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Article(id=1148106724181012897, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1148106708670477182, articleNumber=1003-3033(2025)03-0107-08, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2025.03.0400, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1729008000000, receivedDateStr=2024-10-16, revisedDate=1734710400000, revisedDateStr=2024-12-21, acceptedDate=null, acceptedDateStr=null, onlineDate=1751659573836, onlineDateStr=2025-07-05, pubDate=1743091200000, pubDateStr=2025-03-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1751659573836, onlineIssueDateStr=2025-07-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1751659573836, creator=13701087609, updateTime=1751659573836, updator=13701087609, issue=Issue{id=1148106708670477182, tenantId=1146029695717560320, journalId=1146031787341344770, year='2025', volume='35', issue='3', pageStart='1', pageEnd='268', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1751659570138, creator=13701087609, updateTime=1757401518130, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1172190184155238915, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1148106708670477182, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1172190184155238916, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1148106708670477182, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=107, endPage=114, ext={EN=ArticleExt(id=1149767349588377952, articleId=1148106724181012897, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Research on explosion process of fire extinguishing bombs and scattering characteristics of fire extinguishing agents, columnId=1149733269173878863, journalTitle=China Safety Science Journal, columnName=Safety engineering technology, runingTitle=null, highlight=null, articleAbstract=

In order to further study the detonating effect of UAV，and improve the fire extinguishing efficiency of fire bombs，ANSYS Workbench software was used to establish a finite element model of fire bombs，and the explosion and dispersion process of fire extinguishing agent was simulated to clarify the impact of different detonation heights on the dispersion characteristics of fire extinguishing agent. Meanwhile，full-scale experiments on the vertical dropping of fire extinguishing bombs by unmanned aerial vehicles at different detonation heights were conducted. The results show that the simulation data such as the explosion process of fire extinguishing bomb，the throwing process of fire extinguishing agent and the spreading radius of fire extinguishing agent are in good agreement with the full-scale test results. After the fire extinguishing bomb explodes，the extinguishing agent disperses in the air in a cone shape and spread evenly in the horizontal direction，and the spreading shape is roughly circular. With the increase of detonation height，the landing time of fire extinguishing agent increases，and the horizontal velocity of fire extinguishing agent decreases. The increase of landing time plays a dominant role relative to the decrease of horizontal velocity，resulting in the increase of the spreading radius of fire extinguishing agent with the increase of detonation height. When the detonation height of the fire extinguishing bomb increases from 5 to 12 m，the numerical simulation data of the fire extinguishing agent spread radius increases from 2.04 to 3.56 m，and the error between the numerical simulation data and the experimental data is within 5%.

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为深入研究无人机(UAV)竖直投放灭火弹的引爆效果，提升灭火弹灭火效率，利用ANSYS Workbench软件建立灭火弹有限元模型，模拟灭火剂的爆炸抛洒过程，明确不同引爆高度对灭火剂抛洒特性的影响；同时开展不同引爆高度下UAV竖直投放灭火弹的全尺寸试验。结果表明：灭火弹爆炸过程、灭火剂抛洒过程与灭火剂铺展半径等仿真数据与全尺寸试验结果吻合度良好。灭火弹爆炸后，灭火剂在空中呈锥形弥散，在水平方向上铺展均匀，铺展形状大致为圆形;随着引爆高度增加，灭火剂落地时间延长，灭火剂水平速度减小，落地时间的延长相对于水平速度的降低起到主导作用，导致灭火剂铺展半径随引爆高度增加而增加。当灭火弹引爆高度从5 m增加至12 m时，灭火剂铺展半径数值模拟计算数据由2.04 m增大至3.56 m，数值模拟计算数据与试验数据的误差均在5%以内。

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李 聪 (1991—)，男，安徽淮南人，博士，副教授，主要从事高高原火灾、火灾图像识别方面的研究。E-mail：。

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2 中国民航大学 民航热灾害防控与应急重点实验室，天津 300300, bio={"img":"Tu0vDB+RSMnPLEpJs195pA==","content":"

李 聪 (1991—)，男，安徽淮南人，博士，副教授，主要从事高高原火灾、火灾图像识别方面的研究。E-mail：。

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李 聪 (1991—)，男，安徽淮南人，博士，副教授，主要从事高高原火灾、火灾图像识别方面的研究。E-mail：。

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figureFileSmall=XqlMpYfYr8URIFR0XmI6mA==, figureFileBig=zCv2syATKV1d4f+zAgiHZg==, tableContent=null), ArticleFig(id=1165678373591327187, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=EN, label=Table 1, caption=

Model parameters at different detonation heights

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工况序号 灭火弹引爆高度/m 垂直初速度/(m·s-1)
1 12 21.23
2 10 22.14
3 8 23.00
4 6 23.84
5 5 24.25
), ArticleFig(id=1165678373641658836, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=CN, label=表1, caption=

不同引爆高度下的模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
工况序号 灭火弹引爆高度/m 垂直初速度/(m·s-1)
1 12 21.23
2 10 22.14
3 8 23.00
4 6 23.84
5 5 24.25
), ArticleFig(id=1165678373700379093, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=EN, label=Table 2, caption=

TNT material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/(kg·m-3) 爆速/(m·s-1) 爆压/Pa A/Pa
1 630 6 930 2.1×1010 3.738×1011
B/Pa R1 R2 w
3.747×109 4.15 0.9 0.35
), ArticleFig(id=1165678373763293654, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=CN, label=表2, caption=

TNT材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/(kg·m-3) 爆速/(m·s-1) 爆压/Pa A/Pa
1 630 6 930 2.1×1010 3.738×1011
B/Pa R1 R2 w
3.747×109 4.15 0.9 0.35
), ArticleFig(id=1165678373809430999, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=EN, label=Table 3, caption=

Material parameters of water-based fire extinguishing agent

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ρ0/(kg·m-3) v/(m·s-1) γ0 S1
1 000 1 480 0.49 2.56
S2 S3 a —
-1.986 0.228 6 1.397 —
), ArticleFig(id=1165678373889122776, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=CN, label=表3, caption=

水基灭火剂参数

, figureFileSmall=null, figureFileBig=null, tableContent=
ρ0/(kg·m-3) v/(m·s-1) γ0 S1
1 000 1 480 0.49 2.56
S2 S3 a —
-1.986 0.228 6 1.397 —
), ArticleFig(id=1165678373956231641, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=EN, label=Table 4, caption=

PVC material parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/(kg·m-3) 热膨胀系数/ ℃-1 杨氏模量/Pa
1 392 1.273×10-4 2.861×109
泊松比 拉伸屈服强度/Pa 拉伸极限强度/Pa
0.4 4.671×107 4.671×107
), ArticleFig(id=1165678374019146202, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=CN, label=表4, caption=

PVC材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/(kg·m-3) 热膨胀系数/ ℃-1 杨氏模量/Pa
1 392 1.273×10-4 2.861×109
泊松比 拉伸屈服强度/Pa 拉伸极限强度/Pa
0.4 4.671×107 4.671×107
), ArticleFig(id=1165678374094643675, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=EN, label=Table 5, caption=

Fire extinguishing agent spreading radius

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引爆高度/m 试验数据/m 数值模拟计算数据/m
5.00 2.28 2.04
6.00 2.36 2.33
8.00 2.46 2.57
10.00 2.82 3.11
12.00 3.70 3.56
), ArticleFig(id=1165678374149169628, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1148106724181012897, language=CN, label=表5, caption=

灭火剂铺展半径

, figureFileSmall=null, figureFileBig=null, tableContent=
引爆高度/m 试验数据/m 数值模拟计算数据/m
5.00 2.28 2.04
6.00 2.36 2.33
8.00 2.46 2.57
10.00 2.82 3.11
12.00 3.70 3.56
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灭火弹爆炸过程及灭火剂抛洒特性研究
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李聪 1, 2 , 何泽群 1 , 杨高豪 1 , 许文博 1 , 王悦朋 3
中国安全科学学报 | 安全工程技术 2025,35(3): 107-114
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中国安全科学学报 | 安全工程技术 2025, 35(3): 107-114
灭火弹爆炸过程及灭火剂抛洒特性研究
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李聪1, 2 , 何泽群1, 杨高豪1, 许文博1, 王悦朋3
作者信息
  • 1 中国矿业大学(北京) 应急管理与安全工程学院，北京 100083
  • 2 中国民航大学 民航热灾害防控与应急重点实验室，天津 300300
  • 3 山东龙翼航空科技有限公司，山东 济宁 272106

    • 李 聪 (1991—)，男，安徽淮南人，博士，副教授，主要从事高高原火灾、火灾图像识别方面的研究。E-mail：。

Research on explosion process of fire extinguishing bombs and scattering characteristics of fire extinguishing agents
Cong LI1, 2 , Zequn HE1, Gaohao YANG1, Wenbo XU1, Yuepeng WANG3
Affiliations
  • 1 School of Emergency Management and Safety Engineering，China University of Mining and Technology-Beijing，Beijing 100083，China
  • 2 Key Laboratory of Civil Aviation Thermal Hazards Prevention and Emergency Response，Civil Aviation University of China，Tianjin 300300，China
  • 3 Shandong Longyi Aviation Technology Co.，Ltd.，Jining Shandong 272106，China
出版时间: 2025-03-28 doi: 10.16265/j.cnki.issn1003-3033.2025.03.0400
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摘要
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为深入研究无人机(UAV)竖直投放灭火弹的引爆效果，提升灭火弹灭火效率，利用ANSYS Workbench软件建立灭火弹有限元模型，模拟灭火剂的爆炸抛洒过程，明确不同引爆高度对灭火剂抛洒特性的影响；同时开展不同引爆高度下UAV竖直投放灭火弹的全尺寸试验。结果表明：灭火弹爆炸过程、灭火剂抛洒过程与灭火剂铺展半径等仿真数据与全尺寸试验结果吻合度良好。灭火弹爆炸后，灭火剂在空中呈锥形弥散，在水平方向上铺展均匀，铺展形状大致为圆形;随着引爆高度增加，灭火剂落地时间延长，灭火剂水平速度减小，落地时间的延长相对于水平速度的降低起到主导作用，导致灭火剂铺展半径随引爆高度增加而增加。当灭火弹引爆高度从5 m增加至12 m时，灭火剂铺展半径数值模拟计算数据由2.04 m增大至3.56 m，数值模拟计算数据与试验数据的误差均在5%以内。

灭火弹  /  爆炸过程  /  灭火剂  /  抛洒特性  /  无人机(UAV)  /  数值模拟  /  铺展半径

In order to further study the detonating effect of UAV，and improve the fire extinguishing efficiency of fire bombs，ANSYS Workbench software was used to establish a finite element model of fire bombs，and the explosion and dispersion process of fire extinguishing agent was simulated to clarify the impact of different detonation heights on the dispersion characteristics of fire extinguishing agent. Meanwhile，full-scale experiments on the vertical dropping of fire extinguishing bombs by unmanned aerial vehicles at different detonation heights were conducted. The results show that the simulation data such as the explosion process of fire extinguishing bomb，the throwing process of fire extinguishing agent and the spreading radius of fire extinguishing agent are in good agreement with the full-scale test results. After the fire extinguishing bomb explodes，the extinguishing agent disperses in the air in a cone shape and spread evenly in the horizontal direction，and the spreading shape is roughly circular. With the increase of detonation height，the landing time of fire extinguishing agent increases，and the horizontal velocity of fire extinguishing agent decreases. The increase of landing time plays a dominant role relative to the decrease of horizontal velocity，resulting in the increase of the spreading radius of fire extinguishing agent with the increase of detonation height. When the detonation height of the fire extinguishing bomb increases from 5 to 12 m，the numerical simulation data of the fire extinguishing agent spread radius increases from 2.04 to 3.56 m，and the error between the numerical simulation data and the experimental data is within 5%.

fire extinguishing bomb  /  explosion process  /  fire extinguishing agent  /  scattering characteristics  /  unmanned air vehicle (UAV)  /  numerical simulation  /  spreading radius
李聪, 何泽群, 杨高豪, 许文博, 王悦朋. 灭火弹爆炸过程及灭火剂抛洒特性研究. 中国安全科学学报, 2025 , 35 (3) : 107 -114 . DOI: 10.16265/j.cnki.issn1003-3033.2025.03.0400
Cong LI, Zequn HE, Gaohao YANG, Wenbo XU, Yuepeng WANG. Research on explosion process of fire extinguishing bombs and scattering characteristics of fire extinguishing agents[J]. China Safety Science Journal, 2025 , 35 (3) : 107 -114 . DOI: 10.16265/j.cnki.issn1003-3033.2025.03.0400
正文
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0 引言
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近年来，无人机(Unmanned Air Vehicle，UAV)技术被广泛应用于应急救援、电力巡检、物流配送等领域[1-2]。因UAV具备机动灵活、受地形限制小、安全效能高等优点，针对森林和草原火灾等复杂场景，其搭载灭火弹的灭火方式逐渐被应用于这些场景的火灾扑救工作中[3]。因此，研究不同引爆高度下灭火剂抛洒特性对复杂场景的火灾防控和应急救援具有重要意义。
许多学者开展了关于灭火弹的理论和试验研究。李云峰等[4-5]利用Fluent软件探究爆破瞬间灭火弹内流场的分布特征，发现发生器排气孔的对称结构有利于形成均匀的压力场。朱聪等[6-7]使用LS-DYNA模拟UAV搭载森林灭火弹灭火的过程，研究装药结构对灭火弹灭火剂抛洒的影响及抛洒特性。杨丽等[8]仿真研究了超细粉体灭火弹爆炸后的抛洒特性，提出了评估其灭火效能的方法。何亚丽等[9]采用硝酸钾粉末、镁粉和铝粉等烟火药，混合制成灭火弹的中心抛洒药，优化了中心抛洒药的配方。康会峰等[10]设计了分瓣式气动弹射灭火弹结构，该结构有利于扩大灭火剂的布散范围，提升灭火弹的飞行稳定性。郑学昭等[11]设计了UAV搭载灭火弹系统，该系统可利用UAV飞行动力消除发射灭火弹时产生的后坐力，提升了灭火弹的发射精度。
以上研究主要集中在灭火弹的结构、材料和投掷系统方面，而灭火弹在不同引爆高度条件下爆炸对灭火剂抛洒特性的影响研究较少。为此，笔者将模拟UAV垂直投放灭火弹后的爆炸过程，开展UAV投弹的全尺寸试验，探究不同引爆高度对灭火弹爆炸过程、灭火剂抛洒速度和灭火剂铺展半径等抛洒特性的影响，为优化灭火弹应用流程提供数据支持与理论依据。
1 灭火弹爆炸数值模拟和试验设计
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1.1 灭火弹爆炸数值模拟设置
灭火弹主要由水基灭火剂、三硝基甲苯(Trinitrotoluene，TNT)引爆药和聚氯乙烯(Polyvinyl Chloride，PVC)壳体组成。
为提升运算效率，将灭火弹模型简化为圆柱体，并建立其1/4模型[12]。将灭火弹模型置于0.8 m×0.8 m×1.3 m的立方体空气域中，如图1所示。简化后的灭火弹高0.4 m、半径0.1325 m、外壳厚0.003 m;灭火弹内部由发泡胶、引爆药和灭火剂3部分构成。在ANSYS Workbench[13]中划分模型网格，网格单元总数约为13万。灭火弹投放高度为35 m，表1给出了不同引爆高度下的模型参数。
TNT炸药质量为1.25g，高能炸药模型的爆炸产物状态方程[14]为：
P   =   A ( 1 - w / R 1 V ) e x p ( - R 1 V )   + B ( 1 - w / R 2 V ) e x p ( - R 2 V )   +   w E 0 / V
式中：P为压力，Pa；A、B分别为控制高压段和中压段压力变化的拟合参数，Pa；R1为高压阶段压力随体积变化的敏感度常数；R2为调节中压阶段的动态响应常数;w为能量在不同阶段的分配常数；V为爆炸产物的体积与爆炸前的初始体积之比；E0为初始能量密度，J/m3。TNT的状态参数[15]取值见表2。
水基灭火剂的状态方程为[16]：
P = ρ 0 v 2 μ 1 + 1 - γ 0 2 μ - a μ 2 2 1 - ( S 1 - 1 ) μ - S 2 μ 2 μ + 1 - S 3 μ 3 ( μ + 1 ) 2 2 + ( γ 0 + a μ ) e
式中：ρ0为水基灭火剂的初始密度，kg/m3；v为水基灭火剂的冲击速度，m/s；μ为黏度系数；μ=ρ/ρ0-1，其中，ρ为水基灭火剂在当前时间步的密度，kg/m3；γ0为状态方程系数；a为γ0的修正系数；e为初始单位体积内的内能，J/m3；S1、S2、S3分别为影响线性、二次和三次关系的拟合系数。表3给出了水基灭火剂的参数取值；表4给出了PVC外壳的材料参数。
1.2 UAV投弹试验设置
UAV投放灭火弹的全尺寸试验设置如图2所示。试验主要设备包括大载荷UAV、灭火弹、高清摄像机等。试验的主要控制参数与表1保持一致，UAV距离地面的飞行高度(即灭火弹投放高度)设置为35 m，通过在灭火弹上设置激光测距仪，可以精确跟踪灭火弹在下落过程中距离地面的距离，进而精准控制灭火弹在5 ~12 m的范围内爆炸。在试验过程中，当试验场地处于无风环境时，控制UAV至试验场地的正上方，稳定在投放高度35 m后投放灭火弹，并按照表1中的不同引爆高度处使灭火弹爆炸。利用在地面上布置的摄像机与UAV机载摄像机拍摄灭火弹爆炸及灭火剂抛洒过程。待到灭火剂弥散结束落地后，测量记录灭火剂铺展半径并使用UAV载摄像头从俯视视角拍摄灭火剂在地面的铺展情况。为便于观察灭火剂的抛洒特性，水基灭火剂中添加了红色染料。
2 灭火剂抛洒特性分析
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2.1 灭火弹爆炸过程
图3展示了灭火弹投放高度为35 m，不同引爆高度下，灭火剂抛洒特性动态演化过程。可以看出：在爆炸发生2 ms内，引爆药爆炸产生的气体(简称爆炸气体)推动灭火剂形成液体环，此时计算空间中流场主要由3层流体组成，分别为内部爆炸气体、灭火剂组成的连续液体环和外部空气；2 ms时爆炸气体对弹壳的冲击力超过PVC屈服极限，由于引爆药位于灭火弹中心轴线距离灭火弹底部0.15 m处，灭火弹中部在爆炸过程中承受了最大的冲击力和压力，弹壳开始从弹体中部开始碎裂。在2 ms后弹壳进一步碎裂，液体环在爆炸气体作用下沿径向膨胀，液体环逐渐变薄，在8 ms时由于液体环内外界面压力的不稳定增长，外部扰动施加在液体环上的力大于其自身的黏聚力，灭火剂从原本连续的液态开始破碎为离散的液滴并与空气形成混合性云雾，由于灭火弹中部承受了最大的冲击力和压力，中部灭火剂在爆炸后获得了更大的动量，从而更易克服液体间黏聚力，这一现象在中部灭火剂最先得以显现。通过对比分析不同引爆高度下灭火弹的爆炸过程，可以观察到10 ms时，随着引爆高度的逐渐降低，中部灭火剂的离散程度呈现出明显的增强趋势。这一现象的产生是由于在较低的引爆高度下，爆炸时灭火剂具有更大的速度，其使得灭火剂形成的连续液体环变得更为不稳定，从而在爆炸过程中更容易破碎成离散的液滴。
图4给出了灭火弹引爆高度为5 m时，UAV竖直投放灭火弹试验现场拍摄的灭火剂爆炸抛洒过程。可以看出，灭火弹在引爆高度爆炸后，灭火弹弹壳瞬间破碎，爆炸后0.04 s时水基灭火剂向四周抛洒，灭火剂在爆炸后主要受到爆炸气体的推力、重力、空气阻力的作用，0.28 s时其在空中呈锥形弥散，1.20 s时灭火剂落地结束弥散。
图5是灭火弹引爆高度5 m工况下，试验现场UAV机载摄像设备在35 m高空拍摄的灭火剂铺展范围俯视图。可以观察到，爆炸后灭火剂铺展范围大致呈圆形，灭火剂在水平方向上铺展均匀；同时，灭火剂在铺展范围内分布均匀，爆炸后绝大部分灭火剂会直接落地铺展，少部分灭火剂在空中弥散。
2.2 灭火剂抛洒速度
图6为灭火弹在引爆高度10和5 m处，离散液滴在水平方向上达到稳定阶段时，在距离灭火弹底部0.05、0.15和0.25 m处3个参照点的模拟水平速度。可以看出，10 和5 m引爆高度处，中部参照点的速度都明显高于上部参照点与下部参照点，这是由于引爆药位于灭火弹中心轴线，距离灭火弹底部0.15 m处，灭火弹中部在爆炸过程中承受了最大的冲击力和压力，这导致中部灭火剂在爆炸后获得了更大的动量，因此，灭火剂爆炸后的铺展半径主要由灭火弹中部灭火剂的位移距离决定；文中选择中部参照点跟踪分析。
提取仿真模型中部参照点在水平方向与竖直方向上的速度，参照点速度变化如图7所示。可以看出，在水平方向上，参照点的运动过程大致可分为加速阶段、减速阶段、平稳阶段。爆炸后，爆炸气体膨胀推动灭火剂沿径向加速运动，爆炸后2.5 ms作用在灭火剂上的爆炸作用力与气动阻力达到平衡，参照点结束加速阶段，速度达到最大。在爆炸气体完成对灭火剂的加速作用后，灭火剂组成的连续液体环外部气动阻力大于内部所受爆炸作用力，参照点进入减速阶段，2.5 ~9 ms内参照点速度迅速下降，直至参照点在9 ms时破碎为离散的液滴，其速度下降速率稍有放缓，9 ms后参照点速度逐渐稳定，进入平稳阶段。在UAV灭火弹投放过程中，引爆高度的变化对灭火弹爆炸及灭火剂抛洒特性具有显著影响。随着引爆高度的降低，灭火弹爆炸时引爆药的初始能量增大，爆炸后传递给灭火剂的能量也增大，因此，当引爆高度降低、达到平稳阶段后，参照点的水平速度逐渐增加。与水平速度不同，由于灭火剂在垂直方向上的速度不仅受到爆炸气体的作用影响，还受到自身初始速度影响，爆炸气体未与灭火剂未完全分离时，其变化趋势较为复杂。在9 ms内，此时参照点还未破碎为离散的液滴，参照点垂向速度变化较为剧烈，当爆炸气体与灭火剂分离后，参照点垂向速度逐渐稳定。随着引爆高度的降低，爆炸气体压力也增大，稳定后的灭火剂垂向速度也逐渐增大，灭火弹引爆高度与参照点垂向速度呈负相关性。
2.3 灭火剂铺展半径
灭火弹爆炸后灭火剂在初速度确定的竖直平面内运动过程中仅受到空气阻力与重力作用。空气阻力的大小与速度的平方成正比，方向与速度方向相反：
f = - k v r 2
式中：f为参照点受到的空气阻力，N；k为空气阻力系数；vr为参照点速度，m/s。
在中部参照点运动平面内以参照点为原点，水平方向为x轴，竖直方向为y轴建立坐标系，令r=(x y)T为参照点的位矢，根据牛顿第二定律，有：
f + m g = m r
式中：m为参照点质量，kg；g为重力加速度，m/s2；r为参照点的加速度矢量。由于空气阻力方向与速度方向相反，则：
f = - k v 2 r ' = - k v x v x 2 + v y 2 v y v x 2 + v y 2 T
r ' = v x / v x 2 + v y 2 v y / v x 2 + v y 2 T
式中：vx为速度在x轴方向上的分量，m/s；vy为速度在y轴方向上的分量，m/s；r'为参照点速度方向的单位矢量。
式(4)可改写为：
m d v x d t = - k v x v x 2 + v y 2 m d v y d t = - k v y v x 2 + v y 2 - m g
提取爆炸后20 ms参照点水平速度与竖直速度，计算其速度方向与水平方向的夹角，以此为初始值代入该非线性方程组，使用Python求解该非线性方程，得到速度随时间变化的情况。在每个时间步上对速度积分，得到灭火剂的铺展半径。数值模拟计算与试验结果数据对比见表5。
灭火剂铺展半径与引爆高度呈正相关性，例如：当灭火弹引爆高度从5 m增加至12 m时，灭火剂铺展半径数值模拟计算数据由2.04 m增大至3.56 m。灭火剂的铺展半径主要受到落地时间和水平速度的共同影响。一方面引爆高度的增加会导致灭火剂的落地时间增加，灭火剂在空中抛洒的时间增加，从而增大铺展半径。另一方面由于灭火剂水平运动速度随引爆高度的增加而略有降低，从8.89 m/s降至6.99 m/s，从而减小铺展半径。随着引爆高度的增加，灭火剂落地时间的增大起到了主导作用，导致灭火剂铺展半径随引爆高度增加而增加。试验数据与数值模拟计算数据的误差均在5%以内，处于误差允许的范围，证明了数值模拟的准确性。
3 结论
收起
1) 灭火弹爆炸后，灭火剂在空中呈锥形弥散，在水平方向上铺展均匀，铺展形状大致为圆形。灭火弹中部受爆炸气体的影响更为显著，中部灭火剂获得更大动量。
2) 灭火剂的铺展半径主要受到落地时间和水平速度的共同影响，随着引爆高度的增加，灭火剂落地时间延长相对于水平速度降低起到主导作用，导致灭火剂铺展半径随引爆高度的增加而增加。
3) 灭火剂铺展半径与引爆高度呈正相关性，灭火弹引爆高度从5m增加至12 m，灭火剂铺展半径数值模拟计算数据由2.04m增大至3.56 m；数值模拟计算数据与试验数据的误差均在5%以内。
基金
收起
  • 国家自然科学基金资助(52304274)
  • 国家重点研发计划项目(2022YFC3090502)
  • 中国民航大学民航热灾害防控与应急重点实验室开放基金资助(RZH2023-KF-02)
  • 中央高校基本科研业务费专项资金(2023ZKPYAQ06)
  • 中央高校基本科研业务费专项资金(2023ZKPYAQ04)
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2025年第35卷第3期
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doi: 10.16265/j.cnki.issn1003-3033.2025.03.0400
  • 接收时间：2024-10-16
  • 首发时间：2025-07-05
  • 出版时间：2025-03-28
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  • 收稿日期：2024-10-16
  • 修回日期：2024-12-21
基金
国家自然科学基金资助(52304274)
国家重点研发计划项目(2022YFC3090502)
中国民航大学民航热灾害防控与应急重点实验室开放基金资助(RZH2023-KF-02)
中央高校基本科研业务费专项资金(2023ZKPYAQ06)
中央高校基本科研业务费专项资金(2023ZKPYAQ04)
作者信息
    1 中国矿业大学(北京) 应急管理与安全工程学院，北京 100083
    2 中国民航大学 民航热灾害防控与应急重点实验室，天津 300300
    3 山东龙翼航空科技有限公司，山东 济宁 272106
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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