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
计量
- 文章访问数: 584
- HTML全文浏览量: 122
- PDF下载量: 205
- 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
- 刊出日期: 2026-08-05

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, Shanxi 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 } $的决定系数R²分别为0.9771和0.9258，表明模型和实验数据拟合良好。在模型中，对煤尘最大爆炸压力（$ {{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

HTML全文

图 1 实验装置

Figure 1. Experimental device

下载: 全尺寸图片幻灯片

图 2 实验现场

Figure 2. Experimental site

下载: 全尺寸图片幻灯片

图 3 响应量残差正态概率图

Figure 3. Normal probability plot of residuals for response variable

下载: 全尺寸图片幻灯片

图 4 响应量预测值-实际值图

Figure 4. Plot of predicted values vs. actual values for response variable

下载: 全尺寸图片幻灯片

图 5 响应量残差-实验编号图

Figure 5. Plot of residuals vs. experiment number for response variable

下载: 全尺寸图片幻灯片

图 6 响应量杠杆值-实验编号图

Figure 6. Plot of leverage vs. experiment number for response variable

下载: 全尺寸图片幻灯片

图 7 响应量p_max响应曲面图

Figure 7. Response value p_max response surface plot

下载: 全尺寸图片幻灯片

图 8 响应量$ {\dot{p}}_{\max } $响应曲面图

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

下载: 全尺寸图片幻灯片

表 1 煤样各组分及元素质量分数

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

下载: 导出CSV

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

下载: 导出CSV

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	$\dot {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	25.7920	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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

参考文献(34)

[1]	DING J F, YAN X Q, CHEN L, et al. Effect of airflow velocity in vessel-pipelines on dust explosion during pneumatic conveying [J]. Powder Technology, 2024, 447: 120230. DOI: 10.1016/J.POWTEC.2024.120230.
[2]	赵峰宇, 高伟, 聂仲恒, 等. 含磷抑爆剂对煤尘爆炸抑制机理的原位分析 [J]. 清华大学学报(自然科学版), 2024, 64(6): 959–964. DOI: 10.16511/j.cnki.qhdxxb.2024.22.016. ZHAO F Y, GAO W, NIE Z H, et al. In-situ analysis of the inhibition mechanism of phosphorus-containing inhibitor on coal dust explosion [J]. Journal of Tsinghua University (Science and Technology), 2024, 64(6): 959–964. DOI: 10.16511/j.cnki.qhdxxb.2024.22.016.
[3]	高嘉慧, 陈曦, 范超男, 等. 离子液体对煤尘表面润湿性能影响的试验研究 [J]. 矿业安全与环保, 2023, 50(4): 7–12. DOI: 10.19835/j.issn.1008-4495.2023.04.002. GAO J H, CHEN X, FAN C N, et al. Experimental study on the effect of ionic liquid on surface wettability of coal dust [J]. Mining Safety & Environmental Protection, 2023, 50(4): 7–12. DOI: 10.19835/j.issn.1008-4495.2023.04.002.
[4]	CHEN X, BAI X, FAN C N, et al. Experimental investigation of atomization characteristics of sonic blasting nozzle based on De-Laval dynamics [J]. Energy, 2024, 297: 131188. DOI: 10.1016/j.energy.2024.131188.
[5]	张延松, 徐畅, 秦江, 等. 纳米复合抑爆粉体抑制甲烷煤尘混合爆炸动力学机理研究 [J]. 安全与环境学报, 2024, 24(11): 4296–4305. DOI: 10.13637/j.issn.1009-6094.2024.0731. ZHANG Y S, XU C, QIN J, et al. Study on the dynamic mechanism of nanocomposite explosion suppression powder in mitigating the combined explosion of methane and coal dust [J]. Journal of Safety and Environment, 2024, 24(11): 4296–4305. DOI: 10.13637/j.issn.1009-6094.2024.0731.
[6]	国家矿山安全监察局事故调查和统计司. 山东能源集团肥城矿业公司梁宝寺煤矿“8·20”较大煤尘爆炸事故案例 [EB/OL]. (2021-07-27)[2021-07-27]. https://www.chinamine-safety.gov.cn/zfxxgk/fdzdgknr/sgcc/sgalks/202107/t20210727_393063.shtml.
[7]	国务院安委会办公室. 国务院安委会办公室关于陕西省榆林市神木市百吉矿业有限责任公司李家沟煤矿“1·12”重大煤尘爆炸等四起煤矿事故的通报 [EB/OL]. (2019-01-29)[2020-12-06]. https://www.gov.cn/zhengce/zhengceku/2019-10/31/content_5447171.htm.
[8]	国家矿山安全监察局事故调查和统计司. 黑龙江龙煤集团双鸭山矿业公司双阳煤矿“11·28”重大瓦斯爆炸事故案例 [EB/OL]. (2025-01-16)[2025-01-16]. http://nmg.chinamine-safety.gov.cn/Item/13386.aspx.
[9]	江丙友, 洪汉, 苏明清, 等. 密闭管道内瓦斯爆炸卷扬沉积煤尘爆炸传播特性 [J]. 煤炭学报, 2024, 49(4): 1941–1951. DOI: 10.13225/j.cnki.jccs.2023.1095. JIANG B Y, HONG H, SU M Q, et al. Characterization of explosion propagation of coal dust deposited by gas explosion convolutions in closed pipelines [J]. Journal of China Coal Society, 2024, 49(4): 1941–1951. DOI: 10.13225/j.cnki.jccs.2023.1095.
[10]	张江石, 孙龙浩. 分散度对煤粉爆炸特性的影响 [J]. 煤炭学报, 2019, 44(4): 1154–1160. DOI: 10.13225/j.cnki.jccs.2018.1499. ZHANG J S, SUN L H. Effect of dispersity on explosion characteristics of coal dust [J]. Journal of China Coal Society, 2019, 44(4): 1154–1160. DOI: 10.13225/j.cnki.jccs.2018.1499.
[11]	刘天奇, 李雨成, 罗红波. 不同变质程度煤尘爆炸压力特性变化规律实验研究 [J]. 爆炸与冲击, 2019, 39(9): 095403. DOI: 10.11883/bzycj-2018-0265. LIU T Q, LI Y C, LUO H B. Experimental study on explosion pressure variation law of coal dust with different degrees of metamorphism [J]. Explosion and Shock Waves, 2019, 39(9): 095403. DOI: 10.11883/bzycj-2018-0265.
[12]	刘天奇. 不同煤质煤尘云与煤尘层最低着火温度实验研究 [J]. 燃烧科学与技术, 2019, 25(5): 445–450. DOI: 10.11715/rskxjs.R201807010. LIU T Q. Experimental study on minimum ignition temperature of coal dust cloud and coal dust layer of different metamorphism [J]. Journal of Combustion Science and Technology, 2019, 25(5): 445–450. DOI: 10.11715/rskxjs.R201807010.
[13]	ZHOU Y, LI G, JIN L J, et al. In situ analysis of catalytic effect of calcium nitrate on Shenmu coal pyrolysis with pyrolysis vacuum ultraviolet photoionization mass spectrometry [J]. Energy & Fuels, 2018, 32(2): 1061–1069. DOI: 10.1021/acs.energyfuels.7b02385.
[14]	TAN B, SHAO Z Z, XU B, et al. Analysis of explosion pressure and residual gas characteristics of micro-nano coal dust in confined space [J]. Journal of Loss Prevention in the Process Industries, 2020, 64: 104056. DOI: 10.1016/j.jlp.2020.104056.
[15]	LIU S S, XU J D, GONG J H, et al. Experimental study of methane explosion containing coal dust in flame instability and pressure variation process [J]. Process Safety and Environmental Protection, 2023, 178: 675–684. DOI: 10.1016/J.PSEP.2023.08.072.
[16]	LIU L, MAO X Y, JING Y H, et al. Study on the explosion mechanism of low-concentration gas and coal dust [J]. Fire, 2024, 7(12): 475. DOI: 10.3390/fire7120475.
[17]	YU M G, LI S S, ZHAI F E, et al. Effects of volatile contents on the deflagration characteristics and soot formation of methane/coal volatiles hybrid explosion using reaction kinetics simulation [J]. Fuel, 2022, 319: 123767. DOI: 10.1016/j.fuel.2022.123767.
[18]	WANG J C, LI H T, DIAO S T, et al. Reactive behaviors and mechanism of methane/coal dust hybrid explosions inhibited by NH₄H₂PO₄ and (NH₄)₂HPO₄: a combined ReaxFF-MD and DFT study [J]. Chemical Engineering Journal, 2024, 498: 155577. DOI: 10.1016/j.cej.2024.155577.
[19]	LI Z B, ZHAO W C, LI C, et al. The characteristics and mechanism of core-shell structure fly ash/KH₂PO₄ composite inhibitor in suppressing coal dust explosions [J]. Journal of Loss Prevention in the Process Industries, 2025, 94: 105533. DOI: 10.1016/j.jlp.2024.105533.
[20]	KHURI A I, MUKHOPADHYAY S. Response surface methodology [J]. WIREs Computational Statistics, 2010, 2(2): 128–149. DOI: 10.1002/wics.73.
[21]	FERREIRA S L C, BRUNS R E, FERREIRA H S, et al. Box-Behnken design: an alternative for the optimization of analytical methods [J]. Analytica Chimica Acta, 2007, 597(2): 179–186. DOI: 10.1016/j.aca.2007.07.011.
[22]	陈春燕, 龙思华, 肖国清, 等. 基于响应面方法的甘薯粉尘爆炸研究 [J]. 中国安全科学学报, 2017, 27(1): 42–47. DOI: 10.16265/j.cnki.issn1003-3033.2017.01.008. CHEN C Y, LONG S H, XIAO G Q, et al. Sweet potato dust explosion study based on response surface methodology [J]. China Safety Science Journal, 2017, 27(1): 42–47. DOI: 10.16265/j.cnki.issn1003-3033.2017.01.008.
[23]	JIANG J H, XIA C Y, YAO J, et al. Vulnerability analysis of HSR bridge under near-field blast based on response surface method [J]. Structures, 2023, 55: 983–994. DOI: 10.1016/j.istruc.2023.06.053.
[24]	赵振保, 阎杰, 谢军, 等. 煤尘抑尘剂优化设计的试验研究 [J]. 北京理工大学学报, 2022, 42(11): 1213–1218. DOI: 10.15918/j.tbit1001-0645.2022.075. ZHAO Z B, YAN J, XIE J, et al. Experiment and optimization method for coal dust restrain reagent [J]. Transactions of Beijing Institute of Technology, 2022, 42(11): 1213–1218. DOI: 10.15918/j.tbit1001-0645.2022.075.
[25]	梁文俊, 任思达, 马贺, 等. 环境友好型煤尘抑制剂的制备 [J]. 环境工程学报, 2017, 11(9): 5091–5096. DOI: 10.12030/j.cjee.201609118. LIANG W J, REN S D, MA H, et al. Preparation of environment-friendly coal dust inhibitor [J]. Chinese Journal of Environmental Engineering, 2017, 11(9): 5091–5096. DOI: 10.12030/j.cjee.201609118.
[26]	REN S S, JING D J, GE S C, et al. Investigate the optimum design of atomizing nozzles for coal dust suppression by using multifactor level response surface methodology [J]. Process Safety and Environmental Protection, 2024, 190: 245–261. DOI: 10.1016/j.psep.2024.07.010.
[27]	聂百胜, 张豪, 宫婕, 等. 煤粉爆炸宏细观四阶段反应机理 [J]. 中国矿业大学学报, 2023, 52(6): 1129–1145. DOI: 10.13247/j.cnki.jcumt.20230376. NIE B S, ZHANG H, GONG J, et al. Macro and micro four-stage reaction mechanism of pulverized coal explosion [J]. Journal of China University of Mining & Technology, 2023, 52(6): 1129–1145. DOI: 10.13247/j.cnki.jcumt.20230376.
[28]	王相. 复合粉体抑爆剂对煤尘爆炸的抑制特性及机理研究 [D]. 青岛: 山东科技大学, 2019: 25–31. DOI: 10.27275/d.cnki.gsdku.2019.000015. WANG X. Research on the explosion suppression characteristics and mechanism of composite powder explosion suppressant for coal dust explosion [D]. Qingdao: Shandong University of Science and Technology, 2019: 25–31. DOI: 10.27275/d.cnki.gsdku.2019.000015.
[29]	BAITHALU R, MISHRA S R, PATTNAIK P K, et al. Optimizing shear and couple stress analysis for the magneto-micropolar dissipative nanofluid flow toward an elongating surface: a comprehensive RSM-ANOVA investigation [J]. Journal of Thermal Analysis and Calorimetry, 2024, 149(4): 1697–1713. DOI: 10.1007/S10973-023-12741-w.
[30]	EL-MAS S M, HASSAAN M A, EL-SUBRUITI G M, et al. Box-Behnken design optimization of 2D Ti₃C₂T_x MXene nanosheets as a microwave-absorbing catalyst for methylene blue dye degradation [J]. Chemical Engineering Journal, 2024, 500: 156969. DOI: 10.1016/j.cej.2024.156969.
[31]	CHAURASIA S, DUTTA H, SINGH S, et al. Electrical discharge machining of super alloy incoloy 925: a study based on box Behnken design and response surface methodology [J]. Physica Scripta, 2024, 99(10): 105055. DOI: 10.1088/1402-4896/AD7B25.
[32]	贺杰, 程凯, 张金. 氧化煤尘的爆炸特性及其变化规律 [J]. 煤矿安全, 2023, 54(3): 67–72. DOI: 10.13347/j.cnki.mkaq.2023.03.012. HE J, CHENG K, ZHANG J. Explosion characteristics and variation of oxidized coal dust [J]. Safety in Coal Mines, 2023, 54(3): 67–72. DOI: 10.13347/j.cnki.mkaq.2023.03.012.
[33]	WANG S Y, SHI Z C, PENG X, et al. Effect of the ignition delay time on explosion severity parameters of coal dust/air mixtures [J]. Powder Technology, 2019, 342: 509–516. DOI: 10.1016/j.powtec.2018.10.020.
[34]	郑默, 李晓霞. ReaxFF MD模拟揭示的煤热解挥发分自由基反应的竞争与协调 [J]. 化工学报, 2022, 73(6): 2732–2741. DOI: 10.11949/0438-1157.20220110. ZHENG M, LI X X. Revealing reaction compromise in competition for volatile radicals during coal pryolysis via ReaxFF MD simulation [J]. CIESC Journal, 2022, 73(6): 2732–2741. DOI: 10.11949/0438-1157.20220110.