883/bzycj-2025-0045

基于Box-Behnken响应面的煤尘爆炸强度多因子耦合效应的实验研究

doi: 10.11883/bzycj-2025-0045

太原理工大学安全与应急管理工程学院，山西太原 030024

基金项目: 国家自然科学基金（52174195，51704145）

详细信息

作者简介:
郭宏泽（2000－　），男，硕士研究生，guohz777@163.com

通讯作者:
陈　曦（1987－　），男，副教授，chenxi01@tyut.edu.cn

中图分类号: O389
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- 文章访问数: 516
- HTML全文浏览量: 75
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- 被引次数: 0
出版历程
- 收稿日期: 2025-02-18
- 修回日期: 2025-06-06
- 网络出版日期: 2025-06-10

Experimental study of the multi-factor coupling effect of coal dust explosion intensity based on Box-Behnken response surface

College of Safety and Emergency Management and Engineering, Taiyuan University of Technology, Taiyuan 030024, China

摘要

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（t_d）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（p_max）及最大爆炸压力上升速率（$ {\dot{p}}_{\max } $）。使用Design-Expert软件分析实验结果，建立了响应量p_max和$ {\dot{p}}_{\max } $的二次回归模型。结果显示，在方差分析中，p_max和$ {\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 } $）影响最大的单因素是点火能量（E）和点火延迟（t_d），对最大爆炸压力上升速率（$ {\dot{p}}_{\max } $）影响最大的单因素是煤尘粒径（D）和点火延迟（t_d）。影响p_max的显著双因素交互作用是ρD、ρE、ρt_d、Dw、wE、wt_d和Et_d，而影响$ {\dot{p}}_{\max } $的显著双因素交互作用是ρt_d、Dw、Dt_d、wt_d和Et_d。其中，点火延迟（t_d）在响应量p_max和$ {\dot{p}}_{\max } $中起决定性作用。
- 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 (t_d). The explosion process was monitored by measuring pressure changes, and the maximum explosion pressure (response value p_max) 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 p_max 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 p_max and $ {\dot{p}}_{\max } $ is 0.9771 and 0.9258, respectively, indicating a good fit between the model and experimental data. The single factors with the greatest influence on the maximum explosion pressure (p_max) are ignition energy (E) and ignition delay(t_d), 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 p_max are ρD, ρE, ρt_d, Dw, wE, wt_d, and Et_d, wheras the significant two-factor interaction affecting $ {\dot{p}}_{\max } $ are ρt_d, Dw, Dt_d, wt_d, and Et_d. Among these, ignition delay (t_d) plays a decisive role in response values p_max and $ {\dot{p}}_{\max } $.
- Coal dust explosion /
- Explosion intensity /
- Box-Behnken experimental design /
- Response surface methodology

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图 1 实验装置

Figure 1. Experimental devic

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图 2 实验现场

Figure 2. Experimental site

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图 3 响应量残差正态概率图

Figure 3. Normal Probability Plot of Residuals for Response Variable

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图 4 响应量预测值-实际值图

Figure 4. Plot of Predicted Values vs. Actual Values for Response Variable

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图 5 响应量残差-实验编号图

Figure 5. Plot of residuals vs. experiment number for Response Variable

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图 6 响应量杠杆值-实验编号图

Figure 6. Plot of leverage vs. experiment number for Response Variable

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图 7 响应量p_max响应曲面图

Figure 7. Response value p_max response surface plot

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图 8 响应量$ {\dot{p}}_{\max } $响应曲面图

Figure 8. Response value $ {\dot{p}}_{\max } $ response surface plot

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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	t_d/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	t_d/ms	p_max/MPa	p_max/(MPa·s⁻¹)	p_max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
方差来源	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\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
来源	自由度	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\dot{p}}_{\max } $	p_max	$ {\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
t_d	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
ρt_d	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
Dt_d	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
wt_d	1	0.0002	15.07	0.0002	15.07	6.94	8.13	0.0145	0.0088
Et_d	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
t_d²	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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